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列联表关联模型中的顺序约束评分参数AI 解读

The row effects and column effects models for two-way contingency tables have parameters for the row and column categories pertaining to the association between the variables. For classifications having ordered categories, it is often reasonable to assume that the association parameters have a corresponding ordering. This article proposes order-restricted estimates of the association parameters in these models. The maximum likelihood solution can be determined by the…

条件异方差时间序列模型AI 解读

Under the traditional linear time series or regression setting, the conditional variance of one-step-ahead prediction is time invariant. Experience in conjunction with data analysis, however, suggests that the variability of a process might well depend on the available information. This reality has motivated extensive research to relax the constant variance assumption imposed by the traditional linear time series model, and several classes of generalized parametric models…

分支曲线的非参数估计AI 解读

The spline smoothing approach to nonparametric regression is extended to cover the estimation of curves that branch at certain specified points in time. This extension is motivated and illustrated by data from an experiment on sunflowers. Apart from providing insight into this particular data-analytic problem, the work described demonstrates the power of the roughness penalty approach in coping with curve estimation of a nonstandard kind. Particularly in the context of…

分层两阶段抽样中的广义方差函数AI 解读

Generalized variance functions (GVF's) are used in a number of sample surveys as a convenient method of publishing sampling errors. The method consists of estimating the relative variance (relvariance) of an estimator of a total T by using a model with the form a + b/T. Using the prediction approach to finite population sampling, some asymptotic theory is presented for estimators of totals that are linear combinations of sample cluster means from stratified, two-stage…

公布效应下的重复抽样AI 解读

The generation and public dissemination of information from surveys or polls may be expected to modify or condition the private attitudes or intentions it is hoped to measure. Thus the application of statistics to human affairs is often characterized by a reactivity or reflexivity that may even negate its findings or predictions. Bandwagon, funding, or floating voter effects arising from the publication of political polls are well known. Forecasts of expected visitor numbers…

模型季节调整的不确定性与极小极大滤波器构造AI 解读

Unobserved component autoregressive integrated moving average models are often the cornerstone of model-based seasonal adjustment procedures. Unfortunately these models are inherently underidentified and ad hoc assumptions must be made prior to the analysis. This article investigates the effect of seasonal adjustment filters on a class of observationally equivalent models. Bounds on the mean squared error (MSE) associated with arbitrary linear filters are derived. The…

若干常用非参数检验的样本量确定AI 解读

The article discusses the problem of determining the number of observations required by some common nonparametric tests, so that the tests have power at least 1 – β against alternatives that differ sufficiently from the hypothesis being tested. It is shown that the number of observations depends on certain simple probabilities. A method is suggested for fixing the value of the appropriate probability when determining sample size.

大型稀疏多项分布的拟合优度检验AI 解读

A goodness-of-fit statistic D 2 is introduced for use in multinomial distributions. Pearson's X2 and D 2 are both approximately normally distributed when the sample size N is not large relative to the number of multinomial categories k. Under sequences of local alternative hypotheses the test based on D 2 exhibits moderate power when the X2 test is biased. Application is made to the analysis of large sparse contingency tables. A theorem is presented that describes the…

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非标准条件下最大似然估计与似然比检验的渐近性质AI 解读

Large sample properties of the likelihood function when the true parameter value may be on the boundary of the parameter space are described. Specifically, the asymptotic distribution of maximum likelihood estimators and likelihood ratio statistics are derived. These results generalize the work of Moran (1971), Chant (1974), and Chernoff (1954). Some of Chant's results are shown to be incorrect. The approach used in deriving these results follows from comments made by Moran…

可计算的 MINQUE 型方差分量估计AI 解读

The minimum norm quadratic unbiased estimator type (MINQUE type) of estimates considered in this article are obtained by requiring identical values for the ratios of the a priori variances to the a priori error variance and letting this common value tend to infinity. The resulting estimates are invariant quadratic unbiased estimators with certain parametric and nonparametric optimality properties: assuming normally distributed random effects the efficiency of the proposed…

随机化回答模型的贝叶斯线性估计量AI 解读

Bayes linear estimators provide simple Bayesian methods and require a minimum of prior specification. In this article, Bayes linear estimators are derived for a variety of randomized response models. Randomized response aims to reduce false responses on sensitive questions, at the expense of some loss of information in each observation. In this context, Bayesian methods are attractive because they permit the incorporation of potentially useful prior information. The basic…

误差的空间自相关与线性回归中 OLS 的相对效率AI 解读

The article considers the efficiency of ordinary least squares (OLS) coefficient estimates relative to generalized least squares (GLS) in a linear regression model where the disturbances follow a spatial autocorrelation pattern. The main result is that the limiting relative efficiency of OLS, as correlation among disturbances increases, tends to either zero or unity for most design matrices and correlation patterns encountered in practice. Which of these cases applies…

回归估计量的方差估计AI 解读

The regression estimator and the ratio estimator are commonly used in survey practice. In the past more attention has been given to the ratio estimator because of its computational ease and applicability for general sampling designs. The ratio estimator is appropriate for populations whose regression line passes close to the origin. If the intercept of the regression line is significantly nonzero, however, it is much less efficient than the regression estimator (Deng 1984).…

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通过数据增广计算后验分布AI 解读

The idea of data augmentation arises naturally in missing value problems, as exemplified by the standard ways of filling in missing cells in balanced two-way tables. Thus data augmentation refers to a scheme of augmenting the observed data so as to make it more easy to analyze. This device is used to great advantage by the EM algorithm (Dempster, Laird, and Rubin 1977) in solving maximum likelihood problems. In situations when the likelihood cannot be approximated closely by…

分层抽样中若干估计量的条件性质AI 解读

The prediction properties of the stratified expansion estimator, the separate and combined ratio estimators, and the separate and combined regression estimators are studied under a model appropriate to a population stratified on a size variable. Several estimators of variance for each total estimator are considered, including standard ones from probability sampling theory, alternative choices derived from a superpopulation model, and the jackknife. The theory is tested in an…

用普通最小二乘分析两阶段抽样数据AI 解读

A reasonably broad class of models for analyzing two-stage samples is considered. For models in this class, ordinary least squares (OLS) estimates are best linear unbiased estimates (BLUE's) and a large variety of exact tests and confidence intervals are available. The necessary computations can be made simply by fitting two models in the ordinary fashion using least squares. The most stringent assumption made is that there are equal numbers of observations taken in each…

大样本散点图矩阵技术AI 解读

High-performance interaction with scatterplot matrices is a powerful approach to exploratory multivariate data analysis. For a small number of data points, real-time interaction is possible and overplotting is usually not a major problem. When the number of plotted points is large, however, display techniques that deal with overplotting and slow production are important. This article addresses these two problems. Topics include density representation by gray scale or by…

随机拨号中 Mitofsky–Waksberg 技术的若干推广AI 解读

To provide greater flexibility and improved methodology for random digit dialing for telephone surveys, this article proposes a class of two-stage sampling techniques for random digit dialing that generalizes the Mitofsky–Waksberg technique in two directions. First, different ways of classifying telephone numbers are allowed; the classification need not be according to whether or not the number is residential. Second, drawing more than one phone number per primary sampling…

广义可加模型：若干应用AI 解读

Generalized additive models have the form η(x) = α + σ fj (x j ), where η might be the regression function in a multiple regression or the logistic transformation of the posterior probability Pr(y = 1 | x) in a logistic regression. In fact, these models generalize the whole family of generalized linear models η(x) = β′x, where η(x) = g(μ(x)) is some transformation of the regression function. We use the local scoring algorithm to estimate the functions fj (xj )…

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图形、变换与回归：回归诊断图形方法导论AI 解读

This handbook provides a detailed, down-to-earth introduction to regression diagnostic analysis, a technique of growing importance for work in applied statistics. Heavily illustrated, with numerous examples to illuminate the discussion, this timely volume outlines methods for regression models, stressing detection of outliers and inadequate models; describes the transformation of variables in an equation, particularly the response; and considers such advanced topics as…

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