This is a preview of subscription content, log in via an institution to check access.
REFERENCES
R. F. Pothoff and M. Whitingill, “Testing for homogeneity. I. The binomial and polynomial distributions. II. The Poisson distribution, ” Biometrika, 53, 167–190 (1966).
P. Vit, “Testing for homogeneity: The geometric distribution, ” Biometrika, 61, 565–568 (1974).
T. K. Wisniewsky, “Testing for homogeneity of a binomial series, ” Biometrika, 55, 426–428 (1968).
M. Engelhardt and L. J. Bain, “Uniformly most powerful unbiased tests on the scale parameter of a Gamma distribution with a nuisance as shape parameter, ” Technometrics, 19, 77–81 (1977).
M. Engelhardt and L. J. Bain, “Construction of optimal unbiased inference procedures for the parameters of the Gamma distribution, ” Technometrics, 20, 818–830 (1978).
L. Holst, “Some conditional limit theorems in exponential families, ” Ann. Probab., 9, 818–830 (1981).
D. A. Fraser, Nonparametric Methods in Statistics, Wiley, New York (1957).
E. L. Lehmann, Testing Statistical Hypotheses, Wiley, New York (1959).
J. Hajek and Z. Sidak, Theory of Rank Tests, Academic CSZV, Prague (1967).
K. R. Parthasarathy, An Introduction to Probability and Measure Theory, Springer, New York (1977).
Eh. M. Kudlaev, “Summation of some independent random quantities with values in locally compact Abelian groups, ” Sov. Math., 33, No. 2, 45–52 (1989).
E. M. Kudlaev, “On the most powerful location and scale invariant tests based on an incomplete set of order statistics, ” J. Math. Sci., 88, 806–813 (1998).
G. Klimov, Probability Theory and Mathematical Statistics, Moscow Univ. Press, Moscow (1986).
V. A. Ivanov, G. I. Ivchenko, and Yu. I. Medvedev, “Discrete problems in probability theory, ” Itogi Nauki Tekh., Ser. Teor. Veroyatn., Mat. Stat., Teor. Kibern., 22, 3–60 (1984).
E. M. Kudlaev, “Decomposable statistics, ” Itogi Nauki Tekh., Ser. Teor. Veroyatn., Mat. Stat., Teor. Kibern., 27, 97–149 (1989).
E. M. Kudlaev and A. Azzuz, “On estimation of distribution parameters in the scheme of decomposable statistics, ” in: Statistical Methods of Estimation and Hypothesis Testing [in Russian], Perm Univ. Press, Perm (1998).
E. M. Kudlaev and A. Azzuz, “The method of moments applied to estimating informative parameters in the scheme of decomposable statistics, ” in: Abstracts of IV Russian Colloquium on Stochastic Methods [in Russian], TVP, Moscow (1997).
E. M. Kudlaev, “Weak convergence of distributions of separable statistics, ” Teor. Veroyatn. Primen., 42, 85–107 (1997).
G. Ivchenko and Yu. Medvedev, Mathematical Statistics [in Russian], Mir, Moscow (1990).
C. R. Rao, Linear Statistical Inference and Its Applications, Wiley, New York (1965).
E. M. Kudlaev, “On an existence theorem for decomposable statistics, ” in: Probabilistic Method of Discrete Mathematics, VSP, Utrecht (1994), pp. 271–286.
V. I. Pagurova, “On a comparison of means of two normal samples, ” Teor. Veroyatn. Primen., 13, 561–568 (1968).
R. C. H. Cheng and M. A. A. Stephen, “Goodness-of-fit tests using Moran's statistics with estimating parameters, ” Biometrika, 76, 385–392 (1969).
B. A. Sevastyanov, A Course in Probability Theory and Mathematical Statistics [in Russian], Nauka, Moscow (1982).
Rights and permissions
About this article
Cite this article
Azzuz, A., Kudlaev, E.M. Decomposable Statistics and Conditional Procedures in Statistical Problems of Neyman Type. Journal of Mathematical Sciences 103, 547–555 (2001). https://doi.org/10.1023/A:1009597927887
Issue Date:
DOI: https://doi.org/10.1023/A:1009597927887