Some Limit Behaviors for Linear EV Model with Replicate Observations

In this article, we establish the asymptotic normality for the LS estimators of the unknown parameters in the linear errors-in-variables (EV) model with replicate observations, which weaken the moment conditions of Zhang and Chen (2002 Zhang, S.G., Chen, X.R. (2002). On asymptotic normality of parameters in linear EV model. Chin. Ann. Math. Ser. B 23(4):495506.[Crossref], [Web of Science ®] , [Google Scholar]). Furthermore, the moderate and large deviations principles for the LS estimators are obtained also.     

议布雷顿森林体系的成立背景及其对最初计划的偏离

布雷顿森林体系的建立对战后的世界政治经济发展发挥了极大的影响力和作用。本文希望通过分析其成立的背景和最初的设想探讨一下在当时的环境下布雷顿森林体系的建立所面临的巨大困难和妥协以及对最初计划的背离及其原因,对历史的真相有一个更准确的认识。     

凡俗世界的歌者--论池莉小说的平民意识

池莉是当代中国文坛执著于颂扬市井平民凡俗生活的作家之一.她坚守平民价值立场,显现出歌颂庸常人物、凡俗人生的写作姿态;运用洒脱通达、幽默风趣而又不动声色的叙述话语和平民化的人物语言,真诚地面对现实人生,描摹日常生活的原生形态;展现困在爱情婚姻中的市井平民的生活.     

社会进步中的技术发展与地理位置的影响关系分析

社会进步,科学技术是第一位的推动力,但技术的发展,也不能勿视地理位置的影响因素。地理环境与古代世界文明中心形成和历史古国的陆路领先技术或海上先进技术;,地理大发现与欧洲国家近代工业、技术革命的崛起;地缘政治与当代世界强国中心地位由英国向美国的转移。联系研究社会进步中的技术发展、地理位置及相关因素,有助于正在走向现代化的中国如何有效利用地理优势,促进经济发展。     

L 1-estimation for varying coefficient models

The varying coefficient model is a useful extension of linear models and has many advantages in practical use. To estimate the unknown functions in the model, the kernel type with local linear least-squares (L ₂) estimation methods has been proposed by several authors. When the data contain outliers or come from population with heavy-tailed distributions, L ₁-estimation should yield better estimators. In this article, we present the local linear L ₁-estimation method and derive the asymptotic distributions of the L ₁-estimators. The simulation results for two examples, with outliers and heavy-tailed distribution, respectively, show that the L ₁-estimators outperform the L ₂-estimators.     

The McDonald Weibull model

For the first time, we propose a five-parameter lifetime model called the McDonald Weibull distribution to extend the Weibull, exponentiated Weibull, beta Weibull and Kumaraswamy Weibull distributions, among several other models. We obtain explicit expressions for the ordinary moments, quantile and generating functions, mean deviations and moments of the order statistics. We use the method of maximum likelihood to fit the new distribution and determine the observed information matrix. We define the log-McDonald Weibull regression model for censored data. The potentiality of the new model is illustrated by means of two real data sets.     

Robust unit root tests with autoregressive errors

ABSTRACT

This article presents a new test for unit roots based on least absolute deviation estimation specially designed to work for time series with autoregressive errors. The methodology used is a bootstrap scheme based on estimating a model and then the innovations. The resampling part is performed under the null hypothesis and, as it is customary in bootstrap procedures, is automatic and does not rely on the calculation of any nuisance parameter. The validity of the procedure is established and the asymptotic distribution of the statistic proposed is proved to converge to the correct distribution. To analyze the performance of the test for finite samples, a Monte Carlo study is conducted showing a very good behavior in many different situations.     

EXPLICIT NONPARAMETRIC CONFIDENCE INTERVALS FOR THE VARIANCE WITH GUARANTEED COVERAGE

ABSTRACT

In this paper, we provide a method for constructing confidence intervals for the variance which exhibits guaranteed coverage probability for any sample size, uniformly over a wide class of probability distributions. In contrast, standard methods achieve guaranteed coverage only in the limit for a fixed distribution or for any sample size over a very restrictive (parametric) class of probability distributions. Of course, it is impossible to construct effective confidence intervals for the variance without some restriction, due to a result of Bahadur and Savage.[1] Bahadur, R. and Savage, L. 1956. The Nonexistence of Certain Statistical Procedures in Nonparametric Problems. Annals of Mathematical Statistics, 25: 1115–1122.  [Google Scholar] However, it is possible if the observations lie in a fixed compact set. We also consider the case of lower confidence bounds without any support restriction. Our method is based on the behavior of the variance over distributions that lie within a Kolmogorov–Smirnov confidence band for the underlying distribution. The method is a generalization of an idea of Anderson,[2] Anderson, T. 1967. Confidence Limits for the Expected Value of an Arbitrary Bounded Random Variable with a Continuous Distribution Function. Bull. ISI, 43: 249–251.  [Google Scholar] who considered only the case of the mean; it applies to very general parameters, and particularly the variance. While typically it is not clear how to compute these intervals explicitly, for the special case of the variance we provide an algorithm to do so. Asymptotically, the length of the intervals is of order n ^?/2 (in probability), so that, while providing guaranteed coverage, they are not overly conservative. A small simulation study examines the finite sample behavior of the proposed intervals.     

Focused Information Criteria,Model Selection,and Model Averaging in a Tobit Model With a Nonzero Threshold

Claeskens and Hjort (2003 Claeskens, G. and Hjort, N. L. 2003. “The Focused Information Criterion”. Journal of the American Statistical Association, 98: 900–945. (with discussion)[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) have developed a focused information criterion (FIC) for model selection that selects different models based on different focused functions with those functions tailored to the parameters singled out for interest. Hjort and Claeskens (2003 Hjort, N. L. and Claeskens, G. 2003. “Frequentist Model Average Estimators”. Journal of the American Statistical Association, 98: 879–899. (with discussion)[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) also have presented model averaging as an alternative to model selection, and suggested a local misspecification framework for studying the limiting distributions and asymptotic risk properties of post-model selection and model average estimators in parametric models. Despite the burgeoning literature on Tobit models, little work has been done on model selection explicitly in the Tobit context. In this article we propose FICs for variable selection allowing for such measures as mean absolute deviation, mean squared error, and expected expected linear exponential errors in a type I Tobit model with an unknown threshold. We also develop a model average Tobit estimator using values of a smoothed version of the FIC as weights. We study the finite-sample performance of model selection and model average estimators resulting from various FICs via a Monte Carlo experiment, and demonstrate the possibility of using a model screening procedure before combining the models. Finally, we present an example from a well-known study on married women's working hours to illustrate the estimation methods discussed. This article has supplementary material online.