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Estimation of support frontiers and boundaries often involves monotone and/or concave edge data smoothing. This estimation problem arises in various unrelated contexts, such as optimal cost and production assessments in econometrics and master curve prediction in the reliability programmes of nuclear reactors. Very few constrained estimators of the support boundary of a bivariate distribution have...
The application of the lasso is espoused in high dimensional settings where only a small number of the regression coefficients are believed to be non‐zero (i.e. the solution is sparse). Moreover, statistical properties of high dimensional lasso estimators are often proved under the assumption that the correlation between the predictors is bounded. In this vein, co‐ordinatewise methods, which are the...
We suggest a new approach, which is applicable for general statistics computed from random samples of univariate or vector‐valued or functional data, to assessing the influence that individual data have on the value of a statistic, and to ranking the data in terms of that influence. Our method is based on, first, perturbing the value of the statistic by ‘tilting’, or reweighting, each data value,...
The support vector machine (SVM) is a powerful binary classification tool with high accuracy and great flexibility. It has achieved great success, but its performance can be seriously impaired if many redundant covariates are included. Some efforts have been devoted to studying variable selection for SVMs, but asymptotic properties, such as variable selection consistency, are largely unknown when...
In the non‐parametric deconvolution problem, to estimate consistently a density or distribution from a sample of data contaminated by additive random noise, it is often assumed that the noise distribution is completely known or that an additional sample of replicated or validation data is available. Methods also have been suggested for estimating the scale of the error distribution, but they require...
Tail dependence models for distributions attracted to a max‐stable law are fitted by using observations above a high threshold. To cope with spatial, high dimensional data, a rank‐based M‐estimator is proposed relying on bivariate margins only. A data‐driven weight matrix is used to minimize the asymptotic variance. Empirical process arguments show that the estimator is consistent and asymptotically...
Community detection in networks is a key exploratory tool with applications in a diverse set of areas, ranging from finding communities in social and biological networks to identifying link farms in the World Wide Web. The problem of finding communities or clusters in a network has received much attention from statistics, physics and computer science. However, most clustering algorithms assume knowledge...
This paper provides methods to estimate finite mixtures from data with repeated measurements non‐parametrically. We present a constructive identification argument and use it to develop simple two‐step estimators of the component distributions and all their functionals. We discuss a computationally efficient method for estimation and derive asymptotic theory. Simulation experiments suggest that our...
We consider a high dimensional regression model with a possible change point due to a covariate threshold and develop the lasso estimator of regression coefficients as well as the threshold parameter. Our lasso estimator not only selects covariates but also selects a model between linear and threshold regression models. Under a sparsity assumption, we derive non‐asymptotic oracle inequalities for...
We derive non‐parametric confidence intervals for the eigenvalues of the Hessian at modes of a density estimate. This provides information about the strength and shape of modes and can also be used as a significance test. We use a data‐splitting approach in which potential modes are identified by using the first half of the data and inference is done with the second half of the data. To obtain valid...
Many clinical studies on non‐mortality outcomes such as quality of life suffer from the problem that the non‐mortality outcome can be censored by death, i.e. the non‐mortality outcome cannot be measured if the subject dies before the time of measurement. To address the problem that this censoring by death is informative, it is of interest to consider the average effect of the treatment on the non‐mortality...
We study the regression relationship between covariates in case–control data: an area known as the secondary analysis of case–control studies. The context is such that only the form of the regression mean is specified, so that we allow an arbitrary regression error distribution, which can depend on the covariates and thus can be heteroscedastic. Under mild regularity conditions we establish the theoretical...
Characterizations of optimal designs are derived for the prediction of individual response curves within the framework of hierarchical linear mixed models. It is shown that the so‐obtained optimal designs may differ substantially from those propagated in the literature so far and that the latter may become useless in terms of their performance.
We extend classical extreme value theory to non‐identically distributed observations. When the tails of the distribution are proportional much of extreme value statistics remains valid. The proportionality function for the tails can be estimated non‐parametrically along with the (common) extreme value index. For a positive extreme value index, joint asymptotic normality of both estimators is shown;...
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