Related papers: Totally Concave Regression
The function-on-function linear regression model in which the response and predictors consist of random curves has become a general framework to investigate the relationship between the functional response and functional predictors.…
Fr\'echet regression has emerged as a promising approach for regression analysis involving non-Euclidean response variables. However, its practical applicability has been hindered by its reliance on ideal scenarios with abundant and…
In this note a new high performance least squares parameter estimator is proposed. The main features of the estimator are: (i) global exponential convergence is guaranteed for all identifiable linear regression equations; (ii) it…
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…
We present a model-based derivative-free method for optimization subject to general convex constraints, which we assume are unrelaxable and accessed only through a projection operator that is cheap to evaluate. We prove global convergence…
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Multivariate adaptive regression splines (MARS) is a popular method for nonparametric regression introduced by Friedman in 1991. MARS fits simple nonlinear and non-additive functions to regression data. We propose and study a natural lasso…
Given a full rank matrix $X$ with more columns than rows, consider the task of estimating the pseudo inverse $X^+$ based on the pseudo inverse of a sampled subset of columns (of size at least the number of rows). We show that this is…
The performance of Least Squares (LS) estimators is studied in isotonic, unimodal and convex regression. Our results have the form of sharp oracle inequalities that account for the model misspecification error. In isotonic and unimodal…
Automated model selection is often proposed to users to choose which machine learning model (or method) to apply to a given regression task. In this paper, we show that combining different regression models can yield better results than…
Estimating linear, mean-square continuous functionals is a pivotal challenge in statistics. In high-dimensional contexts, this estimation is often performed under the assumption of exact model sparsity, meaning that only a small number of…
This paper is about optimal estimation of the additive components of a nonparametric, additive isotone regression model. It is shown that asymptotically up to first order, each additive component can be estimated as well as it could be by a…
In scientific applications, multivariate observations often come in tandem with temporal or spatial covariates, with which the underlying signals vary smoothly. The standard approaches such as principal component analysis and factor…
Nonlinear regression analysis is a popular and important tool for scientists and engineers. In this article, we introduce theories and methods of nonlinear regression and its statistical inferences using the frequentist and Bayesian…
The paper introduces a new estimation method for the standard linear regression model. The procedure is not driven by the optimisation of any objective function rather, it is a simple weighted average of slopes from observation pairs. The…
Envelope methods offer targeted dimension reduction for various models. The overarching goal is to improve efficiency in multivariate parameter estimation by projecting the data onto a lower-dimensional subspace known as the envelope.…
Analysis of covariance is a crucial method for improving precision of statistical tests for factor effects in randomized experiments. However, existing solutions suffer from one or more of the following limitations: (i) they are not…
A new risk bound is presented for the problem of convex/concave function estimation, using the least squares estimator. The best known risk bound, as had appeared in \citet{GSvex}, scaled like $\log(en) n^{-4/5}$ under the mean squared…
We consider the problem of estimating an additive regression function in an inverse regres- sion model with a convolution type operator. A smooth backfitting procedure is developed and asymptotic normality of the resulting estimator is…
This paper develops a uniformly valid and asymptotically nonconservative test based on projection for a class of shape restrictions. The key insight we exploit is that these restrictions form convex cones, a simple and yet elegant structure…