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捕获—再捕获实验的Poisson与多项式模型推断AI 解读

Capture-recapture models have been formulated both as Poisson and as multinomial distributions. Maximum likelihood estimates of parameters under the two models are compared. For parameters which do not involve the population size the asymptotic covariances are shown to be the same.

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含随机效应的广义线性模型估计AI 解读

A conceptually very simple but general algorithm for the estimation of the fixed effects, random effects, and components of dispersion in generalized linear models with random effects is proposed. Conditions are described under which the algorithm yields approximate maximum likelihood or quasi-maximum likelihood estimates of the fixed effects and dispersion components, and approximate empirical Bayes estimates of the random effects. The algorithm is applied to two data sets…

利用病例对照数据拟合前瞻性回归模型AI 解读

We consider fitting prospective regression models to data obtained by case-control or response selective sampling from a finite population with known population totals in each response category. Maximum likelihood estimation is developed and compared with two pseudo-likelihood approaches. The relative efficiencies of the methods are explored in the special case of estimating the parameters of the proportional odds model for ordinal responses. For such applications the method…

Numerical simulations recently reported in the literature have shown that the profile likelihood associated with the estimation of covariance range parameters for a Gaussian field can be multimodal. Here we complement these recent results by considering covari-ances with unknown nugget, scale and range parameters. Estimation is performed in a restricted maximum likelihood framework. For unbounded sampling domains and known range parameter, conditions ensuring asymptotic…

乘法随机效应的准似然分析AI 解读

A quasi-likelihood approach similar to that described by Morton (1987) is found to be particularly simple in the case of measurements subject to two or more sources of multiplicative error. Still further simplification occurs when the effects of interest also are multiplicative. The multiplicative analogue of the balanced ‘split plot’ model is considered in detail: an analysis of gamma deviance replaces the familiar analysis of variance. The efficiency of the…

长度偏倚数据的核密度估计AI 解读

A new kernel density estimator for length biased data which derives from smoothing the nonparametric maximum likelihood estimator is proposed and investigated. It has various advantages over an alternative method suggested by Bhattacharyya, Franklin & Richardson (1988): it is necessarily a probability density, it is particularly better behaved near zero, it has better asymptotic mean integrated squared error properties and it is more readily extendable to related problems…

Two approximate maximum likelihood estimates of the fractal dimension are suggested for random point patterns and planar curves, based on the distributions of the Palm probability and the spectrum.

泊松回归的样本量计算AI 解读

For the Poisson regression model, an exact expression for Fisher's information matrix, based upon the moment generating function of the distribution of covariates, is calculated. This parallels a similar, approximate, calculation by Whittemore (1981) for logistic regression. The resulting asymptotic variance of the maximum likelihood estimate of the parameters is used to calculate the sample size required to test hypotheses about the parameters at a specified significance…

若干纯生过程中最大似然估计的近似AI 解读

We present two simple approximations, one an extension of that given by Choi & Severo (1988), to the maximum likelihood estimate of a parameter λ in the class of birth processes in which the growth rate is the product of λ and some known function of the population size. The data are population sizes taken at a discrete set of time points. The Yule process is discussed in some detail.

基于删失距离的空间点过程强度估计AI 解读

The use of censoring in conjunction with distance-based estimation of the intensity of a spatial point process is considered. Censoring, in this context, may be motivated by practical considerations such as reduction of sampling effort, but it may also be considered as a method for preventing the overlap of search regions and for eliminating edge effects. Maximum likelihood estimators that utilize censored point-plant measurements or censored T-square measurements are…

无重复观测的超结构模型AI 解读

Dolby's (1976) ultrastructural model is investigated with emphasis on the case with no replications and one of the error variances known. It is shown that, in this situation, the maximum likelihood estimators are not consistent. The method of moments estimators are consistent and asymptotically normal and best in Fisher's sense within a broad class of asymptotically normal estimators discussed by Gleser (1983). Some connections with the errors-in-variables model are examined.

位置模型后验均值的一种表示AI 解读

An exact representation of the posterior mean is developed for a location model and the class of priors that are normal scale mixtures. The result makes use of the conditional distribution of the maximum likelihood estimator and Masreliez's theorem. Directions for future development are indicated.

In genetics, the term interclass correlation has been used to refer to the parent-offspring and son-daughter correlations within families. Under the assumption of variable family sizes and normality, we derive the asymptotic variance of the maximum likelihood estimator of the son-daughter interclass correlation.

混合效应模型初始估计的计算：一般矩方法AI 解读

Use of the maximum likelihood method for parameter estimation in a general mixed effects model requires initial estimates for all the model parameters. When the model is complicated, it may not be easy to obtain such estimates, especially estimates of the variances and covariances. A computational strategy is given for obtaining initial estimates. It is based on a general formulation of the method of moments for mixed effects models which allows the variances and covariances…

某些非参数极大似然估计量的大偏差概率AI 解读

Let $(X, \mathscr{A})$ be a measurable space and $\{P_{\vartheta,\tau}\mid\mathscr{A}: \vartheta \in \Theta, \tau \in T\}$ a family of probability measures. Given an appropriate estimator sequence for $\vartheta$, we define a sequence of asymptotic maximum likelihood estimators for $\tau$ and give bounds for its large deviation probabilities under conditions which are natural for the application to the estimation of mixing distributions. This paper generalizes earlier…

用于依赖删失的威布尔模型AI 解读

A bivariate Weibull model is proposed for censored survival data when there may be dependence between the survival and censoring random variables. The model is based on marginal transformations of the Pickands class of bivariate exponential distributions. Assuming the model to hold, the joint distribution of survival and censoring times is shown to be identifiable, and the maximum likelihood estimator of the parameters is shown to be consistent.

序贯设计实验后的估计AI 解读

We investigate the design of experiments for the nonparametric estimation of the root of an unknown regression function. Approaches to this problem include the Robbins-Monro (1951), Venter (1967), and Lai-Robbins (1979, 1981) stochastic approximation procedures and Wu's (1985, 1986) sequential maximum likelihood estimators. Because the regression function is not assumed to belong to a parametric family, only experimentation near to the root is informative and the sequential…

多元测量误差问题中获取真值的二阶段抽样AI 解读

Increasing attention is being given to measurement error models in which the dimension of the proxy or surrogate values is different from that of the missing true values. Even if they are of the same dimension, the error model may not be the simple additive one of observed = true + error, where the error has mean 0. The use of broader models relating true and observed values requires the use of external or internal data containing some true values to calibrate/validate the…

序贯设计实验后的估计AI 解读

We investigate the design of experiments for the nonparametric estimation of the root of an unknown regression function. Approaches to this problem include the Robbins-Monro (1951), Venter (1967), and Lai-Robbins (1979, 1981) stochastic approximation procedures and Wu's (1985, 1986) sequential maximum likelihood estimators. Because the regression function is not assumed to belong to a parametric family, only experimentation near to the root is informative and the sequential…

结构方程模型的多层分析AI 解读

This paper considers the multilevel analysis of structural equation models with unbal anced sampling designs. The analysis is based on the maximum likelihood and the generalized least squares approaches. Basic statistical results for inference such as the asymptotic distribution of the estimators, goodness-of-fit test statistics for the validity of the model and functional constraints are developed. Computationally, the applications of the scoring algorithm and the…

组序贯假设检验后的参数估计AI 解读

Parameter estimation techniques which fail to adjust for the interim analyses of group sequential test designs will introduce bias in much the same way that the repeated use of single sample hypothesis testing causes inflation of the type one statistical error rate. Methods based on the duality of hypothesis testing and interval estimation require definition of an ordering for the outcome space for the test statistic. In this paper, estimation following a group sequential…

危险率变点模型中似然比检验的一个问题AI 解读

A likelihood ratio test for constant hazard against a step change alternative has received considerable attention in recent years. Additional information in the maximum likelihood estimate of the change-point can seriously affect interpretation of test results. Some simple modifications are considered for which exact percentage points can be derived. Monte Carlo power and mean squared error comparisons are encouraging.

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