Testing parametric models in linear-directional regression

TL;DR

This paper introduces a goodness-of-fit test for parametric regression models with scalar responses and directional predictors, utilizing a weighted squared distance between estimators and validated through simulations and a real text mining application.

Contribution

It proposes a novel testing procedure for directional regression models using a projected local approach and provides theoretical and practical validation.

Findings

The test has good finite-sample performance in simulations.

The asymptotic distribution under the null hypothesis is derived.

Application to text mining demonstrates practical utility.

Abstract

This paper presents a goodness-of-fit test for parametric regression models with scalar response and directional predictor, that is, a vector on a sphere of arbitrary dimension. The testing procedure is based on the weighted squared distance between a smooth and a parametric regression estimator, where the smooth regression estimator is obtained by a projected local approach. Asymptotic behavior of the test statistic under the null hypothesis and local alternatives is provided, jointly with a consistent bootstrap algorithm for application in practice. A simulation study illustrates the performance of the test in finite samples. The procedure is applied to test a linear model in text mining.