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In many practical parameter estimation problems, prescreening and parameter selection are performed prior to estimation. In this paper, we consider the problem of estimating a preselected unknown deterministic parameter chosen from a…
The purpose of this article is to develop a general parametric estimation theory that allows the derivation of the limit distribution of estimators in non-regular models where the true parameter value may lie on the boundary of the…
Nonparametric regression is a standard statistical tool with increased importance in the Big Data era. Boundary points pose additional difficulties but local polynomial regression can be used to alleviate them. Local linear regression, for…
Modern image classifiers are very accurate, but the predictions come without uncertainty estimates. Conformal predictors provide uncertainty estimates by computing a set of classes containing the correct class with a user-specified…
We consider the estimation problem in high-dimensional semi-supervised learning. Our goal is to investigate when and how the unlabeled data can be exploited to improve the estimation of the regression parameters of linear model in light of…
We consider the problem of estimating the parameters of a supercritical controlled branching process consistently from a single observed trajectory of population size counts. Our goal is to establish which parameters can and cannot be…
As inductive inference and machine learning methods in computer science see continued success, researchers are aiming to describe ever more complex probabilistic models and inference algorithms. It is natural to ask whether there is a…
This paper presents a model selection technique of estimation in semiparametric regression models of the type Y_i=\beta^{\prime}\underbarX_i+f(T_i)+W_i, i=1,...,n. The parametric and nonparametric components are estimated simultaneously by…
We consider the Bayesian analysis of models in which the unknown distribution of the outcomes is specified up to a set of conditional moment restrictions. The nonparametric exponentially tilted empirical likelihood function is constructed…
The ultimate goal of regression analysis is to obtain information about the conditional distribution of a response given a set of explanatory variables. This goal is, however, seldom achieved because most established regression models only…
Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find…
We are concerned with obtaining well-calibrated output distributions from regression models. Such distributions allow us to quantify the uncertainty that the model has regarding the predicted target value. We introduce the novel concept of…
In this paper, we consider the distributed estimation problem of a linear stochastic system described by an autoregressive model with exogenous inputs (ARX) when both the system orders and parameters are unknown. We design distributed…
Construction of valid statistical inference for estimators based on data-driven selection has received a lot of attention in the recent times. Berk et al. (2013) is possibly the first work to provide valid inference for Gaussian…
We observe a $n$-sample, the distribution of which is assumed to belong, or at least to be close enough, to a given mixture model. We propose an estimator of this distribution that belongs to our model and possesses some robustness…
Machine learning models are often evaluated using point estimates of performance metrics such as accuracy, F1 score, or mean squared error. Such summaries fail to capture the inherent variability induced by stochastic elements of the…
We consider the problem of estimating the common mean of independently sampled data, where samples are drawn in a possibly non-identical manner from symmetric, unimodal distributions with a common mean. This generalizes the setting of…
Most work in neural networks focuses on estimating the conditional mean of a continuous response variable given a set of covariates.In this article, we consider estimating the conditional distribution function using neural networks for both…
Although a few methods have been developed recently for building confidence intervals after model selection, how to construct confidence sets for joint post-selection inference is still an open question. In this paper, we develop a new…
We consider the problem of consistently estimating the conditional distribution $P(Y \in A |X)$ of a functional data object $Y=(Y(t): t\in[0,1])$ given covariates $X$ in a general space, assuming that $Y$ and $X$ are related by a functional…