A comment on “A theoretical basis for perturbation methods” by Krishnamurty Muralidhar and Rathindra Sarathy

Statistics and Computing -     

“三农”问题的多角度观察与系统性解决

一、“三农”问题的由来“三农”问题的表象是延续数千年历史的小农经济、家庭式生产。2004年末,全国13亿人口中仍有7.57亿乡村人口守在不到20亿亩的耕地上。资源的匮乏,土地产出效率的低下,导致了农民的低收入,2004年农村居民人均纯收入2936元,仅为城镇居民的31%;年末农村绝对贫困人口为2610万人,低收入人口为4977万人。与此形成鲜明对比的一组数据是:2004年,全国共有2201万城镇居民得到政府最低生活保障;年末全国参加基本养老保险、失业保险、医疗保险达到3.83亿人次,而“全国”其实是城镇居民。造成城乡发展失调、“三农”问题日益突出的…     

A note on tolerance regions for random vectors and best linear predictors

When a (p+q)-variate column vector (x′,y′)′ has a (p+q)-variate normal density with mean vector (μ₁,μ₂) and covariance matrix Ω, unknown, Schervish (1980) obtains prediction intervals for the linear functions of a future y, given x. He bases the prediction interval on the F-distribution. However, for a specified linear function the statistic to be used is Student's t, since the prediction intervals based on t are shorter than those based on F. Similar results hold for the multivariate linear regression model.     

Exact confidence regions for scale and location parameters based on sample quartiles

In this paper we present relatively simple (ruler, paper, and pencil) nonparametric procedures for constructing joint confidence regions for (i) the median and the inner quartile range for the symmetric one-sample problem and (ii) the shift and ratio of scale parameters for the two-sample case. Both procedures are functions of the sample quartiles and have exact confidence levels when the populations are continuous. The one-sample case requires symmetry of first and third quartiles about the median.

The confidence regions we propose are always convex, nested for decreasing confidence levels and are compact for reasonably large sample sizes. Both exact small sample and approximate large sample distributions are given.     

消费信贷、流动性约束与城镇居民消费——基于PSTR模型的实证分析

本文利用中国2004-2013年的省级数据,建立PSTR模型实证分析消费信贷对城镇居民消费影响。实证分析结果表明:城镇居民对于收入变化和消费信贷变化均具有过度敏感性,但是高收入居民的收入敏感系数和消费信贷敏感系数均低于低收入居民,而利率变动对居民消费影响并不显著。进一步分析表明,城镇居民对于收入变化和消费信贷变化具有过度敏感性并非是消费者的短视所引致,而是由于流动性约束引发的。     

Some Remarks on The Paper by Theodorescu and Wolff: "Sequential Estimation of Expectations in the Presence of Trend"

Recently Theodoresu and Wolff have proposed a sequence of random variables for estimating a sequence of constants satisfying a certain recurrence equation. Their problem, which is similar to some arising in stochastic approximation theory, was solved by using techniques from this theory. The present paper shows that the theory of sums of independent random variables is a more natural tool for tackling this problem.     

Some algebra and geometry for hierarchical models, applied to diagnostics

Recent advances in computing make it practical to use complex hierarchical models. However, the complexity makes it difficult to see how features of the data determine the fitted model. This paper describes an approach to diagnostics for hierarchical models, specifically linear hierarchical models with additive normal or t -errors. The key is to express hierarchical models in the form of ordinary linear models by adding artificial `cases' to the data set corresponding to the higher levels of the hierarchy. The error term of this linear model is not homoscedastic, but its covariance structure is much simpler than that usually used in variance component or random effects models. The re-expression has several advantages. First, it is extremely general, covering dynamic linear models, random effect and mixed effect models, and pairwise difference models, among others. Second, it makes more explicit the geometry of hierarchical models, by analogy with the geometry of linear models. Third, the analogy with linear models provides a rich source of ideas for diagnostics for all the parts of hierarchical models. This paper gives diagnostics to examine candidate added variables, transformations, collinearity, case influence and residuals.