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maximum likelihood statistic; tables of critical values; two-sided hypotheses; normal population
Let the random variable $X$ have the normal distribution $N(\mu,\sigma^2)$. Explicit formulas for maximum likelihood estimator of $\mu,\sigma$ are derived under the hypotheses $\mu+c\sigma\leq m + \delta, \mu-c\sigma\geq m-\delta$, where $c,m,\delta$ are arbitrary fixed numbers. Asymptotic distribution of the likelihood ratio statistic for testing this hypothesis is derived and some of its quantiles are presented.
[1] H. Chernoff: On the distribution of the likelihood ratio. Ann. Math. Stat., 25, 1954, 573 - 578. DOI 10.1214/aoms/1177728725 | MR 0065087 | Zbl 0056.37102
[2] H. Chernoff: Large-sample theory: parametric case. Ann. Math. Stat., 27, 1956, 1 - 22. DOI 10.1214/aoms/1177728347 | MR 0076245 | Zbl 0072.35703
[3] D. J. Cowden: Statistical Methods in Quality Control. Englewood Cliffs, Prentice Hall 1957.
[4] H. Crarner: Mathematical Methods of Statistics. Princeton, Princelon University Press 1966.
[5] Ch. Eisenhart M. W. Hastay, W A. Wallis: Selected Techniques of Statistical Analysis for Scientific and Industrial Research and Production and Management Engineering. New York, McGraw-Hill 1947. MR 0023505
[6] P. L. Feder: On the distribution of the log likelihood ratio test statistic when the true parameter is "near" the boundaries of the hypothesis regions. Ann. Math. Stat., 39, 1968, 2044 to 2055. DOI 10.1214/aoms/1177698032 | Zbl 0212.23002
[7] L. Schmetterer: Introduction to Mathematical Statistics. Berlin, Springer - Verlag 1974. MR 0359100 | Zbl 0295.62001
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