Dependence modeling, copulas, high-dimensional statistics, kernel smoothing, statistical modeling of conditional distributions
Abstract: " Extending the results of Bellec, Lecué and Tsybakov to the setting of sparse high-dimensional linear regression with unknown variance, we show that two estimators, the Square-Root Lasso and the Square-Root Slope can achieve the optimal minimax prediction rate, which is (s/n) log(p/s), up to some constant, under some mild conditions on the design matrix. Here, n is the sample size, p is the dimension and s is the sparsity parameter. We also prove optimality for the estimation error in the lq-norm, with q in [1,2] for the Square-Root Lasso, and in the l2 and sorted l1 norms for the Square-Root Slope. Both estimators are adaptive to the unknown variance of the noise. The Square-Root Slope is also adaptive to the sparsity s of the true parameter. Next, we prove that any estimator depending on s which attains the minimax rate admits an adaptive to s version still attaining the same rate. We apply this result to the Square-root Lasso. Moreover, for both estimators, we obtain valid rates for a wide range of confidence levels, and improved concentration properties as in [Bellec, Lecué and Tsybakov, 2017] where the case of known variance is treated. Our results are non-asymptotic. "
Abstract: " We discuss the so-called "simplifying assumption" of conditional copulas in a general framework. We introduce several tests of the latter assumption for non- and semiparametric copula models. Some related test procedures based on conditioning subsets instead of point-wise events are proposed. The limiting distribution of such test statistics under the null are approximated by several bootstrap schemes, most of them being new. We prove the validity of a particular semiparametric bootstrap scheme. Some simulations illustrate the relevance of our results. "
2017 - 2018 :
2016 - 2017 :
Work in progress
Abstract: " We study nonparametric estimators of conditional Kendall's tau, a measure of concordance between two random variables given some covariates. We prove non-asymptotic bounds with explicit constants, 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."
Abstract: " We show 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. We prove the consistency and the asymptotic normality of a family of penalized approximate maximum likelihood estimators, including the equivalent of the logit and probit regressions in our framework. Then, we detail specific algorithms 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. A small simulation study compares their finite sample properties. Finally, we apply all these estimators to a dataset of European stock indices."
Abstract: " Conditional Kendall's tau is a measure of dependence between two random variables, conditionally on some covariates. We study nonparametric estimators of such quantities using kernel smoothing techniques. Then, we assume a regression-type relationship between conditional Kendall's tau and covariates, in a parametric setting with possibly a large number of regressors. This model may be sparse, and the underlying parameter is estimated through a penalized criterion. The theoretical properties of all these estimators are stated. We prove non-asymptotic bounds with explicit constants that hold with high probability. We derive their consistency, their asymptotic law and some oracle properties. Some simulations and applications to real data conclude the paper."
Conferences & communications:
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