Some New Goodness-of-Fit Tests Based on Stochastic Sample Quantiles

This article introduces some new tests for goodness-of-fit based on the differences between the sample quantiles and stochastic sample quantiles derived from the null distribution. Because stochastic sample quantiles for given sample observations are random, randomized statistics are derived, of which the qth quantile and the expectation are chosen as test statistics. Under uniform hypothesis, the asymptotic distributions of some new test statistics are given, respectively. The powers of the new tests under certain alternatives are examined. They are more powerful tests for the hypotheses concerned.

[1]  Ralph B. D'Agostino,et al.  Goodness-of-Fit-Techniques , 2020 .

[2]  Binning methodology for nonparametric goodness-of-fit test , 2003 .

[3]  R. Serfling.  Approximation Theorems of Mathematical Statistics , 1980 .

[4]  Y. A. Hegazy,et al.  Some New Goodness‐Of‐Fit Tests Using Order Statistics , 1975 .

[5]  M. Stephens.  EDF Statistics for Goodness of Fit and Some Comparisons , 1974 .

[6]  AN Kolmogorov-Smirnov,et al.  Sulla determinazione empírica di uma legge di distribuzione , 1933 .

[7]  F. Mosteller.  On Some Useful "Inefficient" Statistics , 1946 .

[8]  Domingo Morales,et al.  New Goodness-of-Fit Tests Based on Sample Quantiles , 2007, Commun. Stat. Simul. Comput..

[9]  D. Darling,et al.  A Test of Goodness of Fit , 1954 .

[10]  A. Martin-Löf.  On the composition of elementary errors , 1994 .

[11]  Uniformity tests under quantile categorization , 2005 .

[12]  J. Tukey,et al.  Non-Parametric Estimation. I. Validation of Order Statistics , 1945 .

[13]  J. H. Venter,et al.  Asymptotic Distributions for Quadratic Forms with Applications to Tests of Fit , 1973 .

[14]  H. Cramér.  On the composition of elementary errors: Second paper: Statistical applications , 1928 .

[15]  掛下 伸一,et al.  Non Parametric Estimationについて , 1965 .

[16]  Timothy R. C. Read,et al.  Goodness-Of-Fit Statistics for Discrete Multivariate Data , 1988 .

[17]  Pandu R. Tadikamalla,et al.  3 Computer simulation of order statistics , 1998, Order statistics.