We study nonlinear regression models whose both response and predictors are measured with errors and distorted as single-index models of some observable confounding variables, and propose a multicovariate-adjusted procedure. We first examine the relationship between the observed primary...

In this paper, we consider the estimation problem of a correlation coefficient between unobserved variables of interest. These unobservable variables are distorted in a multiplicative fashion by an observed confounding variable. Two estimators, the moment-based estimator and the direct plug-in...

Nonlinear mixed-effects (NLME) models and generalized linear mixed models (GLMM) are popular in the analyses of longitudinal data and clustered data. Covariates are often introduced to partially explain the large between individual (cluster) variation. Many of these covariates, however, contain...

We discuss a type of confounder dimension reduction summary which retains all of the information in the covariates about both an outcome variable and an intervention or grouping variable. These sufficient dimension reduction summaries share much with sufficient statistics for parameters indexing...

Mixtures of common factor analyzers (MCFA), thought of as a parsimonious extension of mixture factor analyzers (MFA), have recently been developed as a novel approach to analyzing high-dimensional data, where the number of observations n is not very large relative to their dimension p. The key...

In this paper, we propose functional contour regression (FCR) for dimension reduction in the functional regression context. FCR achieves dimension reduction using the empirical directions on the functional predictor in contours defined on the response variable. It is more efficient than the...

In this article, we introduce two new families of multivariate association measures based on power divergence and alpha divergence that recover both linear and nonlinear dependence relationships between multiple sets of random vectors. Importantly, this novel approach not only characterizes...

The main result of this article states that one can get as many as D+1 modes from just a two component normal mixture in D dimensions. Multivariate mixture models are widely used for modeling homogeneous populations and for cluster analysis. Either the components directly or modes arising from...

Change point detection in sequences of functional data is examined where the functional observations are dependent. Of particular interest is the case where the change point is an epidemic change (a change occurs and then the observations return to baseline at a later time). The theoretical...

In this paper, we address the problem of regression estimation in the context of a p-dimensional predictor when p is large. We propose a general model in which the regression function is a composite function. Our model consists in a nonlinear extension of the usual sufficient dimension reduction...