Functional Modelling and Classification of Longitudinal Data*

Abstract. We review and extend some statistical tools that have proved useful for analysing functional data. Functional data analysis primarily is designed for the analysis of random trajectories and infinite‐dimensional data, and there exists a need for the development of adequate statistical estimation and inference techniques. While this field is in flux, some methods have proven useful. These include warping methods, functional principal component analysis, and conditioning under Gaussian assumptions for the case of sparse data. The latter is a recent development that may provide a bridge between functional and more classical longitudinal data analysis. Besides presenting a brief review of functional principal components and functional regression, we develop some concepts for estimating functional principal component scores in the sparse situation. An extension of the so‐called generalized functional linear model to the case of sparse longitudinal predictors is proposed. This extension includes functional binary regression models for longitudinal data and is illustrated with data on primary biliary cirrhosis.     

国内外高校后勤管理模式比较与分析

高校后勤管理是高校管理体制改革中的一个重要问题。文章介绍了德、英、法、美、日五国三种不同的高校后勤管理模式 ,并与我国高校后勤管理模式进行了比较与分析 ,以期对我国高校后勤社会化改革有所借鉴     

Asymptotic properties of the maximum-likelihood estimator for a class of birth-and-death processes admitting a unique stationary distribution

The asymptotic properties of the maximum-likelihood estimator of the parameter vector for a class of birth-and-death processes admitting a unique stationary distribution are studied. Also, it is shown that identifiability of the parameter vector with respect to the likelihood implies that the Fisher information matrix is of full rank. Two special cases of biological interest are presented. One of these, the exponential birth-and-death process, is proposed as a more appropriate model of density dependence than the logistic process.     

A STOCHASTIC LOGISTIC MODEL WITH TIME DELAY

The stochastic version of the logistic model for population growth is generalized to take account of continuously distributed time delay with an exponentially decaying kernel. The theory of diffusion processes is used to analyse the probability density function of the population size. The explicit expression for the stationary distribution is worked out and the effect of time delay on various statistics is discussed.     

失地农民城市融入水平及影响因素分析——基于武汉市的调查数据

农民失去土地之后,既有别于传统农民,又不同于城市居民,成为一个边缘群体。失地农民城市融入问题是城市化进程中亟需解决的重要问题。由经济状况、社会互动和心理认同三个一级维度和相应二级指标构成的指标体系衡量失地农民城市融入水平,并以武汉市失地农民为例进行实证分析。二元Logistic回归分析表明年龄、性别、受教育年限、是否愿意在城市生活的心理偏好、土地补偿标准、社会保障政策满意度等个体因素和政策因素共同影响失地农民城市融入水平。从经济、社会、心理多维度,从政府、社会和个体多主体出发,促进失地农民城市融入是今后努力方向。     

利率市场化条件下上市商业银行财务风险评价

选取上市商业银行2011~2013年的14个财务指标,首先运用因子分析法提取主因子,其次将提取的主因子进行聚类分析,改变传统的二分类,将财务风险划分为四类,最后通过寻找各类银行财务风险之间具有显著性差异的指标,并对这些指标提取主因子,采用多分类Logistic回归法构建一个上市商业银行财务风险评测模型,以期能有效地识别风险,实证结果表明,模型预测能力较好。     

New Folded Models for the Log-Transformed Norwegian Fire Claim Data

Folded distributions are useful models in statistics. However, not much is known beyond the folded normal distribution introduced in the 1960s. Here, we introduce several new folded distributions. Statistical properties of each distribution are derived. Applications are provided to the Norwegian fire claim data.     

A simple alternative to the likelihood ratio test in a logistic discrimination problem

We consider the problem of hypothesis-testing under a logistic model with two dichotomous independent variables. In particular, we consider the case in which the coefficients β₁, and β₂ of these variables are known on an a priori basis to not be of opposite sign. For this situation we show that there exists a simple nonparametric altenative to the likelihood ratio test for testing H₀: β₁ = β₂ = 0 VS.H₁ at least one β₁ = 0. We find the asympotic relative efficiency of this test and show that it exceeds 0.90 under a wide range of conditions. We also given an example.     

Nonparametric prediction analysis for binary data

A nonparametric inference algorithm developed by Davis and Geman (1983) is extended problem. The algorithm and applied to a medical prediction employs an estimation procedure for acquiring pairwise statistics among variables of a binary data set, allows for the data-driven creation of interaction terms among the variables, and employs a decision rule which asymptotically gives the minimum expected error. The inference procedure was designed for large data sets but has been extended via the method of cross-validation to encompass smaller data sets.     

Likelihood-based cross-validation score for selecting the smoothing parameter in maximum penalized likelihood estimation

Maximum penalized likelihood estimation is applied in non(semi)-para-metric regression problems, and enables us exploratory identification and diagnostics of nonlinear regression relationships. The smoothing parameter A controls trade-off between the smoothness and the goodness-of-fit of a function. The method of cross-validation is used for selecting A, but the generalized cross-validation, which is based on the squared error criterion, shows bad be¬havior in non-normal distribution and can not often select reasonable A. The purpose of this study is to propose a method which gives more suitable A and to evaluate the performance of it.

A method of simple calculation for the delete-one estimates in the likeli¬hood-based cross-validation (LCV) score is described. A score of similar form to the Akaike information criterion (AIC) is also derived. The proposed scores are compared with the ones of standard procedures by using data sets in liter¬atures. Simulations are performed to compare the patterns of selecting A and overall goodness-of-fit and to evaluate the effects of some factors. The LCV-scores by the simple calculation provide good approximation to the exact one if λ is not extremeiy smaii Furthermore the LCV scores by the simple size it possible to select X adaptively They have the effect, of reducing the bias of estimates and provide better performance in the sense of overall goodness-of fit. These scores are useful especially in the case of small sample size and in the case of binary logistic regression.