On Testing Independence and Goodness-of-fit in Linear Models

By Arnab Sen, Bodhisattva Sen. 2013

55 citations recorded by the source corpus.

We consider a linear regression model and propose an omnibus test to simultaneously check the assumption of independence between the error and the predictor variables, and the goodness-of-fit of the parametric model. Our approach is based on testing for independence between the residual obtained from the parametric fit and the predictor using the Hilbert--Schmidt independence criterion (Gretton et al. (2008)). The proposed method requires no user-defined regularization, is simple to compute, based merely on pairwise distances between points in the sample, and is consistent against all alternatives. We develop distribution theory for the proposed test statistic, both under the null and the alternative hypotheses, and devise a bootstrap scheme to approximate its null distribution. We prove the consistency of the bootstrap scheme. A simulation study shows that our method has better power than its main competitors. Two real datasets are analyzed to demonstrate the scope and usefulness of our method.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/4a3d38828f77cb87ee3c43ad9084f82cf3d5c055

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Citations in the corpus

Measuring Association on Topological Spaces Using Kernels and Geometric Graphs (2020, background): “, [81, 15, 86, 38, 103, 102, 41, 106, 47, 76, 82, 67, 53, 88, 61, 14, 10] and the references therein, however none of them satisfy (II).”
A New Coefficient of Correlation (2019, unknown): “…Gamboa, Klein, and Lagnoux 2018; Weihs, Drton, and Meinshausen 2018; Deb and Sen 2019), kernel-based methods (Gretton et al. 2005, 2008; Sen and Sen 2014; Pfister et al. 2018; Zhang et al. 2018), information theoretic coefficients (Linfoot 1957; Kraskov, Stogbauer, and Grassberger 2004;…”
A Projection-based Conditional Dependence Measure with Applications to High-dimensional Undirected Graphical Models. (2015, background): “Another related work is Sen and Sen (2014), where the focus is on testing the independence between the error and the predictor variables in the linear regression problem.”
Multivariate Rank-Based Distribution-Free Nonparametric Testing Using Measure Transportation (2019, unknown): “[133] Sen, A.”
Nonparametric independence testing via mutual information (2017, background): “Related work here includes Neumeyer (2009), Neumeyer and Van Keilegom (2010), M¨uller, Schick and Wefelmeyer (2012), Sen and Sen (2014) and Shah and B¨uhlmann (2017).”