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一阶自相关误差下线性回归估计量的效率比较AI 解读

This article compares several estimators for linear regression models with first-order autocorrelated errors. Asymptotic variances of the estimators of regression coefficients are obtained up to order T −2 for the maximum likelihood, the iterated Prais-Winsten, and the iterated Cochrane—Orcutt methods. It is shown that the first two methods are equivalent in efficiency and that the last is less efficient. This loss in efficiency is due to the effect of the initial…

检验误差：有限总体中整数参数的极大似然估计AI 解读

In a probability model for possible errors in the inspection of a finite lot containing defective items, it is shown how maximum likelihood estimation is affected by whether the sampling is carried out with or without replacement. These changes are examined by developing a method for simultaneous maximization over an integer and a scalar parameter. A new method for the bounding of the integer solution is introduced. The results show that the parameter estimates in the…

Markov 假设下面板数据的分析AI 解读

Methods for the analysis of panel data under a continuous-time Markov model are proposed. We present procedures for obtaining maximum likelihood estimates and associated asymptotic covariance matrices for transition intensity parameters in time homogeneous models, and for other process characteristics such as mean sojourn times and equilibrium distributions. Generalizations to handle covariance analysis and to the fitting of certain nonhomogeneous models are presented, and…

有效得分、方差分解与蒙特卡洛方差缩减AI 解读

Monte Carlo “swindles” or variance reduction techniques exploit the experimenter's knowledge of the stochastic structure governing the simulated data to construct more precise estimates of unknown parameters. Alternatively, one can reduce the number of replications (and thus the cost) needed to gain a desired level of precision. This article reviews the common case of swindles based on variance decompositions for estimating efficiencies and variances of location and…

多元伽马—泊松模型AI 解读

This article extends the multivariate gamma-Poisson model of repeated events, developed by Arbous and Kerrich (1951) and Bates and Neyman (1952), by (a) compounding it with a Dirichlet distribution in the analysis of cross-sectional data and by (b) allowing individual rates to shift at the start of the second period in the analysis of two-period longitudinal data. The first extension allows individuals to specialize in particular types of events. The model is shown to…

突变理论在生物科学统计建模中的应用AI 解读

Although catastrophe theory has been applied with mixed success to many problems in the biosciences, very few of these applications have used any form of statistical modeling. We present examples of the applications of statistical catastrophe theory in the analysis of experimental data. These include examples of hysteresis effects, bifurcation effects, and the full cusp catastrophe model. The methods of statistical catastrophe theory draw upon the theories of parameter…

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函数关系、随机系数与非线性回归：动力学数据应用AI 解读

List of Contents.- 1. An example from physiology.- 1.1 The experiment and the data.- 1.2 The model.- 2. The general linear model.- 2.1 Independent observations with the same variance.- 2.2 Correlated observations with known covariance matrix.- 2.3 Correlated observations with unknown covariance matrix.- 2.4 The general linear model with estimated weights.- 3. The linear functional relation.- 3.1 Introduction.- 3.2 The model and the estimates.- 3.3 Comments on the model.- 3.4…

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非参数逐步多重比较程序AI 解读

Nonparametric multiple comparisons are discussed, with particular emphasis given to stepwise procedures. Nonparametric analogs of the stepwise all-subset procedure of Einot and Gabriel are presented, along with an ad hoc nonparametric analog of the Newman—Keuls procedure. These new procedures are compared among themselves and with nonstepwise procedures based on Type I error levels and comparisonwise power. It is shown that these stepwise nonparametric procedures control…

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不连续分布下 Kolmogorov 型拟合优度检验的精确功效AI 解读

Goodness-of-fit tests of Kolmogorov type reject a null hypothesis H 0 : F(x) = F*(x) whenever the graph of the sample cumulative distribution function crosses one of two boundary functions, G 1(x), G 2(x). The best-known example of a test of this type is the Kolmogorov—Smirnov test D. When the true cumulative distribution function F(x) is continuous, a number of algorithms are available for calculating the exact powers of such tests. In this article it is shown that such…

谱估计的数据驱动选择：拓展交叉验证方法的适用范围AI 解读

I develop methods of objectively choosing a spectrum estimate from a general class C of available estimates. C can, for example, simultaneously include Blackman—Tukey and autoregressive estimates, so the statistician no longer needs to choose one type or the other arbitrarily. The methods work by extending the applicability of existing cross-validatory techniques through the introduction of generalized leave-out-one spectrum estimates. As special cases, I obtain new…

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稳健尺度估计量：长尾对称分布下的有限样本表现AI 解读

This article presents the results of a Monte Carlo study of the robustness of scale estimates in the presence of long-tailed, symmetric distributions. The article examines the performance of several families of estimates in samples of size 20 from several distributions. The family of A-estimators, finite sample approximations to the asymptotic variance of M-estimators of location, appears to be more robust than the sample standard deviation, the median absolute deviation…

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Gauss–Markov 模型下的实验合并AI 解读

Consider two experiments with homoscedastic models E(Yi ) = Xi θ + Zi ψ, V(Yi ) = σ2 Ini (i = 1, 2). The matrix gi = X'i (Ini — Zi (Z'iZi )Xi can be called the information matrix of linear estimable functions of θ for experiment i. The information matrix g for the combined data (Y 1, Y 2) may be similarly defined. A proof of g ⩾ g 1 + g 2 (⩾ in the sense of nonnegative definiteness) is given, and equality is interpreted. g = g 1 + g 2 if and only if all best linear unbiased…

回归函数的置信带AI 解读

A method for obtaining (conservative) confidence bands for regression functions in low dimensions is given. Of particular importance is the applicability of the method to nonparametric regression. Computations, examples, and comparisons indicate the effectiveness of the method.

稀疏多项分布的改进拟合优度统计量AI 解读

A new goodness-of-fit statistic for sparse multinomials is proposed. It is assumed that the null distribution exhibits smoothness. The test statistic is based on the maximum posterior estimator probability estimates of Simonoff (1983). Computer simulations are used to estimate the null distribution, significance levels, and the power function of the test. It is shown that power of the test is a great improvement over that of the standard tests if the alternative distribution…

利用增补辅助信息的回溯观测估计响应概率AI 解读

When augmented by suitable auxiliary information, retrospective data can identify response probabilities. The auxiliary information may take the form of data on marginal distributions or appropriate structural assumptions. When a combination of retrospective observation and auxiliary information suffices in principle to identify response probabilities, practical use of this fact requires that statistically sound and computationally tractable estimation methods be available.…

多元随机效应一般线性模型中经验贝叶斯估计量的均方误差性质AI 解读

Estimation of an individual's regression coefficients is considered in a multivariate general linear model, where it is assumed that the individual's coefficients β k are subject to both fixed effects and random effects over different individuals. The mean squared error matrix of a natural estimator of β k is derived for any individual k, in the general situation where all parameters of the model must be estimated, and is shown to be smaller than the mean squared error…

非线性预测理论与有限总体比例估计AI 解读

The prediction approach to finite population inference is developed for a general nonlinear model. An estimator of the finite population total and an estimator of its variance are derived, and the asymptotic properties of both are obtained when the random variables in the model are independent. The theory is applied to the problem of estimating the total number of units that have a specified characteristic. An empirical study is presented, which confirms that a nonlinear…

分层样本推断：非线性统计量三种方法的二阶分析AI 解读

For stratified samples and nonlinear statistics that can be expressed as functions of estimated totals, second-order asymptotic expansions of the linearization, jackknife, and balanced repeated-replication variance estimators are obtained. Based on these, comparisons are made in terms of their biases. Some higher order asymptotic equivalence results are also established. The special case of a combined ratio estimator is investigated in detail. Some results on bias reduction…