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估计量与样本量的序贯联合选择AI 解读

For certain point and interval estimation problems, sequential procedures are proposed for choosing an estimator (from the class of trimmed means with trimming proportion in a specified range) as well as a sample size on which to base the estimator. It is shown that these procedures, which do not require knowledge of the best trimming proportion or the asymptotic variance of the corresponding trimmed mean, are asymptotically efficient with respect to the procedure that uses…

序贯实验设计的二阶效率AI 解读

In the sequential design of experiments an experimenter performs experiments sequentially to make an eventual inference about the true state of nature. A Bayesian formulation of this problem is considered. The parameter space is assumed finite and there are a finite number of repeatable experiments. Sufficient conditions are given for a procedure to be second order efficient as the sampling costs approach zero. The asymptotic analysis of a related Markov control problem is…

测量误差协方差矩阵由估计获得时的多元变量误差模型估计AI 解读

The errors-in-variables model in which the unobserved true values satisfy multiple linear restrictions is considered. Under the assumptions that the unobservable true values are normally distributed and that an estimator of the covariance matrix of the measurement error is available, the maximum likelihood estimators are derived. The limiting properties of the estimators are obtained for a wide range of assumptions, including the assumption of fixed true values.

分层抽样中的渐近正态性与 BootstrapAI 解读

This paper is about the asymptotic distribution of linear combinations of stratum means in stratified sampling, with and without replacement. Both the number of strata and their size is arbitrary. Lindeberg conditions are shown to guarantee asymptotic normality and consistency of variance estimators. The same conditions also guarantee the validity of the bootstrap approximation for the distribution of the $t$-statistic. Via a bound on the Mallows distance, situations will be…

含无差别区间问题中 Student t 检验的替代方法AI 解读

Consider a sample from a normal population with mean, $\mu$, and variance unknown. Suppose it is desired to test $H_0:\mu \leq \mu_0$ versus $H_1:\mu \geq \mu_1$, with the region $H^I_1:\mu_0 < \mu < \mu_1$ being a (nonempty) indifference zone. It is shown that the usual Student's $t$-test is inadmissible for this problem. An alternative test is proposed. The two sided problem with indifference region is also discussed. By contrast with the above result, the usual Student's $t$…

一维自回归误差过程下的最优与极小极大精确处理设计AI 解读

A theory is developed following work by Williams (1952) and Kiefer (1960) for exact treatment designs in one dimension in which the errors are a stationary process. It is shown that the designs which achieve the minimax value of any of a wide class of functionals on the information matrix for estimation of treatment differences have a special property. If the process is autoregressive of order $p$ then a random piece of the design of length $p + 1$ exhibits uncorrelated…

摘要暂缺

Jack Kiefer 在实验设计之外的研究AI 解读

This article is a survey of Jack Kiefer's published works in areas other than design of experiments. The approximately 50 articles can be divided into categories by subject matter. These categories will be discussed individually in the following review. At times Jack worked in several areas simultaneously and ideas from one area sometimes influenced work in another. Some of these influences are noted in the following survey, as the categories are discussed in roughly the…

贝叶斯推断中参数模型选择的一则札记AI 解读

This note is concerned with how to replace assessment of a "true" prior on a nonparametric family of distributions--which is usually infeasible--by assessment of an approximating prior with support in a parametrized subfamily, in such a way that the posterior derived from the parametric model is close to the "true" posterior. In general it is not sufficient that the approximating prior be close to the true prior in the sense of weak convergence, and we characterize the…

删失数据线性回归的一致性结果AI 解读

Buckley and James (1979) proposed an estimation method for linear regression models with unspecified residual distribution and right-censored response variables. In this paper we consider weak consistency of the regression parameter estimators under regularity conditions which avoid restrictions on the censoring patterns.

对称统计量的不变性原理AI 解读

We derive invariance principles for processes associated with symmetric statistics of arbitrary order. Using a Poisson sample size, such processes can be viewed as functionals of a Poisson Point Process. Properly normalized, these functionals converge in distribution to functionals of a Gaussian random measure associated with the distribution of the observations. We thus obtain a natural description of the limiting process in terms of multiple Wiener integrals. The results…

摘要暂缺

一个非参数最大似然估计问题的简单解法AI 解读

Three approaches to a nonparametric maximum likelihood problem are considered. One, based on the method of "sieves", is shown to include the other two. The sieve considered is a double exponential convolution sieve. A closed form solution is given for certain values of the sieve parameter.

广义 Kaplan–Meier 估计量AI 解读

In the theory of competing risks, the nonparametric Kaplan-Meier estimator plays an important role. In this paper, a bivariate nonparametric estimator for the competing risk problem is given, which for the special case of independent causes gives the Kaplan-Meier estimator. This paper also introduces a matrix $w$, through which dependent models for the competing problem can be studied. These results also indicate the special case on the matrix $w$ for which the bounds to the…

已知协方差下线性试验的比较AI 解读

For two linear experiments $d_1 = L(X_1\beta, V_1)$ and $d_2 = L(X_2\beta, V_2)$ where the covariances $V_1$ and $V_2$ are known and can be singular or nonsingular, we characterize the following relations: $d_1$ at least as good as $d_2, d_1$ better than $d_2$, and $d_1$ equivalent to $d_2$. Sometimes only a subset of parameters is of interest to the experimenter. We extend the above relations between $d_1$ and $d_2$ to estimation of a common subset of parameters and give…

二次损失下位置参数的同时估计AI 解读

Simultaneous estimation of $p(p \geq 3)$ location parameters are considered under quadratic loss. Explicit estimators which dominate the best invariant one are given mainly when coordinates of the best invariant one are independently, identically and symmetrically distributed. Effectiveness of integration by parts in evaluating the risk function of the dominating estimator is shown for three typical continuous distributions (uniform, double exponential and $t$). Further…

位置估计量与分布的分散程度AI 解读

In the location estimation problem, translation equivariant estimators are considered. It is shown that under a mild regularity condition the distribution of such estimators is more spread out than a particular distribution which is defined in terms of the sample size and the density of the i.i.d. observations. Some consequences of this so-called spread-inequality are discussed, namely the Cramer-Rao inequality, an asymptotic minimax inequality and the efficiency of the…

多元线性回归若干参数的不变置信序列AI 解读

Let $\mathbf{X}_1, \mathbf{X}_2,\cdots$ be independent $p$-variate normal vectors with $E \mathbf{X}_\alpha \equiv \beta \mathbf{Y}_\alpha, \alpha = 1,2,\cdots$ and same p.d. dispersion matrix $\Sigma$. Here $\beta: p \times q$ and $\Sigma$ are unknown parameters and $\mathbf{Y}_\alpha$'s are known $q \times 1$ vectors. Writing $\beta = (\beta'_1 \beta'_2)' = (\beta_{(1)}\beta_{(2)})$ with $\beta_i: p_i \times q(p_1 + p_2 = p)$ and $\beta_{(i)}: p \times q_i(q_1 + q_2 = q)$,…

线性模型的最优贝叶斯实验设计AI 解读

Optimal Bayesian experimental designs for estimation and prediction in linear models are discussed. The designs are optimal for estimating a linear combination of the regression parameters $\mathbf{c}^T\theta$ or prediction at a point where the expected response is $\mathbf{c}^T\mathbf{\theta}$ under squared error loss. A distribution on $\mathbf{c}$ is introduced to represent the interest in particular linear combinations of the parameters. In the usual notation for linear…

We consider the nearly linear regression problem when the assumed first degree model is contaminated by some small constant, and the design space consists of finitely many points, symmetrically distributed on the interval $\lbrack -1/2, 1/2\rbrack$. Under the usual squared loss function for the estimation of the slope and the intercept, and with the use of the least squares estimators, the problem is to find the designs which are optimal in the sense of minimizing the…

核型分位数估计量的相对亏损AI 解读

In this paper the asymptotic relative deficiency of the sample $q$-quantile with respect to kernel type estimators of the $q$-quantile is evaluated. The comparison is based on the mean square errors of the estimators. The result suggests a purely analytic measure of performance within the class of kernels. It is notable that a similar situation occurs when kernel estimators of a distribution function are studied.

回归函数核估计量的积分平方误差性质AI 解读

Weak laws of large numbers and central limit theorems are proved for integrated square error of kernel estimators of regression functions. The regressor is assumed to take values in $\mathbb{R}^p$, and the regressand, $X$, to be real valued. It is shown that in many cases, integrated square error is asymptotically normally distributed and independent of the $X$-sample. As an application, a test for the regression function (such as that proposed by Konakov) is seen to be…

非参数回归中交叉验证近邻估计的一致性AI 解读

Under suitable conditions, we show that the cross-validated nearest neighbor estimates for the unknown smooth regression function in $R^p$ is asymptotically consistent.

生长曲线的非参数回归分析AI 解读

In recent years, nonparametric curve estimates have been extensively explored in theoretical work. There has, however, been a certain lack of convincing applications, in particular involving comparisons with parametric techniques. The present investigation deals with the analysis of human height growth, where longitudinal measurements were collected for a sample of boys and a sample of girls. Evidence is presented that kernel estimates of acceleration and velocity of height,…