Related papers: The $\alpha$--regression for compositional data: a…
Compositional data have two unique characteristics compared to typical multivariate data: the observed values are nonnegative and their summand is exactly one. To reflect these characteristics, a specific regularized regression model with…
High-dimensional multivariate spatial-temporal data arise frequently in a wide range of applications; however, there are relatively few statistical methods that can simultaneously deal with spatial, temporal and variable-wise dependencies…
Deep learning methods achieve remarkable predictive performance in modeling complex, large-scale data. However, assessing the quality of derived models has become increasingly challenging, as more classical statistical assumptions may no…
Spherical regression explores relationships between variables on spherical domains. We develop a nonparametric model that uses a diffeomorphic map from a sphere to itself. The restriction of this mapping to diffeomorphisms is natural in…
We consider the problem of adaptive estimation of the regression function in a framework where we replace ergodicity assumptions (such as independence or mixing) by another structural assumption on the model. Namely, we propose adaptive…
Cylindrical data frequently arise across various scientific disciplines, including meteorology (e.g., wind direction and speed), oceanography (e.g., marine current direction and speed or wave heights), ecology (e.g., telemetry), and…
Spatial dependent data frequently occur in many fields such as spatial econometrics and epidemiology. To deal with the dependence of variables and estimate quantile-specific effects by covariates, spatial quantile autoregressive models…
We propose to approximate the conditional expectation of a spatial random variable given its nearest-neighbour observations by an additive function. The setting is meaningful in practice and requires no unilateral ordering. It is capable of…
We introduce a tunable loss function called $\alpha$-loss, parameterized by $\alpha \in (0,\infty]$, which interpolates between the exponential loss ($\alpha = 1/2$), the log-loss ($\alpha = 1$), and the 0-1 loss ($\alpha = \infty$), for…
In this paper, we study nonparametric models allowing for locally stationary regressors and a regression function that changes smoothly over time. These models are a natural extension of time series models with time-varying coefficients. We…
Compositional data consist of known compositions vectors whose components are positive and defined in the interval (0,1) representing proportions or fractions of a "whole". The sum of these components must be equal to one. Compositional…
Linear least-squares regression with a "design" matrix A approximates a given matrix B via minimization of the spectral- or Frobenius-norm discrepancy ||AX-B|| over every conformingly sized matrix X. Another popular approximation is…
Compositional data consists of vectors of proportions whose components sum to 1. Such vectors lie in the standard simplex, which is a manifold with boundary. One issue that has been rather controversial within the field of compositional…
We develop joint confidence regions for linear regression coefficients when the regressors and errors are jointly stationary and ergodic with unspecified serial dependence. The method applies random smoothing, using an independent auxiliary…
Segmented regression models offer model flexibility and interpretability as compared to the global parametric and the nonparametric models, and yet are challenging in both estimation and inference. We consider a four-regime segmented model…
Microbiome data are complex in nature, involving high dimensionality, compositionally, zero inflation, and taxonomic hierarchy. Compositional data reside in a simplex that does not admit the standard Euclidean geometry. Most existing…
Regression by composition provides a flexible framework for constructing conditional distributions through sequential group actions. However, when multiple flows act on the same distribution, the model becomes non-identifiable, leading to…
The function-on-function regression model is fundamental for analyzing relationships between functional covariates and responses. However, most existing function-on-function regression methodologies assume independence between observations,…
For the last two decades, high-dimensional data and methods have proliferated throughout the literature. Yet, the classical technique of linear regression has not lost its usefulness in applications. In fact, many high-dimensional…
The linear regression models are widely used statistical techniques in numerous practical applications. The standard regression model requires several assumptions about the regres- sors and the error term. The regression parameters are…