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A quantile goodness-of-fit test applicable to distributions with non-differentiable densities. (English) Zbl 0930.62015
Author’s summary: The asymptotic distribution of the random vector of differences between theoretical probabilities and their estimates, based on the sample quantiles and on an estimate of the unknown parameter, is derived in a setting not requiring differentiability of the densities. By means of this result, asymptotically chi-square distributed goodness-of-fit test statistics are constructed for the exponential and for the Laplace distribution.

MSC:
62E20 Asymptotic distribution theory in statistics
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References:
[1] J. Anděl: Mathematical Statistics. SNTL, Prague 1978.
[2] E. Bofinger: Goodness-of-fit test using sample quantiles. J. Roy. Statist. Soc. Ser. B 35 (1973), 277-284. · Zbl 0263.62029
[3] L. N. Bolshev: Cluster analysis. Bull. Inst. Internat. Statist. 43 (1969), 411-425. · Zbl 0227.62037
[4] H. Cramér: Mathematical Methods of Statistics. Princeton University Press, Princeton 1946. · Zbl 0063.01014
[5] R. B. D’Agostino: An omnibus test for normality for moderate and large size samples. Biometrika 58 (1971), 341-348. · Zbl 0227.62060
[6] R. C. Dahiya, J. Gurland: Pearson chi-squared test of fit with random intervals. Biometrika 59 (1972), 147-153. · Zbl 0232.62017
[7] J. K. Ghosh: A new proof of the Bahadur representation of quantiles and an application. Ann. Math. Statist. 42 (1971), 1957-1961. · Zbl 0235.62006
[8] P. J. Huber: Robust Statistics. Wiley, New York 1981. · Zbl 0536.62025
[9] N. L. Johnson S. Kotz, N. Balakrishnan: Continuous Univariate Distributions – 1. Wiley, New York 1994. · Zbl 0811.62001
[10] I. A. Koutrouvelis, J. Kellermeier: A goodness-of-fit test based on the empirical characteristic function when the parameters must be estimated. J. Roy. Statist. Soc. Ser. B 43 (1981), 173-176. · Zbl 0473.62037
[11] J. A. J. Metz P. Haccou, E. Meelis: On the Shapiro-Wilk test and Darling’s test for exponentiality. Biometrika 50 (1994), 527-530.
[12] D. S. Moore: A chi-square statistic with random cell boundaries. Ann. Math. Statist. 42 (1971), 147-156. · Zbl 0218.62015
[13] M. S. Nikulin: Chi-square test for continuous distributions with location and scale parameters. Theor. Veroyatnost. i Primenen. 18 (1973), 583-592.
[14] M. S. Nikulin: On a quantile test. Theor. Veroyat. i Primenen. 19 (1974), 431-434. · Zbl 0313.62018
[15] D. Pollard: Asymptotics via empirical processes. Statist. Sci. 4 (1989), 341-366. · Zbl 0955.60517
[16] C. R. Rao: Linear Statistical Inference and Its Applications. Wiley, New York 1973. · Zbl 0256.62002
[17] S. S. Shapiro, M. B. Wilk: An analysis variance test of normality. Biometrika 52 (1965), 591-611. · Zbl 0134.36501
[18] S. S. Shapiro, M. B. Wilk: An analysis of variance test for the exponential distribution (complete samples). Technometrics 14 (1972), 355-370. · Zbl 0234.62030
[19] G. S. Watson: The \(\chi^2\) goodness-of-fit test for normal distributions. Biometrika 44 (1957), 336-348. · Zbl 0081.36002
[20] G. S. Watson: On chi-square goodness-of-fit tests for continuous distributions. J. Roy. Statist. Soc. Ser. B 20 (1958), 44-72. · Zbl 0086.12701
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