Data driven chi-square test for uniformity with unequal cells

The power of Pearson's chi-square test for uniformity depends heavily on the choice of the partition of the unit interval involved in the form of the test statistic. We propose a selection rule which chooses a proper partition based on the data. This selection rule leads usually to essentially unequal cells well suited to the observed distribution. We investigate the corresponding data driven chi-square test and present a Monte Carlo simulation study. The conclusion is that this test achieves a high and very stable power for a large class of alternatives, and is much more stable than any other test we compare to.

[1]  Andrew R. Barron,et al.  Minimum complexity density estimation , 1991, IEEE Trans. Inf. Theory.

[2]  K. Pearson.  On the Criterion that a Given System of Deviations from the Probable in the Case of a Correlated System of Variables is Such that it Can be Reasonably Supposed to have Arisen from Random Sampling , 1900 .

[3]  Wilbert C.M. Kallenberg,et al.  Consistency and Monte Carlo Simulation of a Data Driven Version of smooth Goodness-of-Fit Tests , 1995 .

[4]  Wilbert C.M. Kallenberg.  The penalty in data driven Neyman's tests , 2000 .

[5]  J. Oosterhoff,et al.  THE CHOICE OF CELLS IN CHI–SQUARE TESTS , 1985 .

[6]  M. Quine,et al.  EFFICIENCIES OF CHI-SQUARE AND LIKELIHOOD RATIO GOODNESS-OF-FIT TESTS , 1985 .

[7]  Wilbert C.M. Kallenberg,et al.  Data-Driven Smooth Tests When the Hypothesis is Composite , 1997 .

[8]  R. L. Eubank,et al.  Optimal Grouping, Spacing, Stratification, and Piecewise Constant Approximation , 1988 .

[9]  T. Ledwina,et al.  Intermediate Approach to Comparison of Some Goodness-of-Fit Tests , 2001 .

[10]  Vanishing shortcoming and asymptotic relative efficiency , 2000 .

[11]  Jorma Rissanen,et al.  Density estimation by stochastic complexity , 1992, IEEE Trans. Inf. Theory.

[12]  Wilbert C.M. Kallenberg,et al.  Power approximations to and power comparison of smooth goodness-of-fit tests , 1994 .

[13]  E. Hannan,et al.  On stochastic complexity and nonparametric density estimation , 1988 .

[14]  Terry L King.  Smooth Tests of Goodness of Fit , 1991 .

[15]  T. Ledwina.  Data-Driven Version of Neyman's Smooth Test of Fit , 1994 .

[16]  T. Ledwina,et al.  Data-Driven Rank Tests for Independence , 1999 .

[17]  Malgorzata Bogdan.  Data driven versions of pearson's chisquare test for uniformity , 1995 .

[18]  A. Wald,et al.  On the Choice of the Number of Class Intervals in the Application of the Chi Square Test , 1942 .

[19]  Yu. I. Ingster.  Adaptive chi-square tests , 2000 .

[20]  B. F. Schriever,et al.  The Number of Classes in Chi-Squared Goodness-of-Fit Tests , 1985 .

[21]  P. Major,et al.  An approximation of partial sums of independent RV'-s, and the sample DF. I , 1975 .