Related papers: Hypotheses tests in boundary regression models
The likelihood ratio statistic, with its asymptotic $\chi^2$ distribution at regular model points, is often used for hypothesis testing. At model singularities and boundaries, however, the asymptotic distribution may not be $\chi^2$, as…
We revisit the outlier hypothesis testing framework of Li \emph{et al.} (TIT 2014) and derive fundamental limits for the optimal test. In outlier hypothesis testing, one is given multiple observed sequences, where most sequences are…
Limit distributions for the greatest convex minorant and its derivative are considered for a general class of stochastic processes including partial sum processes and empirical processes, for independent, weakly dependent and long range…
Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models…
This paper studies a machine learning regression problem as a multivariate approximation problem using the framework of the theory of random functions. An ab initio derivation of a regression method is proposed, starting from postulates of…
The object of study is the problem of testing for uniformity of the multinomial distribution. We consider tests based on symmetric statistics, defined as the sum of some function of cell-frequencies. Mainly, attention is focused on the…
We consider a nonparametric autoregression model under conditional heteroscedasticity with the aim to test whether the innovation distribution changes in time. To this end we develop an asymptotic expansion for the sequential empirical…
This work proposes a machine-learning framework for constructing statistical models of errors incurred by approximate solutions to parameterized systems of nonlinear equations. These approximate solutions may arise from early termination of…
Consider the nonparametric regression model Y=m(X)+E, where the function m is smooth but unknown, and E is independent of X. An estimator of the density of the error term E is proposed and its weak consistency is obtained. The contribution…
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…
In this paper, we propose a general method for testing composite hypotheses. Our idea is to use confidence limits to define stopping and decision rules. The requirements of operating characteristic function can be satisfied by adjusting the…
Deep nonparametric regression, characterized by the utilization of deep neural networks to learn target functions, has emerged as a focus of research attention in recent years. Despite considerable progress in understanding convergence…
We investigate hypothesis testing in nonparametric additive models estimated using simplified smooth backfitting (Huang and Yu, Journal of Computational and Graphical Statistics, \textbf{28(2)}, 386--400, 2019). Simplified smooth…
We consider goodness-of-fit tests of symmetric stable distributions based on weighted integrals of the squared distance between the empirical characteristic function of the standardized data and the characteristic function of the standard…
In this article, we study nonparametric inference problems in the context of multivariate or functional time series, including testing for goodness-of-fit, the presence of a change point in the marginal distribution, and the independence of…
We propose a framework for hypothesis testing on conditional probability distributions, which we then use to construct statistical tests of functionals of conditional distributions. These tests identify the inputs where the functionals…
We show that the mean-model parameter is always orthogonal to the error distribution in generalized linear models. Thus, the maximum likelihood estimator of the mean-model parameter will be asymptotically efficient regardless of whether the…
Consider a random vector $(X,Y)$ and let $m(x)=E(Y|X=x)$. We are interested in testing $H_0:m\in {\cal M}_{\Theta,{\cal G}}=\{\gamma(\cdot,\theta,g):\theta \in \Theta,g\in {\cal G}\}$ for some known function $\gamma$, some compact set…
We consider the problem of estimating the joint distribution of $n$ independent random variables. Our approach is based on a family of candidate probabilities that we shall call a model and which is chosen to either contain the true…
In this paper we present a series of results that permit to extend in a direct manner uniform deviation inequalities of the empirical process from the independent to the dependent case characterizing the additional error in terms of…