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Admissible and minimax estimators of \(\lambda ^ r\) in the gamma distribution with truncated parameter space. (English) Zbl 0611.62026
The paper contains a criterion for minimaxity of estimators for the parameter \(\lambda^ r\) of the gamma distribution with truncated parameter space. A further result explicitly gives admissible estimators for the same problem. The results are applied to several other classes of distributions.
Reviewer: H.Strasser

62F10 Point estimation
62C20 Minimax procedures in statistical decision theory
Full Text: DOI EuDML
[1] Ghosh M, Meeden G (1977) Admissibility of linear estimators in the one parameter exponential family. Ann Statist 5:772–778 · Zbl 0385.62006 · doi:10.1214/aos/1176343899
[2] Ghosh JK, Singh R (1970) Estimation of the reciprocal of the scale parameter of a gamma density. Ann Inst Statist Math 22:51–55 · Zbl 0218.62029 · doi:10.1007/BF02506322
[3] Iliescu D, Vodâ K (1979) Some notes on Pareto distribution. Rev Roumaine Math Pures Appl 4:328–337
[4] Karlin S (1958) Admissibility for estimation with quadratic loss. Ann Math Statist 29:406–436 · Zbl 0131.17805 · doi:10.1214/aoms/1177706620
[5] Katz MW (1961) Admissible and minimax estimates of parameters in truncated spaces. Ann Math Statist 32:136–142 · Zbl 0129.32603 · doi:10.1214/aoms/1177705146
[6] Lehmann EL (1983) Theory of point estimation. John Wiley & Sons · Zbl 0522.62020
[7] Ralescu D, Ralescu S (1981) A class of nonlinear admissible estimators in the one-parameter exponential family. Ann Statist 9:177–183 · Zbl 0452.62005 · doi:10.1214/aos/1176345344
[8] Sharma D (1984) An estimating the variance of a generalized Laplace distribution. Metrika 31:85–88 · Zbl 0531.62028 · doi:10.1007/BF01915188
[9] Singh R (1972) Admissible estimators of \(\lambda\)\(\gamma\) in gamma distribution with quadratic loss. Trabajos De Estadistica 23:129–134 · Zbl 0244.62010
[10] Yosushi N (1983) Estimation of the Pareto parameter and its admissibility. Math Jap 28:149–155
[11] Vodâ VG (1982) Burr distribution revisited. Rev Roumaine Math Pures App 27:885–893 · Zbl 0496.62015
[12] Zubrzycki S (1966) Explicit formulas for minimax admissible estimators in some cases of restrictions imposed on the parameter. Zastosowania Matematyki 9:31–52 · Zbl 0152.17703
[13] Kaluszka M (1985) Minimax estimation of some class of functions of the scale parameter in the gamma and other distributions in the case of truncated parameter space (submitted to Zastosowania Matematyki)
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