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Cramér-Rao type inequality and a problem of mixture of distributions

In: Tatra Mountains Mathematical Publications, vol. 7, no. 1
István Vincze
Detaily:
Rok, strany: 1996, 237 - 245
O článku:
In the paper the following problem is considered: Let $X1, X2, …$, $Xn,…$ be an infinite sequence of i.i.d.r.v.'s with distribution function $\int-∞ F(x|θ)d H(θ)$, where $F(x|θ)$ is a known distribution function on the real line, while the parameter $θ$ is also real $(-∞ < θ < ∞)$ having a priori distribution $H(θ)$ which is to be determined by means of the infinite sample given above. The problem to have an explicite way of the solution was raised by H. Robbins (1964) [H. Robbins: The empirical Bayes approach to Statistical decision problems, Ann. Math. Statist. 35 (1964), 1–20], while the present investigation is closely connected with a Cramér–Rao type inequality given by the author (1979) [I. Vincze: On the Cramér–Fréchet–Rao Inequality in the Non-Regular Case}, Contributions to Statistics. (Jaroslav Hájek Memorial Volume), Academia, Prague, 1979, 253–262].
Ako citovať:
ISO 690:
Vincze, I. 1996. Cramér-Rao type inequality and a problem of mixture of distributions. In Tatra Mountains Mathematical Publications, vol. 7, no.1, pp. 237-245. 1210-3195.

APA:
Vincze, I. (1996). Cramér-Rao type inequality and a problem of mixture of distributions. Tatra Mountains Mathematical Publications, 7(1), 237-245. 1210-3195.