Related papers: Minimax Risk in Estimating Kink Threshold and Test…

We provide new theoretical results in the field of inverse regression methods for dimension reduction. Our approach is based on the study of some empirical processes that lie close to a certain dimension reduction subspace, called the…

We consider a linear regression model, with the parameter of interest a specified linear combination of the regression parameter vector. We suppose that, as a first step, a data-based model selection (e.g. by preliminary hypothesis tests or…

We give improved constants for data dependent and variance sensitive confidence bounds, called empirical Bernstein bounds, and extend these inequalities to hold uniformly over classes of functionswhose growth function is polynomial in the…

We consider the problem of estimating an unknown $\theta\in {\mathbb{R}}^n$ from noisy observations under the constraint that $\theta$ belongs to certain convex polyhedral cones in ${\mathbb{R}}^n$. Under this setting, we prove bounds for…

We consider the performance of the bootstrap in high-dimensions for the setting of linear regression, where $p<n$ but $p/n$ is not close to zero. We consider ordinary least-squares as well as robust regression methods and adopt a minimalist…

We consider the issue of performing accurate small sample inference in beta autoregressive moving average model, which is useful for modeling and forecasting continuous variables that assumes values in the interval $(0,1)$. The inferences…

We perform a study on kernel regression for large-dimensional data (where the sample size $n$ is polynomially depending on the dimension $d$ of the samples, i.e., $n\asymp d^{\gamma}$ for some $\gamma >0$ ). We first build a general tool to…

In statistical exercises where there are several candidate models, the traditional approach is to select one model using some data driven criterion and use that model for estimation, testing and other purposes, ignoring the variability of…

This paper examines the precision of estimators of Quantile-Based Risk Measures (Value at Risk, Expected Shortfall, Spectral Risk Measures). It first addresses the question of how to estimate the precision of these estimators, and proposes…

This paper examines nonparametric regression with an exogenous threshold variable, allowing for an unknown number of thresholds. Given the number of thresholds and corresponding threshold values, we first establish the asymptotic properties…

Sparse linear regression is one of the classical and extensively studied problems in high-dimensional statistics and compressed sensing. Despite the substantial body of literature dedicated to this problem, the precise determination of its…

We investigate the stochastic Thresholding Bandit problem (TBP) under several shape constraints. On top of (i) the vanilla, unstructured TBP, we consider the case where (ii) the sequence of arm's means $(\mu_k)_k$ is monotonically…

In this paper we propose a new test of heteroscedasticity for parametric regression models and partial linear regression models in high dimensional settings. When the dimension of covariates is large, existing tests of heteroscedasticity…

We consider the problem of estimating the regression function in functional linear regression models by proposing a new type of projection estimators which combine dimension reduction and thresholding. The introduction of a threshold rule…

Building on recent studies of large-dimensional kernel regression, particularly those involving inner product kernels on the sphere $\mathbb{S}^{d}$, we investigate the Pinsker bound for inner product kernel regression in such settings.…

We consider a binary sequence generated by thresholding a hidden continuous sequence. The hidden variables are assumed to have a compound symmetry covariance structure with a single parameter characterizing the common correlation. We study…

For a regression model, we consider the risk of the maximum likelihood estimator with respect to $\alpha$-divergence, which includes the special cases of Kullback-Leibler divergence, Hellinger distance and $\chi^2$ divergence. The…

The paper studies a problem of constructing simultaneous likelihood-based confidence sets. We consider a simultaneous multiplier bootstrap procedure for estimating the quantiles of the joint distribution of the likelihood ratio statistics,…

One of the most commonly used methods for forming confidence intervals for statistical inference is the empirical bootstrap, which is especially expedient when the limiting distribution of the estimator is unknown. However, despite its…

The overwhelming majority of empirical research that uses cluster-robust inference assumes that the clustering structure is known, even though there are often several possible ways in which a dataset could be clustered. We propose two tests…