Chi-Squared Goodness of Fit Tests with Applications

Chapter 6

Vector-Valued Tests

6.1 Introduction

Different ways of improving goodness of fit tests have been discussed in the literature. For obtaining more powerful and suitable tests, Cochran (1954) proposed to use single degree of freedom, or groups of degrees from the total chi-squared sum. This has been materialized for different classical and modified chi-squared statistics, for which independent chi-squared components with one degree of freedom in the limit have been developed; see Anderson (1994), Rayner (2002), Voinov et al. (2007), Voinov (2010), and also Section 2.3. Lemeshko and Postovalov (1998) and Lemeshko (1998) succeeded in increasing the power of the PF test by a special data grouping method. Their idea was to construct grouping ...