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附带干扰参数与随机干扰参数AI 解读

Let $\{P_{\vartheta,\eta}:(\vartheta, \eta) \in \Theta \times H\}$, with $\Theta \subset \mathbb{R}$ and H arbitrary, be a family of mutually absolutely continuous probability measures on a measurable space $(X, \mathscr{A})$. The problem is to estimate $\vartheta$, based on a sample $(x_1, \cdots, x_n)$ from $\times^n_1 P_{\vartheta,\eta_\nu}$. If $(\eta_1, \cdots, \eta_n)$ are independently distributed according to some unknown prior distribution $\Gamma$, then the…

某些非参数极大似然估计量的大偏差概率AI 解读

Let $(X, \mathscr{A})$ be a measurable space and $\{P_{\vartheta,\tau}\mid\mathscr{A}: \vartheta \in \Theta, \tau \in T\}$ a family of probability measures. Given an appropriate estimator sequence for $\vartheta$, we define a sequence of asymptotic maximum likelihood estimators for $\tau$ and give bounds for its large deviation probabilities under conditions which are natural for the application to the estimation of mixing distributions. This paper generalizes earlier…

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存在干扰参数时的最优中位数无偏估计AI 解读

For exponential families with density \begin{equation*}x \rightarrow C(\theta, \eta)h(x)\exp\lbrack a(\theta)T(x) + \Sigma^p_{i=1} a_i(\theta, \eta)S_i(x)\rbrack, (\theta, \eta) \in \Theta \times H, \Theta \subset \mathbb{R},\end{equation*} $a$ increasing and continuous, there exists for every sample size an estimator for $\theta$ which is--in the class of all median unbiased estimators--of minimal risk for any monotone loss function.

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论 Behrens–Fisher 问题AI 解读

A brief survey of the recent literature leads to the conclusion that approximately similar tests for the Behrens-Fisher problem retain their practical relevance. The asymptotie expansion of the power function of Welch's test is compared with the asymptotie expansion of the power functions of other asymptotically similar tests. Finally, it is shown that in the class of all translation invariant tests the Welch test is asymptotically uniformly most powerful against one-sided…

关于 Behrens–Fisher 问题AI 解读

A brief survey of the recent literature leads to the conclusion that approximately similar tests for the Behrens-Fisher problem retain their practical relevance. The asymptotie expansion of the power function of Welch's test is compared with the asymptotie expansion of the power functions of other asymptotically similar tests. Finally, it is shown that in the class of all translation invariant tests the Welch test is asymptotically uniformly most powerful against one-sided…

最小对比估计量的渐近展开AI 解读

This paper contains an Edgeworth-type expansion for the distribution of a minimum contrast estimator, and expansions suitable for the computation of critical regions of prescribed error (type one) as well as confidence intervals of prescribed confidence coefficient. Furthermore, it is shown that, for one-sided alternatives, the test based on the maximum likelihood estimator as well as the test based on the derivative of the log-likelihood function is uniformly most powerful…

非线性算子与充分性AI 解读

Let $(X, \mathscr{A})$ be a measurable space and $\mathscr{P} \mid \mathscr{A}$ a family of probability measures. Given a sufficient sub-$\sigma$-field, we define the sufficiency operator by assigning to each integrable function a conditional expectation which is independent of $P \in \mathscr{P}$. The operator thus defined is $\mathscr{P}$-a.e. linear, monotone, idempotent, and expectation invariant for every $P \in \mathscr{P}$. Not all of these properties are necessary to…