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It is well known that the minimax rates of convergence of nonparametric density and regression function estimation of a random variable measured with error is much slower than the rate in the error free case. Surprisingly, we show that if…

Modeling signals as linear combinations of atoms from a dictionary is ubiquitous in modern signal processing. In the finite-dimensional setting, whenever atoms depend nonlinearly upon unknown parameters, the signal model is said to be…

Two semimetrics on probability distributions are proposed, given as the sum of differences of expectations of analytic functions evaluated at spatial or frequency locations (i.e, features). The features are chosen so as to maximize the…

In this paper, we propose a new semiparametric regression estimator by using a hybrid technique of a parametric approach and a nonparametric penalized spline method. The overall shape of the true regression function is captured by the…

Adversarial attack perturbs an image with an imperceptible noise, leading to incorrect model prediction. Recently, a few works showed inherent bias associated with such attack (robustness bias), where certain subgroups in a dataset (e.g.…

We propose a semiparametric Bayesian methodology for estimating the average treatment effect (ATE) within the potential outcomes framework using observational data with high-dimensional nuisance parameters. Our method introduces a Bayesian…

This paper introduces a new method for testing the statistical significance of estimated parameters in predictive regressions. The approach features a new family of test statistics that are robust to the degree of persistence of the…

Semi- and non-parametric mixture of regressions are a very useful flexible class of mixture of regressions in which some or all of the parameters are non-parametric functions of the covariates. These models are, however, based on the…

In the context of nonparametric regression models with one-sided errors, we consider parametric transformations of the response variable in order to obtain independence between the errors and the covariates. We focus in this paper on…

Asymptotic lower bounds for estimation play a fundamental role in assessing the quality of statistical procedures. In this paper we propose a framework for obtaining semi-parametric efficiency bounds for sparse high-dimensional models,…

Recently, Su and Cook proposed a dimension reduction technique called the inner envelope which can be substantially more efficient than the original envelope or existing dimension reduction techniques for multivariate regression. However,…

Reviewing the semiclassical theory for the parametric level density fluctuations, we show that for large parametric changes the density correlation function, after rescaling, becomes universal and coincides with the leading asymptotic term…

Cook's [J. Roy. Statist. Soc. Ser. B 48 (1986) 133--169] local influence approach based on normal curvature is an important diagnostic tool for assessing local influence of minor perturbations to a statistical model. However, no rigorous…

Parametric projections let analysts embed new points in real time, but input variations from measurement noise or data drift can produce unpredictable shifts in the 2D layout. Whether and where a projection is locally stable remains largely…

We investigate the parameter estimation of regression models with fixed group effects, when the group variable is missing while group related variables are available. This problem involves clustering to infer the missing group variable…

Semiparametric forecasting and filtering are introduced as a method of addressing model errors arising from unresolved physical phenomena. While traditional parametric models are able to learn high-dimensional systems from small data sets,…

We consider the problem of an agent/robot with non-holonomic kinematics avoiding many dynamic obstacles. State and velocity noise of both the robot and obstacles as well as the robot's control noise are modelled as non-parametric…

Consider a quite arbitrary (semi)parametric model with a Euclidean parameter of interest and assume that an asymptotically (semi)parametrically efficient estimator of it is given. If the parameter of interest is known to lie on a general…

While robust divergence such as density power divergence and $\gamma$-divergence is helpful for robust statistical inference in the presence of outliers, the tuning parameter that controls the degree of robustness is chosen in a…

Quantum interference provides one of the most sensitive probes of quantum mechanics. While linear superposition fixes the positions and quadratic curvature of interference fringes, it remains unclear whether the probabilistic postulate…