A Distribution-Free Test for Regression Parameters

Distribution-Free Distribution Regression

‘Distribution regression’ refers to the situation where a response Y depends on a covariate P where P is a probability distribution. The model is Y = f(P ) + μ where f is an unknown regression function and μ is a random error. Typically, we do not observe P directly, but rather, we observe a sample from P . In this paper we develop theory and methods for distribution-free versions of distributi...

A Distribution-free Test for Deprivation Dominance

The Rawlsian perspective on social policy pays particular attention to the least advantaged members of society, but how should “the least advantaged” be identified? The concept of deprivation dominance operationalizes in part the Rawlsian evaluation of the welfare of the least advantaged members of society, but a statistical procedure for testing deprivation dominance is needed. In this paper, ...

A Distribution-Free Theory of Nonparametric Regression

A Nonparametric Distribution-Free Test for Serial Independence of Errors∗

In this paper, we propose a test for the serial independence of unobservable errors in locationscale models. We consider a Hoeffding-Blum-Kiefer-Rosenblat type empirical process applied to residuals, and show that under certain conditions it converges weakly to the same limit as the process based on true errors. We then consider a generalized spectral test applied to estimated residuals, and ge...

Distribution - Free Tests in Binary Regression Models

SUMMARY This paper proposes the use of Wilcoxon rank sum, Wilcoxon signed rank, and sign statistics for testing certain hypotheses representing zero effects in the linear logistic regression model. A simulation study provides insight into the alternatives for which each test is most powerful. An example with rea 1 data is gi ven for each tes t.