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正态模型能够容忍多大程度的 t 分布偏离AI 解读

Suppose that the normal model is used for data Y 1,…, Y n, but that the true distribution is a t distribution with location and scale parameters ζ and σ and m degrees of freedom. The normal model corresponds to m = ∞. Using a local asymptotic framework where m is allowed to increase with n, two classes of estimands are identified. One small class, which in particular contains the functions of ζ alone, is affected by t-ness only to the second order, and maximum likelihood…

多元分类响应的联合分布与边际分布同步建模AI 解读

We discuss model-fitting methods for analyzing simultaneously the joint and marginal distributions of multivariate categorical responses. The models are members of a broad class of generalized logit and loglinear models. We fit them by improving a maximum likelihood algorithm that uses Lagrange's method of undetermined multipliers and a Newton-Raphson iterative scheme. We also discuss goodness-of-fit tests and adjusted residuals, and give asymptotic distributions of model…

仅少数成分相关时的预测方法比较AI 解读

We consider prediction in a multiple regression model where we also look on the explanatory variables as random. If the number of explanatory variables is large, then the common least squares multiple regression solution may not be the best one. We give a methodology for comparing certain alternative prediction methods by asymptotic calculations and perform such a comparisons for four specific methods. The results indicate that none of these methods dominates the others, and…

基于排序集样本的非参数最大似然估计AI 解读

A ranked set sample consists entirely of independently distributed order statistics and can occur naturally in many experimental settings, including problems in reliability. When each ranked set from which an order statistic is drawn is of the same size, and when the statistic of each fixed order is sampled the same number of times, the ranked set sample is said to be balanced. Stokes and Sager have shown that the edf F n of a balanced ranked set sample from the cdf F is an…

半参数模型中的拟似然估计AI 解读

Suppose the expected value of a response variable Y may be written h(Xβ +γ(T)) where X and T are covariates, each of which may be vector-valued, β is an unknown parameter vector, γ is an unknown smooth function, and h is a known function. In this article, we outline a method for estimating the parameter β, γ of this type of semiparametric model using a quasi-likelihood function. Algorithms for computing the estimates are given and the asymptotic distribution theory for the…

内陆水体限制性营养关系的统计模型AI 解读

The ecological theory of limiting factors holds that the observed level of response in a biological process will be governed by the input factor in least supply—the limiting factor. This theory has formed the basis for numerous attempts by aquatic ecologists to describe the relation between the biological productivity of inland waters and the availability of plant nutrients required for algal growth. Regression analysis has been the primary statistical tool used in the…

皮特曼接近性度量：统计估计量的比较AI 解读

Preface Part I. Introduction 1. Evolution of Estimation Theory Least Squares Method of Moments Maximum Likelihood Uniformly Minimum Variance Unbiased Estimation Biased Estimation Bayes and Empirical Bayes Influence Functions and Resampling Techniques Future Directions 2. PMC Comes of Age PMC: A Product of Controversy PMC as an Intuitive Criterion 3. The Scope of the Book History, Motivation, and Controversy of PMC A Unified Development of PMC Part II. Development of Pitman's…

重捕研究中鞅方法的效率AI 解读

The asymptotic variances of various estimators of the population size from a recapture study are calculated. The estimation methods compared are maximum likelihood and a class of natural martingale estimators with both time variation and behavioural response. It is found that (i) the martingale methods appropriate for time variation or behavioural response are fully efficient, (ii) there is no loss of efficiency at all in allowing for time variation, (iii) there is large…

离散选择的近似广义极值模型AI 解读

Estimation of generalized extreme value (GEV) models of discrete choice is hampered by computational complexity and convergence problems. However, the much simpler estimation routine for multinomial logit can be applied in a two-step procedure so as to test the null hypothesis of multinomial logit against any particular GEV model as an alternative hypothesis. The procedure also produces an approximate estimate of the GEV model. Monte Carlo data, generated alternatively by…

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GLM 用于设定检验的局限：对 Gurmu 与 Trivedi 的评论AI 解读

In this comment on Gurmu and Trivedi's “Variable Augmentation Specification Tests in the Linear Exponential Family,” I show how their generalized linear model (GLM) approach relates to other work in econometrics on specification testing in the linear exponential family. In addition to shedding light on the relationship between the statistics and econometrics literatures on testing in quasi-likelihood frameworks, this comparison reveals some important limitations of GLM as a…

基于核方法的参数密度拟合优度检验AI 解读

Let F denote a distribution function defined on the probability space (Ω, , P ), which is absolutely continuous with respect to the Lebesgue measure in R d with probability density function f . Let f 0 (·,β) be a parametric density function that depends on an unknown p × 1 vector β. In this paper, we consider tests of the goodness-of-fit of f 0 (·,β) for f (·) for some β based on (i) the integrated squared difference between a kernel estimate of f (·) and the quasimaximum…

工具变量估计量分布的替代近似AI 解读

This paper considers the instrument variable and method-of-moments estimators, as generalizations of two-stage least squares and limited information maximum likelihood, of the coefficients of a single equation. Motivated by a simple principle, asymptotic distributions are derived based on a parameter sequence where both the number of instruments and the sample size increase. The approximations to the distributions provided by this sequence are more accurate than traditional…

动态离散选择模型的模拟估计量AI 解读

This paper analyses a new estimator for the structural parameters of dynamic models of discrete choice. Based on an inversion theorem due to Hotz and Miller (1993), which establishes the existence of a one-to-one mapping between the conditional valuation functions for the dynamic problem and their associated conditional choice probabilities, we exploit simulation techniques to estimate models which do not possess terminal states. In this way our Conditional Choice Simulation…

发展中国家外债危机的模拟估计分析AI 解读

Abstract In this paper we develop models of the incidence and extent of external financing crises of developing countries, which lead to multiperiod multinomial discrete choice and discrete/continuous econometric specifications with flexible correlation structures in the unobservables. We show that estimation of these models based on simulation methods has attractive statistical properties and is computationally tractable. Three such simulation estimation methods are…

分组生存数据边际似然的最大化AI 解读

Grouped failure time data occur in studies where subjects are monitored periodically to determine whether failure has occurred in the intervening interval. Here the model under consideration is Cox's (1972, 1975) proportional hazards model, but the commonly used method of partial likelihood needs modification with grouped data due to a potentially large number of ties. This paper demonstrates how the Monte Carlo em algorithm (Wei & Tanner, 1990) can be used on grouped data…

电子显微镜放射自显影中基于 EM 的最大似然估计AI 解读

In this paper we describe a new method for the analysis of electron microscope auto-radiographs. It uses a Poisson model to describe the autoradiographic grain distribution, and the method of maximum likelihood to estimate the radioactive intensities. An iterative procedure is derived from the EM algorithm to produce maximum likelihood estimates. The procedure leads to simple iterative calculations and a complete treatment of edge effects. The resulting method of analysis…

基于估计方程的人类家系遗传分离分析AI 解读

Studies in genetic epidemiology are generally required to collect phenotypes on subjects from human pedigrees that consist of blood relatives and their spouses. One of the main objectives in analyzing pedigree data is to study the segregation of underlying genes that may predispose certain phenotypes and thus cause phenotypic aggregation within pedigrees. Most classical segregation methods are maximum likelihood-based under highly specified distributional assumptions for…

随机向量差分方程渐近性质的一则札记AI 解读

This note analyses a necessary condition for asymptotic normality of the maximum likelihood estimator in a stationary stochastic vector difference equation. It is shown that this condition is satisfied if the error variance matrix is positive definite.

非正则回归AI 解读

In an earlier paper, the author has studied asymptotic properties of maximum likelihood estimates for a class of nonregular models in which the range of the distribution depends on unknown parameters. Examples include Weibull and extreme value distributions. The present paper is concerned with the extension of this theory to the case when covariates are present. The proposed solution involves solving a linear programming problem for the regression parameters, followed by…

移动平均模型的一种简单非迭代估计量AI 解读

We examine a simple noniterative estimator for the parameters of a general moving average process. This non-maximum-likelihood estimator derives moving average model parameters directly from the coefficients of an approximating autoregressive model. The estimator is evaluated through asymptotic expansions and by simulation, and is also compared with maximum likelihood and the related estimator of Durbin (1959). The comparison with maximum likelihood by simulation suggests a…

多元函数估计中的多项式样条及其张量积AI 解读

Let $X_1, \ldots, X_M, Y_1,\ldots, Y_N$ be random variables, and set $\mathbf{X} = (X_1, \ldots, X_M)$ and $\mathbf{Y} = (Y_1, \ldots, Y_N)$. Let $\varphi$ be the regression or logistic or Poisson regression function of $\mathbf{Y}$ on $\mathbf{X}(N = 1)$ or the logarithm of the density function of $\mathbf{Y}$ or the conditional density function of $\mathbf{Y}$ on $\mathbf{X}$. Consider the approximation $\varphi^\ast$ to $\varphi$ having a suitably defined form involving a…

序约束下的置信区间估计AI 解读

This article deals with the construction of confidence intervals when the components of the location parameter $\mu$ of the random variable $\mathbf{X}$, which is elliptically symmetrically distributed, are subject to order restrictions. Several domination results are proved by studying the derivative of the coverage probability of the confidence intervals centered at the improved point estimators. Consequently, we strengthen the previously known results regarding the simple…

具有空间相关误差的回归模型AI 解读

In this article we consider regression models for two-dimensional spatial data when the errors follow a spatial unilateral first-order autoregressive moving average (ARMA) model studied by Basu and Reinsel. We give details on the convenient computation of the generalized least squares (GLS) estimator of the regression parameters in the presence of spatially correlated errors, and compare the GLS estimator to the ordinary least squares (OLS) estimator in some special cases.…