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We develop semiparametrically efficient inference for kernel measures of noise heterogeneity in additive noise models. In many applications, the regression function is estimated using flexible machine learning methods. Downstream procedures…

This paper presents new results on prediction of linear processes in function spaces. The autoregressive Hilbertian process framework of order one (ARH(1) process framework) is adopted. A componentwise estimator of the autocorrelation…

Kernel mean embeddings, a widely used technique in machine learning, map probability distributions to elements of a reproducing kernel Hilbert space (RKHS). For supervised learning problems, where input-output pairs are observed, the…

Machine learning (ML) entered the field of computational micromagnetics only recently. The main objective of these new approaches is the automatization of solutions of parameter-dependent problems in micromagnetism such as fast response…

The analysis of human microbiome data is often based on dimension-reduced graphical displays and clustering derived from vectors of microbial abundances in each sample. Common to these ordination methods is the use of biologically motivated…

Under the reproducing kernel Hilbert spaces (RKHS), we consider the penalized least-squares of the partially functional linear models (PFLM), whose predictor contains both functional and traditional multivariate parts, and the multivariate…

In functional data analysis, functional linear regression has attracted significant attention recently. Herein, we consider the case where both the response and covariates are functions. There are two available approaches for addressing…

Application of nonparametric and semiparametric regression techniques to high-dimensional time series data has been hampered due to the lack of effective tools to address the ``curse of dimensionality.'' Under rather weak conditions, we…

Classical penalized likelihood regression problems deal with the case that the independent variables data are known exactly. In practice, however, it is common to observe data with incomplete covariate information. We are concerned with a…

Functional linear and single-index models are core regression methods in functional data analysis and are widely used for performing regression in a wide range of applications when the covariates are random functions coupled with scalar…

In this paper, a functional partial quantile regression approach, a quantile regression analog of the functional partial least squares regression, is proposed to estimate the function-on-function linear quantile regression model. A partial…

We introduce a recursive algorithm of conveniently general form for estimating the coefficient of a moving average model of order one and obtain convergence results for both correct and misspecified MA(1) models. The algorithm encompasses…

We consider functional linear regression models where functional outcomes are associated with scalar predictors by coefficient functions with shape constraints, such as monotonicity and convexity, that apply to sub-domains of interest. To…

A model for the prediction of functional time series is introduced, where observations are assumed to be continuous random functions. We model the dependence of the data with a nonstandard autoregressive structure, motivated in terms of the…

Motivated by the prevalence of environments in which data is abundant while resources for storage and/or transmission might be scarce, we study linear regression when predictors, their squares, and responses are subject to single-bit…

This paper analyzes the classical linear regression model with measurement errors in all the variables. First, we provide necessary and sufficient conditions for identification of the coefficients. We show that the coefficients are not…

This paper addresses the problem of regression to reconstruct functions, which are observed with superimposed errors at random locations. We address the problem in reproducing kernel Hilbert spaces. It is demonstrated that the estimator,…

Predictive linear and nonlinear models based on kernel machines or deep neural networks have been used to discover dependencies among time series. This paper proposes an efficient nonlinear modeling approach for multiple time series, with a…

A functional (lagged) time series regression model involves the regression of scalar response time series on a time series of regressors that consists of a sequence of random functions. In practice, the underlying regressor curve time…

Mixed spatial autoregressive (SAR) models with numerical covariates have been well studied. However, as non-numerical data, such as functional data and compositional data, receive substantial amounts of attention and are applied to…