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Approximations to the Maximum Likelihood Estimate in Some Pure Birth Processes

若干纯生过程最大似然估计的近似

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.

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Censored Distance-Based Intensity Estimation of Spatial Point Processes

空间点过程的删失距离强度估计

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…

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Identification and Estimation of Dichotomous Latent Variables Models Using Panel Data

利用面板数据识别和估计二元潜变量模型

Identification conditions for binary choice errors-in-variables models are explored. Conditions for the consistency and asymptotic normality of the maximum likelihood estimators of binary choice models with unbounded explanatory variables are given. Two- or three-step estimators to simplify computation are also suggested.

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The Reliability of Ml Estimators of Systems of Demand Equations: Evidence from OECD Countries

需求方程系统最大似然估计量的可靠性:来自OECD国家的证据

In large demand systems, when the unknown error covariance matrix is approximated by its usual maximum likelihood estimator, the coefficient estimates are known to suffer from two problems: (1) the asymptotic standard errors severely understate the sampling variability of the estimates and (2) the efficiency of the maximum likelihood coefficient estimates is greatly impaired. In this paper, the author proposes an alternative estimator for the covariance matrix and evaluates…

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Simultaneous Estimation in Discrete Multivariate Exponential Families

离散多元指数族中的同时估计

Let $X$ have a discrete density of the form $f(x) = t(x)\xi(\theta)\theta^{x_1}_1 \cdots \theta^{x_p}_p$, where $t(x)$ is nonzero on some infinite subset of $Z^p$. Consider simultaneous estimation of the $\theta_i$ under the loss $\mathscr{L}_m(\theta, \delta) = \sum^p_{i = 1} \theta^{-m}_i(\theta_i - \delta_i)^2, m \geq 0$. For integers $m \geq 1$, estimators are found which improve on the maximum likelihood estimator or uniformly minimum variance unbiased estimator. The…

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Use of Nonnull Models for Rank Statistics in Bivariate, Two-Sample, and Analysis of Variance Problems

秩统计量非零假设模型在双变量、两样本与方差分析中的应用

A nonnull model for rank statistics based on Kendall's tau has received quite a bit of attention in the ranking literature lately. In this article, we analyze this model with an eye towards applying it to situations in which nonparametric statistics such as Kendall's tau, the Mann-Whitney/Wilcoxon U, the Jonckheere-Terpstra statistic, the Kruskal-Wallis statistic, and Friedman's statistic for randomized blocks designs are often used. The data for the basic model are a pair…

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Nonparametric Estimation from Cross-Sectional Survival Data

横截面生存数据的非参数估计

In many follow-up studies survival data are often observed according to a cross-sectional sampling scheme. Data of this type are subject to left truncation in addition to the usual right censoring. A number of characteristics and properties of the product-limit estimate, for left-truncated and right-censored data, have been explored and found to be similar to those of the Kaplan-Meier estimate. Under the stationarity assumption, however, it is believed that an alternative…

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A Nonparametric Method for Dealing with Mismeasured Covariate Data

处理协变量测量错误的非参数方法

Mismeasurement of covariate data is a frequent problem in statistical data analysis. However, when true and mismeasured data are obtained for a subsample of the observations, it is possible to estimate the parameters relating the outcome to the covariate of interest. Maximum likelihood methods that rely on parametric models for the mismeasurement have not met with much success. Realistic models for the mismeasurement process are difficult to construct; the form of the…

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Models for Contingency Tables with Known Margins when Target and Sampled Populations Differ

目标总体与抽样总体不同时的已知边际列联表模型

The analysis of two-way contingency tables with known margins is considered. Four methods for estimating the cell probabilities are compared, namely, raking (RAKE), maximum likelihood under random sampling (MLRS), minimum chi-squared (MCSQ), and least squares (LSQ). Assuming random sampling from the target population, these methods are known to be asymptotically equivalent, and small-sample studies have suggested that MCSQ is slightly better than the other methods in average…

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Review Papers: Recent Developments in Nonparametric Density Estimation

综述:非参数密度估计的近期发展

Advances in computation and the fast and cheap computational facilities now available to statisticians have had a significant impact upon statistical research, and especially the development of nonparametric data analysis procedures. In particular, theoretical and applied research on nonparametric density estimation has had a noticeable influence on related topics, such as nonparametric regression, nonparametric discrimination, and nonparametric pattern recognition. This…

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Semiparametric Estimation in the Rasch Model and Related Exponential Response Models, Including a Simple Latent Class Model for Item Analysis

Rasch及相关指数响应模型的半参数估计与潜类别分析

The Rasch model for item analysis is an important member of the class of exponential response models in which the number of nuisance parameters increases with the number of subjects, leading to the failure of the usual likelihood methodology. Both conditional-likelihood methods and mixture-model techniques have been used to circumvent these problems. In this article, we show that these seemingly unrelated analyses are in fact closely linked to each other, despite dramatic…

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Multiple Imputation of Industry and Occupation Codes in Census Public-use Samples Using Bayesian Logistic Regression

用贝叶斯逻辑回归多重插补人口普查行业与职业编码

We describe methods used to create a new Census data base that can be used to study comparability of industry and occupation classification systems. This project represents the most extensive application of multiple imputation to date, and the modeling effort was considerable as well—hundreds of logistic regressions were estimated. One goal of this article is to summarize the strategies used in the project so that researchers can better understand how the new data bases were…

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Use of Nonnull Models for Rank Statistics in Bivariate, Two-Sample, and Analysis of Variance Problems

二元、两样本及方差分析问题中秩统计量的非零假设模型

A nonnull model for rank statistics based on Kendall's tau has received quite a bit of attention in the ranking literature lately. In this article, we analyze this model with an eye towards applying it to situations in which nonparametric statistics such as Kendall's tau, the Mann-Whitney/Wilcoxon U, the Jonckheere-Terpstra statistic, the Kruskal-Wallis statistic, and Friedman's statistic for randomized blocks designs are often used. The data for the basic model are a pair…

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Recent Developments in Nonparametric Density Estimation

非参数密度估计的近期发展

Advances in computation and the fast and cheap computational facilities now available to statisticians have had a significant impact upon statistical research, and especially the development of nonparametric data analysis procedures. In particular, theoretical and applied research on nonparametric density estimation has had a noticeable influence on related topics, such as nonparametric regression, nonparametric discrimination, and nonparametric pattern recognition. This…

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The Asymptotic Variance of the Interclass Correlation Coefficient

类间相关系数的渐近方差

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.

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Optimal Inference in Cointegrated Systems

协整系统中的最优推断

Properties of maximum likelihood estimates of cointegrated systems are studied. Alternative formulations are considered, including a new triangular system error correction mechanism. We demonstrate that full system maximum likelihood brings the problem of inference within the family covered by the locally asymptotically mixed normal asymptotic theory, provided all unit roots have been eliminated by specification and data transformation. Methodological issues provide a major…

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Computing Extended Maximum Likelihood Estimates for Linear Parameter Models

线性参数模型中扩展最大似然估计的计算

SUMMARY Methods are given for computing extended maximum likelihood estimates in which one or more parameter estimates are infinite at the supremum of the likelihood. The results are given for a broad class of regression-like models based on independent observations with linearly related parameters including, in particular, the generalized linear models. The estimation consists of two steps: A linear programming step to identify the infinite components and a more…

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Error Model Diagnostics in the General Linear Model Relevant to the Analysis of Repeated Measurements and Field Experiments

一般线性模型的误差诊断:重复测量与田间试验

SUMMARY The large sample distribution of the recursive residual maximum likelihood residuals from the general linear model with dependent errors is derived. Further results are obtained from this distribution to aid the identification of an appropriate error model in the general linear model.

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Procrustes Methods in the Statistical Analysis of Shape

形状统计分析中的 Procrustes 方法

SUMMARY Two geometrical figures, X and Y, in RK, each consisting of N landmark points, have the same shape if they differ by at most a rotation, a translation and isotropic scaling. This paper presents a model-based Procrustes approach to analysing sets of shapes. With few exceptions, the metric geometry of shape spaces is quite complicated. We develop a basic understanding through the familiar QR and singular value decompositions of multivariate analysis. The strategy…

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Some New Estimators for Small-Area Means With Application to the Assessment of Farmland Values

Regression models that account for main state effects and nested county effects are considered for the assessment of farmland values. Empirical predictors obtained by replacing the unknown variances in the formula of the optimal predictors by maximum likelihood estimates are presented. The computations are carried out by simple iterations between two SAS procedures. Estimators for the prediction variances are derived, and a modification to secure the robustness of the…

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A Quasi-Bayesian Approach to Estimating Parameters for Mixtures of Normal Distributions

正态混合分布参数估计的拟贝叶斯方法

This article proposes a very tractable approach to estimating parameters for mixtures of normal distributions. The analyst proceeds as if, in addition to the data, he or she had observed some pseudo data points drawn from each distribution whose values reflect his or her priors. The approach eliminates the singularities associated with maximum likelihood estimation and offer guidance for choosing among alternative local maximum likelihood estimates. Monte Carlo analysis…

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A Monte Carlo Analysis of Alternative Estimators in Models Involving Selectivity

含选择性模型中替代估计量的蒙特卡洛分析

In a simultaneous-equation model involving selectivity, Monte Carlo and response-surface techniques are used to assess the performance of five estimators commonly applied to a behavioral equation conditioned on an endogenous binary selectivity decision. The estimators include least squares with an exogenous dummy variable for the selectivity decision, three two-stage estimators that employ the estimated probability of the selectivity decision, and full information maximum…

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A note on Seber's model for ring-recovery data

关于环志回收数据Seber模型的一则说明

We provide simple explicit maximum-likelihood estimates for Seber's (1971) model for ring-recovery data, obtaining both the general solution, and the particular estimate satisfying Seber's constraint.

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