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We develop IV Fr\'echet regression (IVFR), an instrumental-variable (IV) method for settings where the outcome is an entire distribution. Framing the problem as an IV regression in 2-Wasserstein space, IVFR extends global Fr\'echet…
RE-EM tree is a tree-based method that combines the regression tree and the linear mixed effects model for modeling univariate response longitudinal or clustered data. In this paper, we generalize the RE-EM tree method to multivariate…
Functional linear regression analysis aims to model regression relations which include a functional predictor. The analog of the regression parameter vector or matrix in conventional multivariate or multiple-response linear regression…
The problem of statistical inference for regression coefficients in a high-dimensional single-index model is considered. Under elliptical symmetry, the single index model can be reformulated as a proxy linear model whose regression…
Generalized linear models are a popular tool in applied statistics, with their maximum likelihood estimators enjoying asymptotic Gaussianity and efficiency. As all models are wrong, it is desirable to understand these estimators' behaviours…
This paper develops a new automatic and location-adaptive procedure for estimating regression in a Functional Single-Index Model (FSIM). This procedure is based on $k$-Nearest Neighbours ($k$NN) ideas. The asymptotic study includes results…
We show that under a linearity condition on the distribution of the predictors, the coefficient in single-index regression can be estimated with the same efficiency as in the case when the link function is known. Thus, the linearity…
Compositional data find broad application across diverse fields due to their efficacy in representing proportions or percentages of various components within a whole. Spatial dependencies often exist in compositional data, particularly when…
This paper develops a point impact linear regression model in which the trajectory of a continuous stochastic process, when evaluated at a sensitive time point, is associated with a scalar response. The proposed model complements and is…
In this paper, we propose a simplex regression model in which both the mean and the dispersion parameters are related to covariates by nonlinear predictors. We provide closed-form expressions for the score function, for Fisher's information…
The multi-index model is a simple yet powerful high-dimensional regression model which circumvents the curse of dimensionality assuming $ \mathbb{E} [ Y | X ] = g(A^\top X) $ for some unknown index space $A$ and link function $g$. In this…
We study a functional linear regression model that deals with functional responses and allows for both functional covariates and high-dimensional vector covariates. The proposed model is flexible and nests several functional regression…
A new class of statistical deformable models is introduced to study high-dimensional curves or images. In addition to the standard measurement error term, these deformable models include an extra error term modeling the individual…
In this paper, we study a functional regression setting where the random response curve is unobserved, and only its dichotomized version observed at a sequence of correlated binary data is available. We propose a practical computational…
Random forests are a statistical learning method widely used in many areas of scientific research because of its ability to learn complex relationships between input and output variables and also its capacity to handle high-dimensional…
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…
In this paper we present a nonparametric method for extending functional regression methodology to the situation where more than one functional covariate is used to predict a functional response. Borrowing the idea from Kadri et al.…
We propose inferential tools for functional linear quantile regression where the conditional quantile of a scalar response is assumed to be a linear functional of a functional covariate. In contrast to conventional approaches, we employ…
Interval-valued data receives much attention due to its wide applications in the fields of finance, econometrics, meteorology and medicine. However, most regression models developed for interval-valued data assume observations are mutually…
This paper develops computationally feasible methods for estimating random effects models in the context of regression modelling of multiple independent time series of discrete valued counts in which there is serial dependence. Given…