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受限参数空间中的稳健固定尺寸置信程序AI 解读

Robust fixed size confidence procedures are derived for the location parameter $\theta$ of a sample of $N$ i.i.d. observations of a scalar random variable $Z$ with CDF $F(z - \theta)$. Here, $\theta$ is restricted to a closed interval $\Omega$ and the uncertainty in $F$ is modeled by an uncertainty class $\mathscr{F}$. These robust confidence procedures are, in turn, based on the solution of a related robust minimax decision problem that is characterized by a zero-one loss…

受限参数空间中的最优固定大小置信程序AI 解读

Optimal fixed size confidence procedures are derived for the mean of a normal random variable with known variance, when the mean is restricted to a compact interval. These confidence procedures are, in turn, based on the solution of a related minimax decision problem which is characterized by a zero-one loss function and a compact interval parameter space. The minimax rules obtained are nonrandomized, admissible, Bayes procedures. The decision-theoretic results are extended…

广义二次损失下正态随机向量均值的极小极大估计AI 解读

An admissible minimax estimate for the mean of a normal random vector with known covariance is derived for a generalized quadratic loss function. This loss function is quadratic in both the estimation error and the unknown mean. The estimate is derived using the method of least favorable prior distributions. The decision rule is linear, and the least favorable prior distribution for the unknown mean is normal with zero mean. The covariance of this least favorable normal…