Summary
In this note some asymptotically optimum tests for testing hypotheses concerning parameters when the observations are dependent are obtained. Test statistics based on the score functions, similar to the one proposed by Rao in the case when the observations are i.i.d. are proposed. Asymptotically UMP tests for one sided hypotheses against one sided alternatives and asymptotically UMP unbiased test for a simple hypothesis against two sided alternatives are derived. In the multiparameter case tests for simple hypotheses that have asymptotically best constant power on some family of surfaces in the parameter space are derived.
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References
Basawa, I. V. and Koul, H. L. (1980). Asymptotically minimax tests of composite hypotheses for non-ergodic type processes, preprint, Michigan State University.
Basawa, I. V. and Prakasa Rao, B. L. S. (1980).Statistical Inference for Stochastic Processes, Academic Press, London.
Basawa, I. V. and Scott, D. J. (1978). Efficient tests for stochastic processes,Sankhyā, A39, 21–31.
Basawa, I. V. and Scott, D. J. (1983).Asymptotic Optimal Inference for Nonergodic Models, Springer-Verlag Lectures notes in Statistics,17, New York.
Billingsley, P. (1968).Convergence of Probability Measures, Wiley, New York.
Crowder, M. J. (1976). Maximum likelihood estimation for dependent observations,J. R. Statist. Soc., B38, 45–53.
Ghosh, J. K. and Chandra, T. (1978). Comparison of tests with same Bahadur efficiency,Sankhyā, A40, 253–277.
Hájek, J. (1970). A characterization of limiting distributions of regular estimates,Zeit. Wahrscheinlichkeitsth.,14, 323–330.
Lecam, L. (1960). Locally asymptotically normal families of distributions,Univ. Calif. Publ. Statist.,3(2), 37–98.
Lehmann, E. L. (1959).Testing Statistical Hypotheses, Wiley, New York.
Rao, C. R. (1948). Large sample tests of statistical hypotheses concerning several parameters with applications to problems of estimations,Proc. Camb. Phil. Soc.,44, 50–57.
Rao, C. R. (1973).Linear Statistical Inference and its Applications, 2nd ed., Wiley, New York.
Roussas, G. G. (1972).Contiguity of Probability Measures, Cambridge University Press, Cambridge.
Sarma, Y. R. (1968). Sur les tests et sur l'estimation de parametres pour certains processus stochastiques stationnaires,Publ. Inst. Statist. Univ. Paris,17, 1–124.
Sorensen, M. (1985). On sequential maximum likelihood estimation for exponential families of stochastic processes,Research Reports No. 130, University Aarhus.
Wald, A. (1943). Tests of statistical hypotheses concerning several parameters when the number of observations is large,Trans. Amer. Math. Soc.,54, 426–482.
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Sarma, Y.R.K. Asymptotic properties of Rao's test for testing hypotheses in discrete parameter stochastic processes. Ann Inst Stat Math 39, 497–512 (1987). https://doi.org/10.1007/BF02491486
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DOI: https://doi.org/10.1007/BF02491486