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Estimation of heterogeneous causal effects - i.e., how effects of policies and treatments vary across subjects - is a fundamental task in causal inference. Many methods for estimating conditional average treatment effects (CATEs) have been…

Statistics Theory · Mathematics 2023-12-27 Edward H. Kennedy , Sivaraman Balakrishnan , James M. Robins , Larry Wasserman

We propose a framework for computing, optimizing and integrating with respect to a smooth marginal likelihood in statistical models that involve high-dimensional parameters/latent variables and continuous low-dimensional hyperparameters.…

Methodology · Statistics 2026-02-10 Omiros Papaspiliopoulos , Timothée Stumpf-Fétizon , Jonathan Weare

We consider the estimation of a scalar parameter, when two estimators are available. The first is always consistent. The second is inconsistent in general, but has a smaller asymptotic variance than the first, and may be consistent if an…

Statistics Theory · Mathematics 2020-06-29 Clément de Chaisemartin , Xavier D'Haultfœuille

In additive models with many nonparametric components, a number of regularized estimators have been proposed and proven to attain various error bounds under different combinations of sparsity and fixed smoothness conditions. Some of these…

Statistics Theory · Mathematics 2020-11-16 Yisha Yao , Cun-Hui Zhang

In this paper, we introduce a new estimator for the emission densities of a nonparametric hidden Markov model. It is adaptive and minimax with respect to each state's regularity--as opposed to globally minimax estimators, which adapt to the…

Statistics Theory · Mathematics 2018-07-17 Luc Lehéricy

For linear time-invariant systems with uncertain parameters belonging to a finite set, we present a purely deterministic approach to multiple-model estimation and propose an algorithm based on the minimax criterion using constrained…

Optimization and Control · Mathematics 2022-07-18 Olle Kjellqvist , Anders Rantzer

We propose a general methodology for the construction and analysis of minimax estimators for a wide class of functionals of finite dimensional parameters, and elaborate on the case of discrete distributions, where the alphabet size $S$ is…

Information Theory · Computer Science 2015-03-11 Jiantao Jiao , Kartik Venkat , Yanjun Han , Tsachy Weissman

In the nonparametric regression setting, we construct an estimator which is a continuous function interpolating the data points with high probability, while attaining minimax optimal rates under mean squared risk on the scale of H\"older…

Statistics Theory · Mathematics 2022-06-28 Julien Chhor , Suzanne Sigalla , Alexandre B. Tsybakov

We consider estimation and inference in a single index regression model with an unknown but smooth link function. In contrast to the standard approach of using kernels or regression splines, we use smoothing splines to estimate the smooth…

Methodology · Statistics 2019-05-28 Arun Kumar Kuchibhotla , Rohit Kumar Patra

Recovering nonlinearly degraded signal in the presence of noise is a challenging problem. In this work, this problem is tackled by minimizing the sum of a non convex least-squares fit criterion and a penalty term. We assume that the…

Signal Processing · Electrical Eng. & Systems 2019-02-27 Marc Castella , Jean-Christophe Pesquet , Arthur Marmin

We propose a two-step pseudo-maximum likelihood procedure for semiparametric single-index regression models where the conditional variance is a known function of the regression and an additional parameter. The Poisson single-index…

Statistics Theory · Mathematics 2017-04-27 Marian Hristache , Weiyu Li , Valentin Patilea

The Multi-Reference Alignment (MRA) problem aims at the recovery of an unknown signal from repeated observations under the latent action of a group of cyclic isometries, in the presence of additive noise of high intensity $\sigma$. It is a…

Statistics Theory · Mathematics 2023-12-14 Subhro Ghosh , Soumendu Sundar Mukherjee , Jing Bin Pan

We propose dimension reduction methods for sparse, high-dimensional multivariate response regression models. Both the number of responses and that of the predictors may exceed the sample size. Sometimes viewed as complementary, predictor…

Statistics Theory · Mathematics 2013-02-14 Florentina Bunea , Yiyuan She , Marten H. Wegkamp

This paper investigates the two-step estimation of a high dimensional additive regression model, in which the number of nonparametric additive components is potentially larger than the sample size but the number of significant additive…

Statistics Theory · Mathematics 2013-01-30 Kengo Kato

Consider the problem of nonparametric estimation of an unknown $\beta$-H\"older smooth density $p_{XY}$ at a given point, where $X$ and $Y$ are both $d$ dimensional. An infinite sequence of i.i.d.\ samples $(X_i,Y_i)$ are generated…

Information Theory · Computer Science 2023-08-29 Jingbo Liu

Assume a (semi)parametrically efficient estimator is given of the Euclidean parameter in a (semi)parametric model. A submodel is obtained by constraining this model in that a continuously differentiable function of the Euclidean parameter…

Statistics Theory · Mathematics 2016-06-27 Chris A. J. Klaassen , Nanang Susyanto

Estimation of a quadratic functional over parameter spaces that are not quadratically convex is considered. It is shown, in contrast to the theory for quadratically convex parameter spaces, that optimal quadratic rules are often rate…

Statistics Theory · Mathematics 2007-06-13 T. Tony Cai , Mark G. Low

This paper investigates some theoretical properties of the Partial Least Square (PLS) method. We focus our attention on the single component case, that provides a useful framework to understand the underlying mechanism. We provide a…

Statistics Theory · Mathematics 2023-10-17 Luca Castelli , Clément Marteau , Irène Gannaz

Nonparametric estimation of nonlocal interaction kernels is crucial in various applications involving interacting particle systems. The inference challenge, situated at the nexus of statistical learning and inverse problems, arises from the…

Statistics Theory · Mathematics 2025-04-24 Xiong Wang , Inbar Seroussi , Fei Lu

The problem of optimal estimation of linear functionals constructed from the unobserved values of a stochastic sequence with periodically stationary increments based on observations of the sequence with stationary noise is considered. For…

Statistics Theory · Mathematics 2021-10-18 Maksym Luz , Mikhail Moklyachuk