Approximate regression models and splines

The literature pertaining to splines in regression analysis is reviewed. Spline regression is motivated as a simple extension of the basic polynomial regression model. Using this framework, the concepts of fixed and variable knot spline regression are developed and corresponding inferential procedures are considered. Smoothing splines are also seen to be an extension of polynomial regression and various optimality properties, as well as inferential and diagnostic methods, for these types of splines are discussed.     

Predicting random effects with an expanded finite population mixed model

Prediction of random effects is an important problem with expanding applications. In the simplest context, the problem corresponds to prediction of the latent value (the mean) of a realized cluster selected via two-stage sampling. Recently, Stanek and Singer [Predicting random effects from finite population clustered samples with response error. J. Amer. Statist. Assoc. 99, 119–130] developed best linear unbiased predictors (BLUP) under a finite population mixed model that outperform BLUPs from mixed models and superpopulation models. Their setup, however, does not allow for unequally sized clusters. To overcome this drawback, we consider an expanded finite population mixed model based on a larger set of random variables that span a higher dimensional space than those typically applied to such problems. We show that BLUPs for linear combinations of the realized cluster means derived under such a model have considerably smaller mean squared error (MSE) than those obtained from mixed models, superpopulation models, and finite population mixed models. We motivate our general approach by an example developed for two-stage cluster sampling and show that it faithfully captures the stochastic aspects of sampling in the problem. We also consider simulation studies to illustrate the increased accuracy of the BLUP obtained under the expanded finite population mixed model.     

On Measuring Uncertainty of Benchmarked Predictors with Application to Disease Risk Estimate

Empirical Bayes (EB) estimates in general linear mixed models are useful for the small area estimation in the sense of increasing precision of estimation of small area means. However, one potential difficulty of EB is that the overall estimate for a larger geographical area based on a (weighted) sum of EB estimates is not necessarily identical to the corresponding direct estimate such as the overall sample mean. Another difficulty is that EB estimates yield over‐shrinking, which results in the sampling variance smaller than the posterior variance. One way to fix these problems is the benchmarking approach based on the constrained empirical Bayes (CEB) estimators, which satisfy the constraints that the aggregated mean and variance are identical to the requested values of mean and variance. In this paper, we treat the general mixed models, derive asymptotic approximations of the mean squared error (MSE) of CEB and provide second‐order unbiased estimators of MSE based on the parametric bootstrap method. These results are applied to natural exponential families with quadratic variance functions. As a specific example, the Poisson‐gamma model is dealt with, and it is illustrated that the CEB estimates and their MSE estimates work well through real mortality data.     

斯密国际贸易理论的动态分析

斯密从国民经济发展的角度探讨国际贸易及其与经济发展的互动关系;其国际贸易理论具有动态分析的特点。他在其著作《国富论》中表达了比较优势的基本思想,强调“后来获得的”要素及运输成本对一国优势地位和对外贸易的影响,认为不发达的农业国可通过学习和采用先进的生产技术获得优势,主张按具体情况对不同产品实行关税政策和渐进式的自由贸易政策。     

A NOTE ON COMPETING VARIANCE ESTIMATORS IN RANDOMISED RESPONSE SURVEYS

When gathering randomised rather than direct responses on a variable of interest relating to sensitive issues, one may use a modified version of the well-known generalised regression predictor of a finite population total. To construct confidence intervals, this paper proposes four alternative variance estimators – modifications to those usable with direct responses – and examines their relative efficiencies through simulations from simple super-population models.     

重温亚当·斯密:对中国经济学未来发展的思考

本文主要通过重温亚当·斯密的学说,提出关于中国经济学未来发展的四点思考:首先,中国经济学应该是伦理的经济学;其次,中国经济学应该是社会科学和历史的科学;再次,中国经济学应该是具有想象力的思维科学,唯有这样,中国经济学才能摆脱落后的、始终追随西方经济学而很少有自己学说创新的贫乏、滞后状态,才能在不远的将来产生出获诺贝尔经济学奖的中国经济学家,这是现实和时代的迫切要求;最后,中国经济学应该是和谐有序的市场经济的科学。     

Classic 1960s articles in educational evaluation

The primary thrust of the interest in educational evaluation which persists today began with the passage of the Elementary and Secondary Education Act of 1965. A study of journal citations was used to identify which of the early 1960s writings have continued to influence evaluation thought in education throughout the 1970s. Five classic articles were identified and reasons for their continued influence are suggested.