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截获数据的统计模型AI 解读

Consider a population of replaceable items of different ages, and suppose that for each item there is a certain measurable attribute that is a monotone function (perhaps random) of the item's age. To fix ideas, we refer to this attribute as deterioration and we assume that as items age their level of deterioration increases. We further assume that as the level of deterioration hits a certain threshold value (perhaps unknown), the item dies and disappears from the population,…

经济时间序列季节性的动态理论研究AI 解读

Several economists, notably Plosser (1978), Sargent (1978), and Wallis (1978) refuted the assumption that the seasonal component of endogenous variables in a dynamic economic model has almost all of its power restricted to what is termed seasonal frequency and its harmonics. In this article, a model with a closed-form solution is formulated to provide more insight into the arguments put forward by economists. It is concluded that univariate seasonal adjustment cannot be…

负遗憾、可选停止与异常值的消除AI 解读

This article examines the phenomenon of negative regret in sequential point estimation, in which a stopping rule used in ignorance of the variance of the distribution sometimes performs better than the best fixed sample size when the variance is known. An explanation in terms of a certain robustifying effect of the stopping rule is given. Results of simulation studies illustrating both negative regret and its explanation are also given. Suppose X 1 X 2, … are iid with mean μ…

多元 Behrens–Fisher 问题的贝叶斯解法AI 解读

We consider the problem of finding the posterior probabilities of ellipsoids for the difference between two multivariate normal means. We do not require the two population covariance matrices to be equal, therefore, our results pertain to the multivariate Behrens—Fisher problem. A Hotelling T 2-like quantity is defined, and its cdf is expressed as a linear combination of the cdf's of some F distributions. This representation enables us to compute desired probabilities…

含单整回归变量时普通最小二乘与广义最小二乘的渐近等价性AI 解读

It is shown that in the multiple regression model y 1 = x 1′β + u t, where u t, is a stationary autoregressive process and x 1 is an integrated m-vector process, the asymptotic distributions of the ordinary least squares (OLS) and generalized least squares (GLS) estimators of β are identical. This generalizes a result obtained by Krämer (1986) for two-variate regression and extends fixed regressor theory developed by Grenander and Rosenblatt (1957). Our approach uses a…

非参数回归中的自助法：局部自适应平滑与置信带AI 解读

The operation of the bootstrap in the context of nonparametric regression is considered. Bootstrap samples are taken from estimated residuals to study the distribution of a suitably recentered kernel estimator. The application of this principle to the problem of local adaptive choice of bandwidth and to the construction of confidence bands is investigated and compared with a direct method based on asymptotic means and variances. The technique of the bootstrap is to replace…

结合专家意见与生存数据的交互式个人电脑可靠性评估AI 解读

In this article I present a new approach for the analysis of life-length data that can be described by a Weibull distribution. The novel feature of my approach pertains to the incorporation of informed judgment or expert opinion into the analysis, using a personal computer in an interactive and user-friendly manner. This approach also provides for incorporating the analyst's opinions on the expertise of the experts. Many of the analyses result in graphical displays, making…

随机样本的双权预测区间AI 解读

This study takes a biweight approach to providing a prediction interval for a single future observation. This problem—equivalent to the problem of estimating quantiles—is of fundamental importance in ascertaining the nature of a process. The prediction or quantile problem is difficult for a robust estimator, since much of the desired information is in the extremes of the sample, whose influence the robust estimator is designed to resist. The situation is further complicated…

有限总体抽样中稳健估计的若干结果AI 解读

The present article examines the robustness of sampling strategies, that is, estimators and sample designs, from the point of view of attaining the minimum value of the Godambe—Joshi lower bound to the expected variance of a strategy. It is shown that asymptotic design unbiasedness is necessary but insufficient for robustness defined in the above sense. The concepts of weak and strong robustness of estimators, for given sampling strategies, are introduced. The article…

复杂调查数据的重采样推断AI 解读

Methods for standard errors and confidence intervals for nonlinear statistics —such as ratios, regression, and correlation coefficients—have been extensively studied for stratified multistage designs in which the clusters are sampled with replacement, in particular, the important special case of two sampled clusters per stratum. These methods include the customary linearization (or Taylor) method and resampling methods based on the jackknife and balanced repeated replication…

Pearson型拟合优度检验：单变量情形AI 解读

Chi-squared tests are proposed for testing goodness of fit when the data may or may not be subject to random censoring. Both the simple and compositive null hypotheses are considered. For the simple null hypothesis the resulting test statistic in the uncensored case differs from Pearson's statistic only in that the expected frequency for cell Aj is taken to be , where is the empirical distribution function, instead of n ∫ A j d F o ; this results in k df instead of the usual…

左截断和／或右删失数据的精确 Kolmogorov 型检验AI 解读

The tests proposed in this article are natural generalizations of the ordinary Kolmogorov—Smirnov one-sample tests based on the product-limit estimator. They can be used with left-truncated and/or right-censored data and, as the ordinary tests, they have the nice properties of being valid for any sample size and any underlying distribution specified by the null hypothesis. The acceptance region for the product-limit estimator consists of a Kolmogorov—Smirnov-type region that…

评估Cox比例风险模型拟合优度的图形方法AI 解读

Suggested here is a simple graphical method for studying the goodness of fit in Cox's regression model for survival data. The method is easy to use, as it does not require the estimation of alternative models and only involves quantities similar to those already appearing in the partial likelihood expression that is needed in the parameter estimation. The rationale behind the graphs is very intuitive: They make a direct comparison between observed and expected failure…

条件对数线性模型检验的功效函数AI 解读

In fitting a log-linear model to data, it is common to examine the P values associated with the conditional likelihood-ratio tests corresponding to a nested sequence of candidate log-linear models. For an appropriate Pitman sequence of models these test statistics are asymptotically independent and chi-squared in distribution. This article is an analytic study of the noncentrality parameters of these limiting distributions, pointing out factors that determine the powers of…

针对中心混合备择的同质性检验AI 解读

A test of homogeneity is derived for a general sampling model. The alternative hypothesis is a mixture over a parameter of the sampling model, centered at the null hypothesis. The test statistic is derived through a score test. Its functional form is independent of the particular mixing distribution. Suppose Yi (i = 1, …, n) are independent random variables with respective probability density (or mass) functions fi (yi ‖ λi). Under the null hypothesis, suppose all λ i…

摘要暂缺

两阶段抽样对 F 统计量的影响AI 解读

The assumption of iid observations that underlies many statistical procedures is called into question when analyzing complex survey data. The population structure—particularly the existence of clusters in two-stage samples that usually exhibit positive intracluster correlation—invalidates the independence assumption. Kish and Frankel (1974) investigated the impact of this fact on regression analysis by using the standard sample-survey-theory framework; Campbell (1977) and…

平衡模型中固定效应与方差分量的最优检验AI 解读

For any analysis-of-variance model with balanced data involving both fixed and random effects, uniformly most powerful unbiased (UMPU) and uniformly most powerful invariant unbiased (UMPIU) tests are derived for the significance of a fixed effect or a variance component, under the assumption of normality of random effects. The tests coincide with the usual F tests. Robustness of the UMPIU test against suitable deviations from normality is established.

模型预测与设计估计能够协调到何种程度？AI 解读

Two general linear model-based predictors, one of the expectation of a finite population total and one of that total itself, are compared with the design-based generalized regression estimator (GRE). First, the predictors are made to conform to the GRE by modifying the regression parameter estimators but retaining the same (optimal) inclusion probabilities. Second, the GRE is made to conform with each of the predictors in turn by modifying the inclusion probabilities but…

处理因变量极端值的替代变换AI 解读

Transformations that could be used to reduce the influence of extreme observations of dependent variables, which can assume either sign, on regression coefficient estimates are studied in this article. Two that seem reasonable on a priori grounds—the extended Box—Cox (BC) and the inverse hyperbolic sine (IHS)—are evaluated in detail. One feature is that the log-likelihood function for IHS is defined for zero values of the dependent variable, which is not true of BC. The…

缩小线性回归置信带宽度的方法AI 解读

When constructing a confidence band in the linear regression model, there have been various efforts made to reduce the width of the band. One of them is to change the shape of a confidence band. Another effort is to restrict the region of the independent variables. This article proposes another possibility to narrow down the width of a band, which is to change the curvature of the band. Following that a theorem is given to combine these devices. Numerical comparisons are…

自动选择的回归平滑参数距最优值有多远？AI 解读

We address the problem of smoothing parameter selection for nonparametric curve estimators in the specific context of kernel regression estimation. Call the “optimal bandwidth” the minimizer of the average squared error. We consider several automatically selected bandwidths that approximate the optimum. How far are the automatically selected bandwidths from the optimum? The answer is studied theoretically and through simulations. The theoretical results include a central…

存在不可忽略无应答的分类结果回归分析AI 解读

We develop a log-linear model for categorical response subject to nonignorable nonresponse. The paper differs from Fay (1986) in its focus on estimation and hypothesis testing in a regression setting, as opposed to imputation in a multivariate setting. We present several new results concerning the existence of solutions on the boundary of the parameter space and the construction of confidence intervals for estimates. We illustrate the method by estimating the proportion of…

两样本比较：t检验、秩和检验与对数秩检验的扩展AI 解读

I consider the problem of testing that two populations are identical with respect to the distribution of a continuous variable against the alternative that values tend to be larger in one population. I observe that the t, rank-sum, and log-rank tests are insensitive for a large class of alternatives that may be expected to occur commonly in practice, propose a criterion for identifying this problem in a particular data set, and propose corresponding extensions of the…