Related papers: Uniform Consistency in Nonparametric Mixture Model…
The large-sample properties of likelihood-based statistical inference under mixture models have received much attention from statisticians. Although the consistency of the nonparametric MLE is regarded as a standard conclusion, many…
We consider nonparametric estimation of the mean and covariance functions for functional/longitudinal data. Strong uniform convergence rates are developed for estimators that are local-linear smoothers. Our results are obtained in a unified…
This paper presents uniform estimation and inference theory for a large class of nonparametric partitioning-based M-estimators. The main theoretical results include: (i) uniform consistency for convex and non-convex objective functions;…
When do nonparametric Bayesian procedures ``overfit''? To shed light on this question, we consider a binary regression problem in detail and establish frequentist consistency for a certain class of Bayes procedures based on hierarchical…
Seemingly unrelated linear regression models are introduced in which the distribution of the errors is a finite mixture of Gaussian components. Identifiability conditions are provided. The score vector and the Hessian matrix are derived.…
In this article, basing on NQD samples, we investigate the fixed design nonparametric regression model, where the errors are pairwise NQD random errors, with fixed design points, and an unknown function. Nonparametric weighted estimator…
Recent research has established sufficient conditions for finite mixture models to be identifiable from grouped observations. These conditions allow the mixture components to be nonparametric and have substantial (or even total) overlap.…
We consider a nonparametric regression model $Y=r(X)+\varepsilon$ with a random covariate $X$ that is independent of the error $\varepsilon$. Then the density of the response $Y$ is a convolution of the densities of $\varepsilon$ and…
We consider the standard non-parametric regression model with Gaussian errors but where the data consist of different samples. The question to be answered is whether the samples can be adequately represented by the same regression function.…
In this article, we propose a class of semiparametric mixture regression models with single-index. We argue that many recently proposed semiparametric/nonparametric mixture regression models can be considered special cases of the proposed…
Univariate or multivariate ordinal responses are often assumed to arise from a latent continuous parametric distribution, with covariate effects which enter linearly. We introduce a Bayesian nonparametric modeling approach for univariate…
We consider heteroscedastic nonparametric regression models, when both the mean function and variance function are unknown and to be estimated with nonparametric approaches. We derive convergence rates of posterior distributions for this…
We develop a uniform inference theory for high-dimensional slope parameters in threshold regression models, allowing for either cross-sectional or time series data. We first establish oracle inequalities for prediction errors, and L1…
In various applications of regression analysis, in addition to errors in the dependent observations also errors in the predictor variables play a substantial role and need to be incorporated in the statistical modeling process. In this…
We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…
Mixtures of Linear Regressions (MLR) is an important mixture model with many applications. In this model, each observation is generated from one of the several unknown linear regression components, where the identity of the generated…
This paper presents uniform convergence rates for kernel regression estimators, in the setting of a structural nonlinear cointegrating regression model. We generalise the existing literature in three ways. First, the domain to which these…
We investigate the nonparametric estimation for regression in a fixed-design setting when the errors are given by a field of dependent random variables. Sufficient conditions for kernel estimators to converge uniformly are obtained. These…
Finite mixtures of regression models provide a flexible modeling framework for many phenomena. Using moment-based estimation of the regression parameters, we develop unbiased estimators with a minimum of assumptions on the mixture…
Regularized regression models are well studied and, under appropriate conditions, offer fast and statistically interpretable results. However, large data in many applications are heterogeneous in the sense of harboring distributional…