Estimators with nondecreasing risk: application of a chi-squared identity

CHI-Squared Test of Independence

Chi-square (X) test is a nonparametric statistical analyzing method often used in experimental work where the data consist in frequencies or ‘counts’ – for example the number of boys and girls in a class having their tonsils out – as distinct from quantitative data obtained from measurement of continuous variables such as temperature, height, and so on. The most common use of the test is to ass...

Information Divergence is more chi squared distributed than the chi squared statistics

For testing goodness of fit it is very popular to use either the χ-statistic or G-statistics (information divergence). Asymptotically both are χ-distributed so an obvious question is which of the two statistics that has a distribution that is closest to the χ-distribution. Surprisingly, when there is only one degree of freedom it seems like the distribution of information divergence is much bet...

Lower Bounds on Bayes Factors for Multinomial Distributions, with Application to Chi-squared Tests of Fit1

Lower bounds on Bayes factors in favor of the null hypothesis in multinomial tests of point null hypotheses are developed. These are then applied to derive lower bounds on Bayes factors in both exact and asymptotic chi-squared testing situations. The general conclusion is that the lower bounds tend to be substantially larger than P-values, raising serious questions concerning the routine use of...

Chi squared automatic interaction detector pdf

Notes on the chi-squared distribution