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渐近最小二乘估计的效率问题及应用AI 解读

Abstract This paper is concerned with the large sample efficiency of the asymptotic least‐squares (ALS) estimators introduced by Gouriéroux, Monfort, and Trognon (1982, 1985) and Chamberlain (1982, 1984). We show how the efficiency of these estimators is affected when additional information is incorporated into the estimation procedure. The relationship between ALS and maximum likelihood is discussed. It is shown that ALS can be used to obtain asymptotically efficient…

对数样条模型的大样本推断AI 解读

Let $f$ be a continuous and positive unknown density on a known compact interval $\mathscr{Y}$. Let $F$ denote the distribution function of $f$ and let $Q = F^{-1}$ denote its quantile function. A finite-parameter exponential family model based on $B$-splines is constructed. Maximum-likelihood estimation of the parameters of the model based on a random sample of size $n$ from $f$ yields estimates $\hat{f, F}$ and $\hat{Q}$ of $f, F$ and $Q$, respectively. Under mild…

随机截断模型与马尔可夫过程AI 解读

Random left truncation is modelled by the conditional distribution of the random variable $X$ of interest, given that it is larger than the truncating random variable $Y$; usually $X$ and $Y$ are assumed independent. The present paper is based on a simple reparametrization of the left truncation model as a three-state Markov process. The derivation of a nonparametric estimator is a distribution function under random truncation is then a special case of results on the…

最小对比估计量的密度AI 解读

Conditions for the existence of the density of a minimum contrast estimator in a parametric statistical family are given together with a formula for this density. The formula is exact if multiple local minima cannot occur; otherwise the formula is an exact expression for the point process of local minima of the contrast function. Although it is not in general feasible to compute the expression for the density, the formula can be used as a basis for further expansion of the…

过度离散泊松回归及其他拟似然模型中的假设检验AI 解读

Test statistics for evaluating the significance of added variables in a regression equation are developed for mixed Poisson models, where the structural parameter φ that determines the mean/variance relationship var(μ; φ) = μ + φ · μ 2 is estimated by the method of moments and the regression coefficients are estimated by quasi-likelihood. The formulas presented for test statistics and related estimating equations are applicable generally to quasi-likelihood models specified…

聚类抽样下多组二乘二列联表共同优势比估计的模拟研究AI 解读

This article presents the results of a simulation study of the estimation of a common odds ratio in multiple-contingency tables when the data are correlated within clusters. The correlation is modeled by the beta-binomial distribution. The three objectives of the study were to determine (a) the variances, biases, and relative efficiencies of the beta-binomial maximum likelihood estimator (MLE), the binomial MLE, and the Mantel-Haenszel estimator of the common odds ratio; (b)…

有序类别列联表的精确推断AI 解读

This article proposes an efficient numerical algorithm for small-sample exact inferences in contingency tables having ordinal classifications. The inferences, which apply conditional on the observed marginal totals, also provide an exact analysis for the log-linear model of linear-by-linear association for cell probabilities. An exact test of independence has a one-sided P value equal to the null probability that model-based maximum likelihood estimates of odds ratios are at…

小样本置信区间AI 解读

In this article we present a technique for constructing one- or two-sided confidence intervals, which are second-order correct in terms of coverage, for either parametric or nonparametric problems. The construction is valid in the presence of nuisance parameters. The situation we consider is this: there are p parameters and we want a confidence interval for some function of them, possibly one of the parameters itself. The p parameters are estimated by M-estimates, which…

高斯权重积分的计算及其在 Logistic-normal 模型中的应用AI 解读

Logistic-normal distributions and related functions arise in a variety of statistical applications of current interest, including binary measurement-error models and the analysis of teratogenicity experiments. Analytic intractability has led to the development of numerous approximations to the desired forms, often with consequences that have not been well studied. A method is developed to compute these forms to arbitrary accuracy, and comparative calculations are made that…

均值变化最大似然检验的渐近分布AI 解读

For the maximum likelihood tests for a change in the mean of independent random variables, it is proved that the limit distribution is a double exponential, i.e. Gumbel, distribution. Our results also explain why the maximum likelihood methods are very powerful on the tails.

基于似然的显著性检验的条件性质AI 解读

This paper considers the conditional properties of the unconditional significance tests based on standardized versions of the maximum likelihood estimate and the score statistic for the case of a simple null hypothesis and a one-parameter model. The properties of the tests are assessed by considering the conditional level of the test given the observed value of a statistic that is locally ancillary near the null model. It is shown that for the test based on the maximum…

定位伯努利变量序列中的变化区段AI 解读

The theory underlying inferences about a single change point in a sequence of independent Bernoulli variables is extended to the two change points problem where the distance between the two change points is known, namely a changed segment. Both null and nonnull distributions of the log likelihood ratio for testing the hypothesis that there is no changed segment against the alternative that there is one of specified length are derived using recurrence equations. The…

条件逻辑回归似然分析中的鞍点修正AI 解读

Barndorfi-Nielsen & Cox (1979) introduced the double saddlepoint approximation to the conditional likelihood function for a structural parameter vector given a sufficient statistic for a nuisance parameter vector. This approximation is considered in some detail for the case of multiple logistic regression models with polytomous outcome states. It is shown that the profile score with saddlepoint correction yields a simple derivation of an approximation to the mean of a…

利用估计得分进行假设检验AI 解读

A method is proposed for testing hypotheses that is very much in the spirit of expected maximum log likelihood estimation and bears much the same relation to it as the likelihood ratio test methodology does to maximum likelihood estimation. For a single test parameter, the method amounts to basing critical regions on the difference between the estimated score and its expectation. In some cases where a sufficient statistic, independent of the test parameter, exists for the…

广义线性回归的主成分估计AI 解读

The generalized linear model (Nelder & Wedderburn, 1972) has become an elegant and practical option to classical least-squares linear model building. We consider the specific problem of generalized linear regression utilizing a set of continuous explanatory variables to model an exponential family response. It is the objective of this paper to develop and present an asymptotically biased principal component parameter estimation technique, as an option to traditional maximum…

立方根渐近理论AI 解读

We establish a new functional central limit theorem for empirical processes indexed by classes of functions. In a neighborhood of a fixed parameter point, an $n^{-1/3}$ rescaling of the parameter is compensated for by an $n^{2/3}$ rescaling of the empirical measure, resulting in a limiting Gaussian process. By means of a modified continuous mapping theorem for the location of the maximizing value, we deduce limit theorems for several statistics defined by maximization or…

社会网络的伪似然估计AI 解读

Interest in log-linear modeling for social-network data has grown steadily since Holland and Leinhardt (1981) proposed their p 1 model. That model was designed for a single binary relationship (directed graph) representing interactions between individuals. It assumed that interactions between pairs of individuals are mutually independent. Subsequent work has extended the model in various ways, including block-modeling and the case of dependence between pairs of individuals.…

缺失数据下均值与协方差结构的伪最大似然估计AI 解读

A nonlinear mean- and covariance-structure model for one or more groups is constructed. The model subsumes the usual linear model considered in the literature. It is then shown how to estimate the parameters of the model and the asymptotic covariance matrix of the parameter estimates using pseudo-maximum likelihood (PML) estimation. The resulting estimates are strongly consistent under general regularity conditions, provided only that the model for the first two moments is…

数据依赖型治疗分配规则下的统计推断AI 解读

In comparing two treatments with dichotomous responses, the randomized play-the-winner rule (Wei and Durham 1978) tends to assign more study subjects to the better treatment. For ethical reasons, this property is desirable for studies on human subjects. The randomized play-the-winner rule, which is a modification of Zelen's play-the-winner rule (Zelen 1969), is not deterministic and is less vulnerable to experimental bias than other adaptive designs. Recently, this design…

比较两个二项比例的若干精确检验统计量的精确性质AI 解读

Using exact unconditional distributions, we evaluated the size and power of four exact test procedures and three versions of the χ2 statistic for the two-sample binomial problem in small-to-moderate sample sizes. The exact unconditional test (Suissa and Shuster 1985) and Fisher's (1935) exact test are the only tests whose size can be guaranteed never to exceed the nominal size. Though the former is distinctly more powerful, it is also computationally difficult. We propose an…

删失程度对置信区间有效性的影响AI 解读

This article examines how the level of censoring affects the validity of confidence intervals constructed from an exponential maximum likelihood estimator under departures from an assumed exponential survival distribution. The motivation for this work is a simulation study by Emerson (1981) suggesting that under Weibull departures from exponentiality, validity of confidence intervals for median survival time improves as censoring increases. To see if this result holds…

模块化非参数子生存估计AI 解读

This article describes new methods for estimating survival distributions based on nonparametric curve estimators. One approach improves the estimation of long-term survival rates. Simulation studies using Weibull and lognormal data show that even in the case found to be least favorable, the new method has less than one-seventh the prediction error of all conventional life-table (LT) or Kaplan–Meier (KM) estimators, even when the LT and KM techniques are optimized for the…

删失对置信区间有效性的影响AI 解读

This article examines how the level of censoring affects the validity of confidence intervals constructed from an exponential maximum likelihood estimator under departures from an assumed exponential survival distribution. The motivation for this work is a simulation study by Emerson (1981) suggesting that under Weibull departures from exponentiality, validity of confidence intervals for median survival time improves as censoring increases. To see if this result holds…

缺失数据下均值与协方差结构的伪极大似然估计AI 解读

A nonlinear mean- and covariance-structure model for one or more groups is constructed. The model subsumes the usual linear model considered in the literature. It is then shown how to estimate the parameters of the model and the asymptotic covariance matrix of the parameter estimates using pseudo-maximum likelihood (PML) estimation. The resulting estimates are strongly consistent under general regularity conditions, provided only that the model for the first two moments is…