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关于 Page 双侧累积和程序的一则注记
A symmetric version of Page's (1954) two-sided cumulative sum procedure is discussed and a formula for the average run length given. Asymptotic normality of run length under suitable normalization is established.
关于Page双侧累积和程序的一则札记
A symmetric version of Page's (1954) two-sided cumulative sum procedure is discussed and a formula for the average run length given. Asymptotic normality of run length under suitable normalization is established.
Hammersley 整数均值估计量的若干性质
Let $X_1, \cdots, X_n$ be i.i.d. $N(i, 1), i = 0, \pm 1, \pm 2,\cdots$. Hammersley [2] proposed $\lbrack\bar{X}_n\rbrack$, the nearest integer to the sample mean, as an estimator of $i$. It is proved that $d$ is minimax and admissible relative to zero-one loss. However, it is shown that relative to squared error loss, the estimator is neither admissible nor minimax.
已知变异系数的正态分布均值估计札记
The purpose of the present note is to find the best possible estimator of the parameter θ in the normal distribution N (θ, aθ2) (θ > 0) where α is a known positive constant. It is shown that neither the sample mean nor the sample standard deviation with suitably chosen constant is any longer the best unbiased estimator in the sense of minimum variance. Among a typical class of unbiased estimators, the one with minimum variance is obtained. It is also shown that the suggested…