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方差不等的单因素设计中 T 多重比较法的修正AI 解读

Tukey's T-method for simultaneous inference in a one-way layout is extended to situations where heterogeneity of variance prevails. The modified method is based on the distribution of the range of iid Student-t variates. The new procedure is exemplified and a table of critical values is provided for its implementation. A different procedure based on a Bonferroni upper bound is also discussed.

关于 Faulkenberry 预测区间构造方法的一则注记AI 解读

Faulkenberry [4] provides a method of obtaining prediction intervals or β-expectation tolerance intervals based on the idea of conditioning on a complete sufficient statistic. The purpose of this note is to examine Faulkenberry's method and show that his claim for its generality is not altogether justified.

通过分组估计正态总体的百分位数AI 解读

In this article we apply the group-testing idea to the estimation of a percentile of a normal population when both the mean and the variance are unknown. The structure is such that we observe the sum of the normal, independent measurements of m units in one single observation (or test). Under the assumption of a fixed total cost T, we have obtained the optimal value of the group size m for both the small-sample and the large-sample (T → ∞) cases. Comparison with the…

SUR 系统中受限残差的使用：若干有限样本结果AI 解读

Consider a system of two seemingly unrelated regression equations: , where X2 is a proper subset of X1, i.e., X1≡(X2: L2), and Σ = (σij) is the disturbance covariance matrix. Let be the -estimators based, respectively, on the restricted estimate of Σ and on the unrestricted estimate S of Σ. This paper derives finite sample variances of the , and examines their efficiency with respect to the are identical to the OLS estimator obtained directly from , and are efficient. On the…

指数族中广义最小二乘估计与最大似然估计的等价性AI 解读

The method of iterative weighted least squares can be used to estimate the parameters in a nonlinear regression model. If the dependent variables are observations from a member of the regular exponential family, then under mild conditions it is shown that the IWLS estimates are identical to those obtained using the maximum likelihood principle. An application is provided to illustrate the results.

估计最大总体均值的单次抽样程序AI 解读

A single-sample procedure is proposed for obtaining asymptotically optimum confidence intervals for the largest mean of k normal populations with common unknown variance.

选择两个二项总体中较优者的改进胜者续采程序AI 解读

A new stopping rule, together with play-the-winner sampling, is used to select the better of two binomial populations. This procedure is designed to reduce the expected number of trials on the poorer population. Numerical results are given which indicate that this procedure performs better (often substantially better) in this sense than existing alternatives. Asymptotic mathematical results are also given.

马尔可夫阶数的小样本假设检验及模拟与水文应用AI 解读

This paper describes admissible hypothesis tests for Markov order, the tests being defined on certain conditioned variables. In the spirit of classical hypothesis testing, the tests have the following appealing properties: The power function is constant on the hypothesis set (and, therefore, the level is not pessimistic), and the test is asymptotically most powerful within the class of tests based on regular estimators. Application of the tests herein derived to simulated…

均匀先验导致的强不一致性AI 解读

Behavior of this type will be called strong inconsistency. Box and Tiao [2, p. 310] might, apparently, tolerate such behavior by the simple device of ignoring (1.3), which, based on a sampling distribution, is regarded as irrelevant to the Bayesian inference. In support orf this, Box and Tiao [2, p. 304] could employ once again a form of argument used to defend a particular improper prior in their analysis of the random effects model; namely, that (a) for any particular x,…

必然分析与自适应推断AI 解读

Statistical inference is examined for the location-scale model, using nonnormal distributions for the error. The development emphasizes necessary analysis that follows as a logical consequence from the data and model alone; only the terminal parts of the analysis use the conventional criteria of estimation and testing. Inferences are obtained concerning the shape of the distribution and concerning the location and scale parameters. Illustrations are included using real and…

迁徙猎鸟调查的发展AI 解读

Estimates of kill and activity in Canadian mail surveys of migratory game birds have been subject to considerable survey errors. This article reviews the design of the surveys and describes the studies undertaken to estimate and correct for these errors. Recent developments in sampling and estimation procedures for these surveys are presented and changes in operational procedures described which have been adopted to implement these developments.

分布无关的两样本尺度检验AI 解读

Several linear rank statistics have been proposed in the literature for the two-sample scale problem. We propose a new class of statistics which are distribution free when the populations are identical, but are not linear rank statistics. Our analogs of the Ansari-Bradley, Mood, and Klotz tests are of particular interest. Each has the same Pitman efficiency as its corresponding linear rank statistic, and yet our small-sample power is significantly higher. In addition, our…

非正交协方差分析的迭代方法AI 解读

This paper develops a method for handling a nonorthogonal analysis of covariance in an iterative manner using balanced analysis of variance residual and expectation operators. In essence, it extends previous work of the author for the nonorthogonal AOV problem to the nonorthogonal AOC problem. The iterative AOC method has the property of guaranteed convergence. In addition, under certain (convergent) conditions, successive approximations to the residual sum of squares for…

列联表中降低均方误差的估计AI 解读

A two-stage estimator is proposed for the cell probabilities in a two-dimensional contingency table. Using a multivariate mean square error criterion, we show that the decision to use either the observed cell probabilities or the estimators assuming row-column independence is approximately dependent upon the noncentrality parameter of the Pearson chi-square statistic x 2. We then derive a decision rule that says to use the independence-assumption estimators when X 2 is less…

回归解的可接受性：重新审视计算精度AI 解读

Longley [10] proposed a set of data for use in testing regression programs. This paper shows that the numerically accurate solution in this example was probably an unreasonable estimate of the regression coefficients. This is true because the accuracy of the data and appropriateness of the model may affect the solution more than the computational method. An easily computed index is derived that can be used to indicate such computational instability. The basic conclusion is…

标准化回归系数的估计AI 解读

Often in reporting the results of a regression analysis, researchers, particularly in the social sciences, choose to standardize the estimators of the regression coefficients into what are called “beta coefficients.” Most studies in which beta coefficients are reported involve linear models which contain stochastic predictor variables. However, in dealing with regression models in which thep redictor variables are nonstochastic, standardized regression coefficients can be…

三个正态总体均值线性组合的序贯估计AI 解读

Suppose μi, σi 2 are the mean and variance of the ith normal population, i = 1, 2, 3 (we assume the parameters to be all unknown). For given nonzero constants λ1, λ2, λ3, suppose μ = Σ3 i=1 λiμi. Sequential procedures have been derived (i) to arrive at a fixed width confidence interval for μ, and (ii) to estimate μ pointwise with minimum risk (loss being squared error). Some desirable asymptotic properties are proved for the stopping times in both cases. Monte Carlo studies…

评论：非可积先验在贝叶斯推断中的作用AI 解读

This illuminating paper by Stone is the latest in a series of papers drawing attention to possible disadvantages of using nonintegrable prior densities. In these comments, I shall attempt to clarify the role of nonintegrable prior densities in Bayesian inference, thereby providing also a delayed answer to James and Stein [5], Dempster [1], Stone [9], Klotz, et al. [6], and Portnoy [7]. More extensive discussion of the ideas introduced will be given in a subsequent paper.

理性预期与分布滞后预期代理AI 解读

exogenous variables which actually generate the variable to be predicted. Empirical researchers, however, have employed a modified (and weaker) form of Muth's hypothesis. Expectations are defined as rational if they fully incorporate all of the information contained in a specified information set that is available at the time that the forecast is made.3 When using distributed lag proxies, researchers implicitly assume that the information set used to generate forecasts…

摘要暂缺

非正交协方差分析的迭代方法AI 解读

This paper develops a method for handling a nonorthogonal analysis of covariance in an iterative manner using balanced analysis of variance residual and expectation operators. In essence, it extends previous work of the author for the nonorthogonal AOV problem to the nonorthogonal AOC problem. The iterative AOC method has the property of guaranteed convergence. In addition, under certain (convergent) conditions, successive approximations to the residual sum of squares for…

关于 Faulkenberry 预测区间构造方法的一则注记AI 解读

Faulkenberry [4] provides a method of obtaining prediction intervals or β-expectation tolerance intervals based on the idea of conditioning on a complete sufficient statistic. The purpose of this note is to examine Faulkenberry's method and show that his claim for its generality is not altogether justified.

标准化回归系数的估计AI 解读

Often in reporting the results of a regression analysis, researchers, particularly in the social sciences, choose to standardize the estimators of the regression coefficients into what are called “beta coefficients.” Most studies in which beta coefficients are reported involve linear models which contain stochastic predictor variables. However, in dealing with regression models in which thep redictor variables are nonstochastic, standardized regression coefficients can be…

选择两个二项总体中较优者的改进胜者续用抽样程序AI 解读

A new stopping rule, together with play-the-winner sampling, is used to select the better of two binomial populations. This procedure is designed to reduce the expected number of trials on the poorer population. Numerical results are given which indicate that this procedure performs better (often substantially better) in this sense than existing alternatives. Asymptotic mathematical results are also given.