Four tests of fit for the beta-binomial distribution

Tests based on the Anderson–Darling statistic, a third moment statistic and the classical Pearson–Fisher X ² statistic, along with its third-order component, are considered. A small critical value and power study are given. Some examples illustrate important applications.     

The asymptotic distribution of a pivotal quantity for a capture-recapture model

A pivotal quantity for a capture-recapture model is introduced and used to construct an asymptotic confidence region for (ε,N), where ε is the capture efficiency and N is the population size. The true confidence levels of certain regions are obtained by simulation. Certain confidence regions for (ε,N) are drawn to show the size of the regions and to show how confidence limits for N depend on ε.     

Multiplicative-interaction logit models for i×j×2 three-way tables

Multiplicative-interaction (M-I) logit models are proposed for three-way IxJx2 contingency tables where the third variable constitutes a binary response. Models are derived by assigning unknown scores to the categories and forming product interactions from them. Asymptotic results under special sampling constraints are derived for maximum likelihood estimates and the goodness-of-fit statistics. The class of models proposed in this paper are found to be useful when no obvious scores are available. An example is included.     

MULTIPLE-RECORD SYSTEMS ESTIMATION USING LATENT CLASS MODELS

Capture–recapture methods (also referred to as 'multiple-record systems') have been widely used in enumerating human populations in the fields of epidemiology and public health. In this article, we introduce latent class models into multiple-record systems to account for unobserved heterogeneity in the population. Two approaches, the full and the conditional likelihood, are proposed to estimate the unknown population abundance. We also suggest rules to diagnose identifiability of the proposed latent class models. The methodologies are illustrated by two real examples: the first is to count the undercount of homelessness in the Adelaide central business district, and the second concerns the incidence of diabetes in a small Italian town.     

我国现阶段农民养老意愿探讨——基于福建省永安、邵武、光泽三县(市)抽样调查的实证研究

以抽样调查数据为基础,利用MNL模型对我国东南部地区农民的养老意愿进行的研究发现,年龄、性别、受教育程度、职业状态等个体特征对农民养老意愿存在显著影响;各家庭特征对农民养老意愿的影响并不明显;不同地区的农民养老意愿存在较大差异。     

Bayesian palaeoclimate reconstruction

Summary.  We consider the problem of reconstructing prehistoric climates by using fossil data that have been extracted from lake sediment cores. Such reconstructions promise to provide one of the few ways to validate modern models of climate change. A hierarchical Bayesian modelling approach is presented and its use, inversely, is demonstrated in a relatively small but statistically challenging exercise: the reconstruction of prehistoric climate at Glendalough in Ireland from fossil pollen. This computationally intensive method extends current approaches by explicitly modelling uncertainty and reconstructing entire climate histories. The statistical issues that are raised relate to the use of compositional data (pollen) with covariates (climate) which are available at many modern sites but are missing for the fossil data. The compositional data arise as mixtures and the missing covariates have a temporal structure. Novel aspects of the analysis include a spatial process model for compositional data, local modelling of lattice data, the use, as a prior, of a random walk with long-tailed increments, a two-stage implementation of the Markov chain Monte Carlo approach and a fast approximate procedure for cross-validation in inverse problems. We present some details, contrasting its reconstructions with those which have been generated by a method in use in the palaeoclimatology literature. We suggest that the method provides a basis for resolving important challenging issues in palaeoclimate research. We draw attention to several challenging statistical issues that need to be overcome.     

Why a time effect often has a limited impact on capture‐recapture estimates in closed populations

The author is concerned with log‐linear estimators of the size N of a population in a capture‐recapture experiment featuring heterogeneity in the individual capture probabilities and a time effect. He also considers models where the first capture influences the probability of subsequent captures. He derives several results from a new inequality associated with a dispersive ordering for discrete random variables. He shows that in a log‐linear model with inter‐individual heterogeneity, the estimator N is an increasing function of the heterogeneity parameter. He also shows that the inclusion of a time effect in the capture probabilities decreases N in models without heterogeneity. He further argues that a model featuring heterogeneity can accommodate a time effect through a small change in the heterogeneity parameter. He demonstrates these results using an inequality for the estimators of the heterogeneity parameters and illustrates them in a Monte Carlo experiment     

ESTIMATION OF DISCRETE CHOICE MODELS WITH MINIMAL VARIATION OF ALTERNATIVE-SPECIFIC VARIABLES

The paper states conditions for minimal variation within the explanatory variables such that the maximum likelihood estimate of the coefficient vector in the discrete choice logit model is unique. Special emphasis is given to the case that (almost) all individuals observe the same set of alternative-specific explanatory variables. The aspect of 'experimental design' in discrete choice models is discussed.     

EXPONENTIAL DISPERSION MODELS AND THE GAUSS-NEWTON ALGORITHM

It is known that the Fisher scoring iteration for generalized linear models has the same form as the Gauss-Newton algorithm for normal regression. This note shows that exponential dispersion models are the most general families to preserve this form for the scoring iteration. Therefore exponential dispersion models are the most general extension of generalized linear models for which the analogy with normal regression is preserved. The multinomial distribution is used as an example.     

自然数方幂和的包含Bernoulli数的精确表示式

证明自然数方幂和可以用多项式表示，并用两种方法给出其系数的包含Ｂｅｒｎｏｕｌｌｉ数的几种精确表示式。