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不可容许的最佳不变估计量：独立同分布情形AI 解读

An example is presented of an inadmissible best invariant point estimator of a location parameter. The extra moment condition of Brown and Fox (1974b) is violated. The example involves two independent, identically distributed observations, an improvement over Perng's (1970) example.

有限总体中样本均值的一项极小极大性质AI 解读

Consider the problem of estimating the mean of a finite population on the basis of a simple random sample. It was proved by Aggarwal (1954) that the sample mean minimizes the maximum expected squared error divided by the population variance $\tau^2$. Aggarwal also stated, but did not successfully prove, that the sample mean minimizes the maximum expected squared error over the populations satisfying $\tau^2 \leq M$ for any fixed positive $M$. It is the purpose of this paper…

随机游走模型参数最小二乘估计量极限分布的计算AI 解读

The limit distribution of the least squares estimator $\\hat{\\alpha}$ of the parameter $\\alpha$ of the first order stochastic difference equation, in the boundary case $\\alpha = 1$, is calculated.

最大似然估计与贝叶斯估计的一致性AI 解读

It is proved in the paper that every possible set of conditions which implies consistency of the maximum likelihood method also implies consistency of Bayes estimates for a large class of prior distributions. The method of the proof is based on a necessary and sufficient condition for the consistency of maximum likelihood estimates which is due to Perlman (1972). Perlman's result is improved as far as certain questions of measurability are concerned.

含干扰参数统计假设的稳健渐近检验AI 解读

A robust version of Neyman's optimal $C(\alpha)$ test is proposed for contamination neighborhoods. The proposed robust test is shown to be asymptotically locally maximin among all asymptotic level $\alpha$ tests. Asymptotic efficiency of the test procedure at the ideal model is investigated. An outlier resistant version of Student's $t$-test is proposed.

二元分布对称性的秩检验AI 解读

The problem is considered of testing symmetry of a bivariate distribution $\mathscr{L}(X, Y)$ against "asymmetry towards high $X$-values," subject to the restriction of invariance under the transformations $(x_i, y_i) \mapsto (g(x_i), g(y_i)) (1 \leq i \leq n)$ for increasing bijections $g$. This invariance restriction prohibits the common reduction to the differences $x_i - y_i$. The intuitive concept of "asymmetry towards high $X$-values" is approached in several ways, and…

Bahadur效率意义下线性秩检验的不可容许性AI 解读

Hajek (1974) has shown that in the two-sample problem the best exact slope for a test of randomness against any particular member of a large class of alternative hypotheses is attained by a linear rank test. Here a new class of two-sample rank tests is constructed, and it is shown that for each linear test there exists a test within the new class which is always at least as efficient in terms of exact Bahadur efficiency irrespective of which alternative hypothesis, is…

弱收敛与单点密度的有效估计AI 解读

We consider estimators for a multivariate probability density at a point. Efficient choices require knowledge of the density and its second derivatives although these are not known. We use consistent, but not necessarily efficient, estimators for these and use them to replace the unknown values in the choices for an efficient estimator. Our second stage estimators and the unattainable efficient choices are asymptotically equivalent. This follows because we show that an…

癌症相关非平稳泊松过程强度函数的非参数估计AI 解读

An attempt is made to model the appearance times of metastases as a nonstationary Poisson process. Three algorithms are developed for this task. The first follows the kernel approach used in probability density estimation by Parzen and Rosenblatt; the second extends the work of Grenander on mortality measurements to a more general censoring scheme appropriate for the present application; the third employs a discrete maximum penalized likelihood approach. We obtain estimates…

多元正态变量绝对值的全正性及其置信集与概率不等式应用AI 解读

Total positivity properties of multivariate densities are useful in deducing positive dependence of random vector components and related probability inequalities. In this paper we determine necessary and sufficient conditions for total positivity of absolute value multinormal variables. The results are applied to obtain positive dependence and associated inequalities for the multinormal and related distributions, e.g., the multivariate $t$ and Wishart distributions.…

所有对象相对“最优者”差距的同时置信区间AI 解读

In practice, comparisons with the "best" are often the ones of primary interest. In this paper, parametric and nonparametric simultaneous upper confidence intervals for all distances from the "best" are derived under the location model. Their improvement upon the results of Bechhofer (1954), Gupta (1956, 1965), Fabian (1962), and Desu (1970) in the parametric case is discussed. In the nonparametric case, no comparable confidence statements were available previously.

基于离散格点观测与保序回归的随机逼近AI 解读

A new non-parametric stochastic approximation procedure for estimating the roots of a non-decreasing regression function is described. The observations are taken on a discrete lattice and the estimation is based on the roots of the sample isotonic regression function fitted to the observed values. Asymptotic properties of the estimator are proven. When specialized to the bio-assay case it gives asymptotic results similar to those obtained by Derman for his up-and-down method…

分层样本推断：线性化、刀切法与平衡重复复制法的性质AI 解读

The asymptotic normality of both linear and nonlinear statistics and the consistency of the variance estimators obtained using the linearization, jackknife and balanced repeated replication (BRR) methods in stratified samples are established. The results are obtained as $L \rightarrow \infty$ within the context of a sequence of finite populations $\{\Pi_L\}$ with $L$ strata in $\Pi_L$ and are valid for any stratified multistage design in which the primary sampling units…

判别分析中正确分类率的渐近展开AI 解读

When classifying an observation into one of $k$ multivariate normal distributions based on samples of correctly classified observations, two estimates of the probability of correct classification, called the apparent and plug-in correct classification rates, are considered. Asymptotic expansions are found for the means and variances of these estimates. It is shown that these expansions can be used to help reduce the bias of the estimates. In the course of finding the…

线性时间序列模型检验的一种方法AI 解读

The purpose of this paper is to develop diagnostic tests for open-loop transfer function models with autoregressive-moving average stochastic disturbances using the efficient scores procedure. The tests proposed are asymptotically equivalent to those based upon the likelihood ratio principle and have the advantage that they do not involve a heavy computational burden. Consideration is given both to the standard case of nonsingular information matrices and to the situation…

We demonstrate the admissible Bayes character of two residual error criteria for subset selection of independent variables in normal multivariate regression models. In particular, suppose a linear model includes the independent variable list $X$, and suppose all additional independent variable subsets of size $s$ (fixed) from list $Z$ are under consideration for inclusion in the model. Let $\mathbf{\Sigma}$ be the regression error covariance matrix and $\hat{\mathbf{\Sigma}}(\hat{\mathbf{\Sigma}}_\mathscr{J})$…

残差分析的新工具AI 解读

Techniques are presented for stepwise selection of observations in order of discrepancy from a linear model, and for assigning a $P$ value to each selected observation. A general class of criteria for discrepancy is defined, and leading members of the class are discussed. Two ways to define the sequence of $P$ values for a general selection criterion are discussed, and their relative advantages are compared. The techniques are illustrated on several data sets using only the…

位置尺度族中最佳不变预测量与最佳无偏预测量的关系AI 解读

In this paper a necessary and sufficient condition for a predictor to be the best invariant predictor in location and scale families is given. Using this condition, it is shown that the best invariant predictor is expressed by a linear combination of the best unbiased predictor and the best unbiased estimator of the scale parameter.

一般 Gauss–Markov 模型中保持最佳线性无偏估计的线性变换AI 解读

Under a general Gauss-Markoff model $\{\mathbf{y}, \mathbf{X,\beta, V}\}$, a necessary and sufficient condition is established for a linear transformation, $\mathbf{F}$, of the observable random vector $\mathbf{y}$ to have the property that there exists a linear function of $\mathscr{Fy}$ which is a BLUE of $\mathbf{X\beta}$. A method for deriving a required BLUE from the transformed model $\{\mathbf{Fy, FX\beta, FVF}'\}$ is also indicated.

最优外推设计恰需 k+1 个点的回归系统AI 解读

The problem of optimal design for linear regression extrapolation is discussed. A restriction is introduced which will ensure that the number of optimal design points is equal to the number of independent regressors.

具有光滑评分函数的次序统计量线性组合的渐近正态性AI 解读

Asymptotic normality of linear combinations of order statistics of the form $T_n = n^{-1} \sum J(i/(n + 1))X_{in}$ is investigated along with a slightly trimmed version of $T_n$. Theorem 5 of Stigler (1974) is extended to show asymptotic normality of $T_n$ for a wide class of score functions. In addition, a proof of Theorem 4 of Stigler (1974) is given.

有界正态均值的估计AI 解读

The problem of estimating a normal mean has received much attention in recent years. If one assumes, however, that the true mean lies in a bounded interval, the problem changes drastically. In this paper we show that if the interval is small (approximately two standard deviations wide) then the Bayes rule against a two point prior is the unique minimax estimator under squared error loss. For somewhat wider intervals we also derive sufficient conditions for minimaxity of the…

伪最大似然估计：理论与应用AI 解读

Let $X_1, \cdots, X_n$ be i.i.d. random variables with probability distribution $F_{\theta, p}$ indexed by two real parameters. Let $\hat{p} = \hat{p}(X_1, \cdots, X_n)$ be an estimate of $p$ other than the maximum likelihood estimate, and let $\hat{\theta}$ be the solution of the likelihood equation $\partial/\partial \theta \ln L(\mathbf{x}, \theta, \hat{p}) = 0$ which maximizes the likelihood. We call $\hat{\theta}$ a pseudo maximum likelihood estimate of $\theta$, and…

替换试验与乘积极限估计量AI 解读

Let $X_1, X_2, \cdots$ be a sequence of i.i.d. nonnegative rv's with nondegenerate df $F$. Define $\tilde{N}(t) = {\tt\#}\{j: X_1 + \cdots + X_j \leq t\}$. In "testing with replacement" (also known as "renewal testing") $n$ independent copies of $\tilde{N}$ are observed each over the time interval $\lbrack 0, \tau \rbrack$ and we are interested in nonparametric estimation of $F$ based on these observations. We prove consistency of the product limit estimator as $n\rightarrow\infty$…