An alternative to model selection in ordinary regression

The weaknesses of established model selection procedures based on hypothesis testing and similar criteria are discussed and an alternative based on synthetic (composite) estimation is proposed. It is developed for the problem of prediction in ordinary regression and its properties are explored by simulations for the simple regression. Extensions to a general setting are described and an example with multiple regression is analysed. Arguments are presented against using a selected model for any inferences.     

A simple estimator for a shared frailty regression model

Summary. We propose a simple estimation procedure for a proportional hazards frailty regression model for clustered survival data in which the dependence is generated by a positive stable distribution. Inferences for the frailty parameter can be obtained by using output from Cox regression analyses. The computational burden is substantially less than that of the other approaches to estimation. The large sample behaviour of the estimator is studied and simulations show that the approximations are appropriate for use with realistic sample sizes. The methods are motivated by studies of familial associations in the natural history of diseases. Their practical utility is illustrated with sib pair data from Beaver Dam, Wisconsin.     

Sampling design proportional to order statistic of auxiliary variable

The sampling designs dependent on sample moments of auxiliary variables are well known. Lahiri (Bull Int Stat Inst 33:133–140, 1951) considered a sampling design proportionate to a sample mean of an auxiliary variable. Sing and Srivastava (Biometrika 67(1):205–209, 1980) proposed the sampling design proportionate to a sample variance while Wywiał (J Indian Stat Assoc 37:73–87, 1999) a sampling design proportionate to a sample generalized variance of auxiliary variables. Some other sampling designs dependent on moments of an auxiliary variable were considered e.g. in Wywiał (Some contributions to multivariate methods in, survey sampling. Katowice University of Economics, Katowice, 2003a); Stat Transit 4(5):779–798, 2000) where accuracy of some sampling strategies were compared, too.These sampling designs cannot be useful in the case when there are some censored observations of the auxiliary variable. Moreover, they can be much too sensitive to outliers observations. In these cases the sampling design proportionate to the order statistic of an auxiliary variable can be more useful. That is why such an unequal probability sampling design is proposed here. Its particular cases as well as its conditional version are considered, too. The sampling scheme implementing this sampling design is proposed. The inclusion probabilities of the first and second orders were evaluated. The well known Horvitz–Thompson estimator is taken into account. A ratio estimator dependent on an order statistic is constructed. It is similar to the well known ratio estimator based on the population and sample means. Moreover, it is an unbiased estimator of the population mean when the sample is drawn according to the proposed sampling design dependent on the appropriate order statistic.     

Shrinkage confidence intervals for the normal mean: Using a guess for greater efficiency

If the unknown mean of a univariate population is sufficiently close to the value of an initial guess then an appropriate shrinkage estimator has smaller average squared error than the sample mean. This principle has been known for some time, but it does not appear to have found extension to problems of interval estimation. The author presents valid two‐sided 95% and 99% “shrinkage” confidence intervals for the mean of a normal distribution. These intervals are narrower than the usual interval based on the Student distribution when the population mean lies in such an “effective interval.” A reduction of 20% in the mean width of the interval is possible when the population mean is sufficiently close to the value of the guess. The author also describes a modification to existing shrinkage point estimators of the general univariate mean that enables the effective interval to be enlarged.     

A bayesian estimator for the dependence function of a bivariate extreme‐value distribution

Any continuous bivariate distribution can be expressed in terms of its margins and a unique copula. In the case of extreme‐value distributions, the copula is characterized by a dependence function while each margin depends on three parameters. The authors propose a Bayesian approach for the simultaneous estimation of the dependence function and the parameters defining the margins. They describe a nonparametric model for the dependence function and a reversible jump Markov chain Monte Carlo algorithm for the computation of the Bayesian estimator. They show through simulations that their estimator has a smaller mean integrated squared error than classical nonparametric estimators, especially in small samples. They illustrate their approach on a hydrological data set.     

An empirical likelihood goodness-of-fit test for time series

Summary. Standard goodness-of-fit tests for a parametric regression model against a series of nonparametric alternatives are based on residuals arising from a fitted model. When a parametric regression model is compared with a nonparametric model, goodness-of-fit testing can be naturally approached by evaluating the likelihood of the parametric model within a nonparametric framework. We employ the empirical likelihood for an α -mixing process to formulate a test statistic that measures the goodness of fit of a parametric regression model. The technique is based on a comparison with kernel smoothing estimators. The empirical likelihood formulation of the test has two attractive features. One is its automatic consideration of the variation that is associated with the nonparametric fit due to empirical likelihood's ability to Studentize internally. The other is that the asymptotic distribution of the test statistic is free of unknown parameters, avoiding plug-in estimation. We apply the test to a discretized diffusion model which has recently been considered in financial market analysis.     

Estimation for Continuous Branching Processes

The maximum-likelihood estimator for the curved exponential family given by continuous branching processes with immigration is investigated. These processes originated from population biology but also model the dynamics of interest rates and development of the state of technology in economics. It is proved that in contrast to branching processes with discrete space and/or time the MLE gives a unified approach to the inference. In order to include singular subdomains of the parameter space we modify the MLE slightly. Consistency and asymptotic normality for the MLE are considered. Concerning the asymptotic theory of the experiments, all three properties LAQ, LAN, and LAMN occur for different submodels     

On the shrinkage of local linear curve estimators

Local linear curve estimators are typically constructed using a compactly supported kernel, which minimizes edge effects and (in the case of the Epanechnikov kernel) optimizes asymptotic performance in a mean square sense. The use of compactly supported kernels can produce numerical problems, however. A common remedy is ridging, which may be viewed as shrinkage of the local linear estimator towards the origin. In this paper we propose a general form of shrinkage, and suggest that, in practice, shrinkage be towards a proper curve estimator. For the latter we propose a local linear estimator based on an infinitely supported kernel. This approach is resistant against selection of too large a shrinkage parameter, which can impair performance when shrinkage is towards the origin. It also removes problems of numerical instability resulting from using a compactly supported kernel, and enjoys very good mean squared error properties.     

基于GRPLS 回归的 中国经济增长影响因素分析

构造一种新的方法———岭- 偏最小二乘回归方法(它既有效消除了因素变量之间的多 重共线性,又克服了传统方法的不足,且使模型更加稳健,具有更强的预测和分析能力) ;并运 用广义岭- 偏最小二乘回归方法分析了我国经济增长的影响因素,为我国制订持续、快速增长 的经济政策提供了有益的参考.     

Testing Inference in Inflated Beta Regressions under Model Misspecification

We consider testing inference in inflated beta regressions subject to model misspecification. In particular, quasi-z tests based on sandwich covariance matrix estimators are described and their finite sample behavior is investigated via Monte Carlo simulations. The numerical evidence shows that quasi-z testing inference can be considerably more accurate than inference made through the usual z tests, especially when there is model misspecification. Interval estimation is also considered. We also present an empirical application that uses real (not simulated) data.