Prediction of long memory processes on same-realisation

For the class of stationary Gaussian long memory processes, we study some properties of the least-squares predictor of _Xn+1$X_{n+1}$ based on (_Xn,…,_X1)$(X_n,\dots ,X_1)$. The predictor is obtained by projecting _Xn+1$X_{n+1}$ onto the finite past and the coefficients of the predictor are estimated on the same realisation. First we prove moment bounds for the inverse of the empirical covariance matrix. Then we deduce an asymptotic expression of the mean-squared error. In particular we give a relation between the number of terms used to estimate the coefficients and the number of past terms used for prediction, which ensures the L²$L^2$- sense convergence of the predictor. Finally we prove a central limit theorem when our predictor converges to the best linear predictor based on all the past.     

基于MixedLogit模型的道路交通统计生命价值评价研究

道路交通统计生命价值是道路交通安全项目经济评价的重要指标。运用意愿选择法和正交试验法设计了出行路径选择的调查问卷。假定时间、死亡风险为常数,费用服从对数正态分布,建立了基于Mixed Logit模型的统计生命价值评价模型。以大连市私家车出行者为调查对象获得调查数据,利用Monte Carlo方法并借助GAUSS软件对模型进行了150次仿真实验。研究表明：模型各参数的估计值具有较强集中性,t检验值具有较强显著性,模型优度比较高。统计生命价值服从参数为0．922和0．814的对数正态分布,其数学期望是35万元,可以作为道路交通安全项目经济评价的参考数据。     

Heterogeneity's Ruses: Some Surprising Effects of Selection on Population Dynamics

As a cohort of people, animals, or machines ages, the individuals at highest risk tend to die or exit first. This differential selection can produce patterns of mortality for the population as a whole that are surprisingly different from the patterns for subpopulations or individuals. Naive acceptance of observed population patterns may lead to erroneous policy recommendations if an intervention depends on the response of individuals. Furthermore, because patterns at the individual level may be simpler than composite population patterns, both theoretical and empirical research may be unnecessarily complicated by failure to recognize the effects of heterogeneity.     

Some Notes on Refereeing

Analysis of longitudinal data using a general linear mixed model requires the specification of a form for the covariance matrix of within-subject observations. Graphical diagnostics, such as the scatterplot matrix, can be of substantial help in making this specification. I introduce another graphical diagnostic, the Partial-Regression-on-Intervenors Scatterplot Matrix (PRISM), which complements the ordinary scatterplot matrix and which is more useful for identifying certain kinds of correlation structures. PRISMs corresponding to several commonly used correlation structures are displayed. The PRISM's usefulness in model specification is illustrated with an example of longitudinal data from a 100-kilometer road race.     

Inference Problems in the Analysis of the Relationship Between Alcohol Consumption and Coronary Heart Disease

Results concerning the dependence of life durations on alcohol use of individuals who die of coronary heart disease are brought into question when no account is taken of the mortality risks associated with other competing diseases. Procedures which restrict the analysis of coronary heart disease to respondents who die of this disease will produce biased estimates of the parameters of interest. Other dimensions of coronary heart disease are neglected by focusing on durations of life and well-constructed sample surveys can provide important new information on how alcohol consumption affects the risks of getting coronary heart disease.     

A Discrete Distribution Arising as a Solution of a Linear Difference Equation: Extension of the Non Central Negative Binomial Distribution

This article considers a discrete distribution that arises as the dominant solution of a linear difference equation. Basic properties and various chance mechanisms that lead to this distribution are given. In particular, its formulation as a weighted distribution and a mixed Poisson process are proposed. Parameter estimation by (a) using a combination of observed frequencies and moments and (b) maximum likelihood are examined. An example of goodness of fit is considered.     

A Stochastic Restricted Two-Parameter Estimator in Linear Regression Model

Özkale and Kaciranlar (2007 Özakle , M. R. , Kaciranlar , S. ( 2007 ). The restricted and unrestricted two-parameter estimators . Commun. Statist. Theor. Meth. 36 : 2707 – 2725 . [Google Scholar]) proposed a two-parameter estimator (TPE) for the unknown parameter vector in linear regression when exact restrictions are assumed to hold. In this article, under the assumption that the errors are not independent and identically distributed, we introduce a new estimator by combining the ideas underlying the mixed estimator (ME) and the two-parameter estimator when stochastic linear restrictions are assumed to hold. The new estimator is called the stochastic restricted two-parameter estimator (SRTPE) and necessary and sufficient conditions for the superiority of the SRTPE over the ME and TPE are derived by the mean squared error matrix (MSEM) criterion. Furthermore, selection of the biasing parameters is discussed and a numerical example is given to illustrate some of the theoretical results.     

On Quadratic Forms of Multivariate t Distribution with Applications

This note mainly aims to illustrate that some quadratic problems are robust in a sense with respect to the probabilistic distributions involved. The secondary moments of the quadratic forms of a multivariate t distribution are calculated. Then, the resulting formulae are applied to the quadratic problems of quadratic sufficiency and quadratic prediction. It is shown by revisiting the two problems that the same conclusions hold when the multivariate normal distribution is replaced with a multivariate t distribution.