Purpose:
Principal component analysis (PCA) is a descriptive exploratory statistical technique that is widely used in complex fields for data mining. However, it is rarely used in ophthalmology. We explored its research potential with a large series of eyes that underwent 3 keratoplasty techniques: Descemet membrane endothelial keratoplasty (DMEK), conventional Descemet stripping automated endothelial keratoplasty (ConDSAEK), or ultrathin-DSAEK (UT-DSAEK).

Methods:
All consecutive DMEK/DSAEK cases conducted in 2016 to 2022 that had ≥24 months of follow-up were included. ConDSAEK and UT-DSAEK were defined as preoperative central graft thickness ≥130 and <130 μm, respectively. Seventy-six patient, disease, surgical practice, and temporal outcome variables were subjected to PCA, including preoperative anterior keratometry, the use of sulfur hexafluoride gas (SF6) versus air for primary tamponade, and postoperative best corrected visual acuity and endothelial cell density. Associations of interest that were revealed by PCA were assessed with the Welch t test or Pearson test.

Results:
A total of 331 eyes were treated with DMEK (n = 165), ConDSAEK (n = 95), or UT-DSAEK (n = 71). PCA showed that ConDSAEK and UT-DSAEK clustered closely, including regarding postoperative best corrected visual acuity, and were clearly distinct from DMEK. PCA and follow-up univariate analyses suggested that in DMEK, 1) flatter preoperative anterior keratometry (average, K1, and K2) associated with more rebubbling (P = 0.004–0.089) and graft detachment (P = 0.007–0.022); 2) graft marking did not affect postoperative endothelial cell density; and 3) lower postoperative endothelial cell density associated with SF6 use (all P > 0.001) and longer surgery (P = 0.005–0.091). All associations are currently under additional investigation in our hospital.

Conclusions:
PCA is a powerful technique that can rapidly reveal clinically relevant associations in complex ophthalmological datasets.@en

Elliptical distributions are a simple and flexible class of distributions that depend on a one-dimensional function, called the density generator. In this article, we study the non-parametric estimator of this generator that was introduced by Liebscher (2005). This estimator depends on two tuning parameters: a bandwidth $h$ -- as usual in kernel smoothing -- and an additional parameter a that control the behavior near the center of the distribution. We give an explicit expression for the asymptotic MSE at a point $x$, and derive explicit expressions for the optimal tuning parameters h and a. Estimation of the derivatives of the generator is also discussed. A simulation study shows the performance of the new methods.@en

The provision of robotic assistance during motor training has proven to be effective in enhancing motor learning in some healthy trainee groups as well as patients. Personalizing such robotic assistance can help further improve motor (re)learning outcomes and cater better to the trainee's needs and desires. However, the development of personalized haptic assistance is hindered by the lack of understanding of the link between the trainee's personality and the effects of haptic guidance during human-robot interaction. To address this gap, we ran an experiment with 40 healthy participants who trained with a robotic device to control a virtual pendulum to hit incoming targets, either with or without haptic guidance. We found that certain personal traits affected how users adapt and interact with the guidance during training. In particular, those participants with an 'Achiever gaming style' performed better and applied lower interaction forces to the robotic device than the average participant as the training progressed. Conversely, participants with the 'Free spirit game style' increased the interaction force in the course of training. We also found an interaction between some personal characteristics and haptic guidance. Specifically, participants with a higher 'Transformation of challenge' trait exhibited poorer performance during training while receiving haptic guidance compared to an average participant receiving haptic guidance. Furthermore, individuals with an external Locus of Control tended to increase their interaction force with the device, deviating from the pattern observed in an average participant under the same guidance. These findings suggest that individual characteristics may play a crucial role in the effectiveness of haptic guidance training strategies.

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In nonparametric statistics, rate-optimal estimators typically balance bias and stochastic error. The recent work on overparametrization raises the question whether rate-optimal estimators exist that do not obey this trade-off. In this work we consider pointwise estimation in the Gaussian white noise model with regression function f in a class of β-Hölder smooth functions. Let ’worst-case’ refer to the supremum over all functions f in the Hölder class. It is shown that any estimator with worst-case bias ≲n^{−β/(2β+1)}≕ψ_n must necessarily also have a worst-case mean absolute deviation that is lower bounded by ≳ψ_n. To derive the result, we establish abstract inequalities relating the change of expectation for two probability measures to the mean absolute deviation.

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U-statistics constitute a large class of estimators, generalizing the empirical mean of a random variable (Formula presented.) to sums over every (Formula presented.) -tuple of distinct observations of (Formula presented.). They may be used to estimate a regular functional (Formula presented.) of the law of (Formula presented.). When a vector of covariates (Formula presented.) is available, a conditional U-statistic describes the effect of (Formula presented.) on the conditional law of (Formula presented.) given (Formula presented.), by estimating a regular conditional functional (Formula presented.). We state nonasymptotic bounds of general conditional U-statistics and study their asymptotics too. Assuming a parametric model of the conditional functional of interest, we propose a regression-type estimator based on conditional U-statistics. Its theoretical properties are derived, first in a nonasymptotic framework and then in two different asymptotic regimes. Some examples are given to illustrate our methods.

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We propose a new concept of codivergence, which quantifies the similarity between two probability measures P₁,P₂ relative to a reference probability measure P₀. In the neighborhood of the reference measure P₀, a codivergence behaves like an inner product between the measures P₁-P₀ and P₂-P₀. Codivergences of covariance-type and correlation-type are introduced and studied with a focus on two specific correlation-type codivergences, the χ²-codivergence and the Hellinger codivergence. We derive explicit expressions for several common parametric families of probability distributions. For a codivergence, we introduce moreover the divergence matrix as an analogue of the Gram matrix. It is shown that the χ²-divergence matrix satisfies a data-processing inequality.

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It is a common phenomenon that for high-dimensional and nonparametric statistical models, rate-optimal estimators balance squared bias and variance. Although this balancing is widely observed, little is known whether methods exist that could avoid the trade-off between bias and variance. We propose a general strategy to obtain lower bounds on the variance of any estimator with bias smaller than a prespecified bound. This shows to which extent the bias-variance trade-off is unavoidable and allows to quantify the loss of performance for methods that do not obey it. The approach is based on a number of abstract lower bounds for the variance involving the change of expectation with respect to different probability measures as well as information measures such as the Kullback-Leibler or χ²-divergence. Some of these inequalities rely on a new concept of information matrices. In a second part of the article, the abstract lower bounds are applied to several statistical models including the Gaussian white noise model, a boundary estimation problem, the Gaussian sequence model and the high-dimensional linear regression model. For these specific statistical applications, different types of bias-variance trade-offs occur that vary considerably in their strength. For the trade-off between integrated squared bias and integrated variance in the Gaussian white noise model, we propose to combine the general strategy for lower bounds with a reduction technique. This allows us to reduce the original problem to a lower bound on the bias-variance trade-off for estimators with additional symmetry properties in a simpler statistical model. In the Gaussian sequence model, different phase transitions of the bias-variance trade-off occur. Although there is a non-trivial interplay between bias and variance, the rate of the squared bias and the variance do not have to be balanced in order to achieve the minimax estimation rate.

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In recent years, implementing a circular economy in cities has been considered by policy makers as a potential solution for achieving sustainability. Existing literature on circular cities is mainly focused on two perspectives: urban governance and urban metabolism. Both these perspectives, to some extent, miss an understanding of space. A spatial perspective is important because circular activities, such as the recycling, reuse, or storage of materials, require space and have a location. It is therefore useful to understand where circular activities are located, and how they are affected by their location and surrounding geography. This study therefore aims to understand the existing state of waste reuse activities in the Netherlands from a spatial perspective, by analyzing the degree, scale, and locations of spatial clusters of waste reuse. This was done by measuring the spatial autocorrelation of waste reuse locations using global and local Moran’s I, with waste reuse data from the national waste registry of the Netherlands. The analysis was done for 10 material types: minerals, plastic, wood and paper, fertilizer, food, machinery and electronics, metal, mixed construction materials, glass, and textile. It was found that all materials except for glass and textiles formed spatial clusters. By varying the grid cell sizes used for data aggregation, it was found that different materials had different ‘best fit’ cell sizes where spatial clustering was the strongest. The best fit cell size is ~7km for materials associated with construction and agricultural industries, and ~20-25km for plastic and metals.The best fit cell sizes indicate the average distance of companies from each other within clusters, and suggest a suitable spatial resolution at which the material can be understood. Hotspot maps were also produced for each material to show where reuse activities are most spatially concentrated.

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In this article, we study bounds on the uniform distance between the cumulative distribution function of a standardized sum of independent centered random variables with moments of order four and its first-order Edgeworth expansion. Existing bounds are sharpened in two frameworks: when the variables are independent but not identically distributed and in the case of independent and identically distributed random variables. Improvements of these bounds are derived if the third moment of the distribution is zero. We also provide adapted versions of these bounds under additional regularity constraints on the tail behavior of the characteristic function. We finally present an application of our results to the lack of validity of one-sided tests based on the normal approximation of the mean for a fixed sample size.@en

Background: Solid evidence of the safety and effectiveness of retinoblastoma (RB) conservative treatment using thermotherapy and systemic chemotherapy with long-term follow-up is scarce, especially in low-resource countries. Aims: This study examined the outcomes of this treatment and associated predictors in Vietnam to strengthen the current RB treatment protocol focusing on preserving eye and vision in low-resource settings. Methods and results: A prospective cohort study was conducted at Ho Chi Minh City Eye Hospital in Vietnam from 2005 to 2019. All eligible patients with bilateral RB (one eye already removed and another eye classified as group A or B) and without previous treatment were recruited. All patients received thermotherapy and six cycles of systemic three-agent chemotherapy repeated every 4 weeks. A standardized questionnaire was used to collect information on study participants' age, symptoms, tumor characteristics, treatment, and outcomes. Among 50 eyes of all 50 patients with a median age of 9 (4–20) months, 34 eyes were in group B (68%). The median follow-up time was 60 (60–84) months. All 139 preserved tumors regressed mostly to type 4 (70.4%) and type 3 (23.7%) scars. Kaplan–Meier analysis found the overall globe-salvage rate at 5 years of 91.9% (95% CI: 80.1%–97.7%). Most eyes (41/50, 82%, 95% CI: 69.2%–90.2%) had a final visual acuity ≥0.1. The visual acuity is higher when tumors regressed to a type 4 scar (p =.007, AOR = 8.098, 95% CI: 1.79–36.53) which also shows less enucleation than a type 3 scar (p =.002, AOR = 0.06, 95% CI: 0.01–0.37%). Gender effect on visual acuity after treatment was significant and may be due to discrimination. No major complications were recorded. Conclusion: Conservative treatment of early-stage RB is safe and effective. Long-term, thorough follow-ups of patients post-treatment are needed. The regression patterns of scars could be a useful indicator of treatment failure.

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Meta-elliptical copulas are often proposed to model dependence between the components of a random vector. They are specified by a correlation matrix and a map g, called density generator. While the latter correlation matrix can easily be estimated from pseudo-samples of observations, the density generator is harder to estimate, especially when it does not belong to a parametric family. We give sufficient conditions to non-parametrically identify this generator. Several nonparametric estimators of g are then proposed, by M-estimation, simulation-based inference, or by an iterative procedure available in the R package ElliptCopulas. Some simulations illustrate the relevance of the latter method.

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In recent years, implementing a circular economy in cities has been considered by policy makers as a potential solution for achieving sustainability. Existing literature on circular cities is mainly focused on two perspectives: urban governance and urban metabolism. Both these perspectives, to some extent, miss an understanding of space. A spatial perspective is important because circular activities, such as the recycling, reuse, or storage of materials, require space and have a location. It is therefore useful to understand where circular activities are located, and how they are affected by their location and surrounding geography. This study therefore aims to understand the existing state of waste reuse activities in the Netherlands from a spatial perspective, by analyzing the degree, scale, and locations of spatial clusters of waste reuse. This was done by measuring the spatial autocorrelation of waste reuse locations using global and local Moran’s I, with waste reuse data from the national waste registry of the Netherlands. The analysis was done for 10 material types: minerals, plastic, wood and paper, fertilizer, food, machinery and electronics, metal, mixed construction materials, glass, and textile. It was found that all materials except for glass and textiles formed spatial clusters. By varying the grid cell sizes used for data aggregation, it was found that different materials had different “best fit” cell sizes where spatial clustering was the strongest. The best fit cell size is ∼7 km for materials associated with construction and agricultural industries, and ∼20–25 km for plastic and metals.The best fit cell sizes indicate the average distance of companies from each other within clusters, and suggest a suitable spatial resolution at which the material can be understood. Hotspot maps were also produced for each material to show where reuse activities are most spatially concentrated.@en

We study the weak convergence of conditional empirical copula processes indexed by general families of conditioning events that have non zero probabilities. Moreover, we also study the case where the conditioning events are chosen in a data-driven way. The validity of several bootstrap schemes is stated, including the exchangeable bootstrap. We define general multivariate measures of association, possibly given some fixed or random conditioning events. By applying our theoretical results, we prove the asymptotic normality of the estimators of such measures. We illustrate our results with financial data.

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This article deals with robust inference for parametric copula models. Estimation using canonical maximum likelihood might be unstable, especially in the presence of outliers. We propose to use a procedure based on the maximum mean discrepancy (MMD) principle. We derive nonasymptotic oracle inequalities, consistency and asymptotic normality of this new estimator. In particular, the oracle inequality holds without any assumption on the copula family, and can be applied in the presence of outliers or under misspecification. Moreover, in our MMD framework, the statistical inference of copula models for which there exists no density with respect to the Lebesgue measure on (Formula presented.), as the Marshall-Olkin copula, becomes feasible. A simulation study shows the robustness of our new procedures, especially compared to pseudo-maximum likelihood estimation. An R package implementing the MMD estimator for copula models is available. Supplementary materials for this article are available online.

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Purpose:It remains unclear whether preoperative central graft thickness (CGT) contributes to visual outcomes of Descemet stripping automated endothelial keratoplasty (DSAEK). This retrospective cohort study examined the ability of preoperative and postoperative CGT to predict 12-month best spectacle-corrected visual acuity (BSCVA) after DSAEK for Fuchs endothelial corneal dystrophy/moderate pseudophakic bullous keratopathy/second graft.Methods:All consecutive patients who underwent DSAEK in 2015 to 2018 were included. The primary end point was 12-month BSCVA. DSAEK-CGT was measured preoperatively and 6 times between postoperative day 8 and month 12. Eyes were divided according to preoperative CGT 130 m (ultrathin-DSAEK threshold) or 6-month postoperative CGT 100 m (mean 6-month postoperative DSAEK-CGT). The t test assessed CGT evolution of the 4 groups over time. Multivariate analyses examined whether preoperative CGT or 6-month CGT categories predicted 12-month BSCVA. Multivariate analysis assessed the preoperative/perioperative factors that predicted 6-month CGT.Results:A total of 108 eyes (68 patients) underwent DSAEK. Preoperative CGT was >130 and ≤130 m in 87 and 21 eyes, respectively. Postoperative CGT was >100 and ≤100 m in 50 and 58 eyes, respectively. Thin 6-month postoperative grafts thinned significantly more relative to preoperative thickness than thick grafts (P < 0.001). Preoperative CGT subgroups did not show this difference. Six-month postoperative CGT (P = 0.01), but not preoperative CGT, predicted 12-month BSCVA. Preoperative CGT strongly predicted 6-month CGT (P = 0.0003).Conclusions:Postoperative, but not preoperative, DSAEK-CGT predicted 6-month BSCVA. The correlation between preoperative and postoperative CGT and interstudy variation in preoperative CGT measurement accuracy may explain literature disparities regarding the importance of preoperative CGT in DSAEK outcomes.

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Several procedures have been recently proposed to test the simplifying assumption for conditional copulas. Instead of considering pointwise conditioning events, we study the constancy of the conditional dependence structure when some covariates belong to general Borel conditioning subsets. We introduce several test statistics based on the equality of conditional Kendall's taus and derive their asymptotic distributions under the null hypothesis. In settings where such conditioning events are not fixed ex ante, we propose a data-driven procedure to recursively build such relevant subsets. This procedure is based on decision trees that maximize the differences between the conditional Kendall's taus, which correspond to the leaves of the trees. Empirical results for such tests are illustrated in the Supplementary Material. Moreover, a study of the conditional dependence between financial stock returns is presented and highlights specific contagion effects of past returns. The last application deals with conditional dependence between coverage amounts in an insurance dataset.@en

Collection of accurate and representative data from agricultural fields is required for efficient crop management. Since growers have limited available resources, there is a need for advanced methods to select representative points within a field in order to best satisfy sampling or sensing objectives. The main purpose of this work was to develop a data-driven method for selecting locations across an agricultural field given observations of some covariates at every point in the field. These chosen locations should be representative of the distribution of the covariates in the entire population and represent the spatial variability in the field. They can then be used to sample an unknown target feature whose sampling is expensive and cannot be realistically done at the population scale. An algorithm for determining these optimal sampling locations, namely the multifunctional matching (MFM) criterion, was based on matching of moments (functionals) between sample and population. The selected functionals in this study were standard deviation, mean, and Kendall's tau. An additional algorithm defined the minimal number of observations that could represent the population according to a desired level of accuracy. The MFM was applied to datasets from two agricultural plots: a vineyard and a peach orchard. The data from the plots included measured values of slope, topographic wetness index, normalized difference vegetation index, and apparent soil electrical conductivity. The MFM algorithm selected the number of sampling points according to a representation accuracy of 90% and determined the optimal location of these points. The algorithm was validated against values of vine or tree water status measured as crop water stress index (CWSI). Algorithm performance was then compared to two other sampling methods: the conditioned Latin hypercube sampling (cLHS) model and a uniform random sample with spatial constraints. Comparison among sampling methods was based on measures of similarity between the target variable population distribution and the distribution of the selected sample. MFM represented CWSI distribution better than the cLHS and the uniform random sampling, and the selected locations showed smaller deviations from the mean and standard deviation of the entire population. The MFM functioned better in the vineyard, where spatial variability was larger than in the orchard. In both plots, the spatial pattern of the selected samples captured the spatial variability of CWSI. MFM can be adjusted and applied using other moments/functionals and may be adopted by other disciplines, particularly in cases where small sample sizes are desired.

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Conditional Kendall's tau is a measure of dependence between two random variables, conditionally on some covariates. We assume a regression-type relationship between conditional Kendall's tau and some covariates, in a parametric setting with a large number of transformations of a small number of regressors. This model may be sparse, and the underlying parameter is estimated through a penalized criterion and a two-step inference procedure. We prove non-asymptotic bounds with explicit constants that hold with high probabilities. We derive the consistency of the latter estimator, its asymptotic law and some oracle properties. Some simulations and applications to real data conclude the paper.

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It is shown how the problem of estimating conditional Kendall's tau can be rewritten as a classification task. Conditional Kendall's tau is a conditional dependence parameter that is a characteristic of a given pair of random variables. The goal is to predict whether the pair is concordant (value of 1) or discordant (value of −1) conditionally on some covariates. The consistency and the asymptotic normality of a family of penalized approximate maximum likelihood estimators is proven, including the equivalent of the logit and probit regressions in our framework. Specific algorithms are detailed, adapting usual machine learning techniques, including nearest neighbors, decision trees, random forests and neural networks, to the setting of the estimation of conditional Kendall's tau. Finite sample properties of these estimators and their sensitivities to each component of the data-generating process are assessed in a simulation study. Finally, all these estimators are applied to a dataset of European stock indices.

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We study nonparametric estimators of conditional Kendall's tau, a measure of concordance between two random variables given some covariates. We prove non-asymptotic pointwise and uniform bounds, that hold with high probabilities. We provide "direct proofs" of the consistency and the asymptotic law of conditional Kendall's tau. A simulation study evaluates the numerical performance of such nonparametric estimators. An application to the dependence between energy consumption and temperature conditionally to calendar days is finally provided.

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