Admissible minimum bias estimation of response surfaces

The minimum bias estimator was introduced as an alternative to the least squares estimator for approximating response functions by low-order polynomials. Here we show how to obtain an admissible estimator with smaller squared bias.     

感官欣赏与理性欣赏的重要环节——音乐欣赏课的教学与实践

本文认为，要提高音乐欣赏能力，使审美意识达到更高的境界，就必须掌握音乐理论基础知识，了解各种不同形式、不同体裁的音乐理作品的风格与特点，从而在理论上为独立分析音乐作品打下一个基础。这是音乐欣赏课的出发点     

利用最小化代价函数方法实现多窗口谱分析

利用最小化代价函数的方法推导了一种谱分析的多窗口。性能分析的结果表明，此方法与离散长球序列多窗口谱分析方法具有相当的估计偏差与方差性能。与离散长球序列多窗口相比，此方法得到的多窗口具有直观的解析表达式而无须求解矩阵的特征分解问题，因而具有较小的计算量。通过对离散白噪声与ＡＲ过程进行的多窗口谱分析对比实验，验证了此方法的有效性和正确性。     

Modeling Endogenous Mobility in Earnings Determination

ABSTRACT

We evaluate the bias from endogenous job mobility in fixed-effects estimates of worker- and firm-specific earnings heterogeneity using longitudinally linked employer–employee data from the LEHD infrastructure file system of the U.S. Census Bureau. First, we propose two new residual diagnostic tests of the assumption that mobility is exogenous to unmodeled determinants of earnings. Both tests reject exogenous mobility. We relax exogenous mobility by modeling the matched data as an evolving bipartite graph using a Bayesian latent-type framework. Our results suggest that allowing endogenous mobility increases the variation in earnings explained by individual heterogeneity and reduces the proportion due to employer and match effects. To assess external validity, we match our estimates of the wage components to out-of-sample estimates of revenue per worker. The mobility-bias-corrected estimates attribute much more of the variation in revenue per worker to variation in match quality and worker quality than the uncorrected estimates. Supplementary materials for this article are available online.     

非定常控制系统的绝对稳定性

从研究中间变量σ情况和判断控制系统解的界及k类函数法来讨论控制系统零解的绝对稳定,并给出了判断非线性非定常系统零解绝对稳定的一种新方法.     

Estimation of the smaller and larger of two exponential location parameters

Assume independent random samples are drawn from two populations which are exponentially distributed with unknown location parameters and a common known scale parameter. We want to estimate the maximum and the minimum of the unknowo location paremeters. In this paper several estimators are proposed which are better than the natural estimations in terms of absolute bias and /or meaqn squared error.     

天下第一绝句《静夜思》——兼谈"床前明月光"何以后来居上

李白的《静夜思》是当代中国知名度最高、普及度最广的小诗,堪称天下第一绝句。诗中物象的亲切性、音韵的和美性、思维的单线性、空间的可变性、时间的永恒性、身心的依存性,组成了一个独一无二的魅力系统。但是,《静夜思》在整个唐代并未受到评论家和诗选家们的青睐。而且"床前明月光"和"举头望明月"两句,也是明代人从李白原句"床前看月光"和"举头望山月"改动而成的。"明月……明月……故乡",不仅大大增强了宇宙间的空明感,强劲延续了望月思乡的诗歌传统,而且大大凸显了明代文人群体的"大明"意识。尤其是明末清初的民族情绪,更使得这两个"明"字别具意味。因为在古典诗文中,"故乡"与"故国"同义。从明清两代开始,中国读者用集体的智慧,小小修改了李白的《静夜思》,大大强化了"作品的绝对独特性",又用集体的热情,一代代人亿万次地持续诵读。时至今日,终于在千淘万汰之后,将"床前明月光……"托上了民族记忆的珠穆朗玛峰。透视一首默默无闻的唐诗演变为天下第一绝句的特殊历程,后人可以在文学创作、作品改编、接受研究等方面获得多向度的启迪。     

Bias Reduction through First-order Mean Correction, Bootstrapping and Recursive Mean Adjustment

Standard methods of estimation for autoregressive models are known to be biased in finite samples, which has implications for estimation, hypothesis testing, confidence interval construction and forecasting. Three methods of bias reduction are considered here: first-order bias correction, FOBC, where the total bias is approximated by the O(T^-1) bias; bootstrapping; and recursive mean adjustment, RMA. In addition, we show how first-order bias correction is related to linear bias correction. The practically important case where the AR model includes an unknown linear trend is considered in detail. The fidelity of nominal to actual coverage of confidence intervals is also assessed. A simulation study covers the AR(1) model and a number of extensions based on the empirical AR(p) models fitted by Nelson & Plosser (1982). Overall, which method dominates depends on the criterion adopted: bootstrapping tends to be the best at reducing bias, recursive mean adjustment is best at reducing mean squared error, whilst FOBC does particularly well in maintaining the fidelity of confidence intervals.     

Risk of Error and the Kappa Coefficient of a Binary Diagnostic Test in the Presence of Partial Verification

The accuracy of a binary diagnostic test is usually measured in terms of its sensitivity and its specificity, or through positive and negative predictive values. Another way to describe the validity of a binary diagnostic test is the risk of error and the kappa coefficient of the risk of error. The risk of error is the average loss that is caused when incorrectly classifying a non-diseased or a diseased patient, and the kappa coefficient of the risk of error is a measure of the agreement between the diagnostic test and the gold standard. In the presence of partial verification of the disease, the disease status of some patients is unknown, and therefore the evaluation of a diagnostic test cannot be carried out through the traditional method. In this paper, we have deduced the maximum likelihood estimators and variances of the risk of error and of the kappa coefficient of the risk of error in the presence of partial verification of the disease. Simulation experiments have been carried out to study the effect of the verification probabilities on the coverage of the confidence interval of the kappa coefficient.     

Inference in the presence of ranking error in ranked set sampling

The author proposes inference techniques for ranked set sample data in the presence of judgment ranking errors. He bases his analysis on the models of Bohn & Wolfe (1994) and Frey (2007a, b), of which parameters are estimated by minimizing a distance measure. He then uses the fitted models to calibrate confidence intervals and tests. He shows the validity of his approach through simulation and illustrates its application through the construction of distribution‐free confidence intervals for the median area of apple tree leaves covered by a spray.