Bias-adjustment and calibration of jackknife variance estimator in the presence of non-response

In this paper, bias-adjustment in the jackknife estimator of variance accredited to Rao and Sitter (1995) has been considered. Then the bias-adjusted Rao and Sitter (1995) estimator has been calibrated such that its expected value under the imputing superpopulation model remains the same as the expected value of the mean squared error of the ratio estimator in the presence of non-response. A simulation study has been performed to compare the six different estimators of variance: out of them four estimators belong to Rao and Sitter (1995) and the other two proposed estimators are named as bias-adjusted and bias-adjusted-cum-calibrated estimators. The empirical relative bias and empirical relative efficiency of the two proposed estimators with respect to the four existing estimators accredited to Rao and Sitter (1995) have been investigated through simulations. The bias-adjusted-cum-calibrated estimator has been found to be an efficient estimator in the case of heteroscadastic populations. The present paper considers the situation of simple random and without replacement sampling. The possibility of obtaining a negative estimate of variance by the estimator due to Kim et al. (2006) has been pointed out.     

An Improved Class of Estimators for the General Population Parameters Using Auxiliary Information

This article suggests an improved class of estimators for estimating the general population parameter using information on an auxiliary variable. The properties of the suggested class of estimators have been studied under large sample approximation. The general results are then applied to estimate the population coefficient of variation of study variable using auxiliary information. An empirical study is given in support of the theoretical results.     

Generalized Symmetric Divergence Measures and the Probability of Error

There are three classical divergence measures exist in the literature on information theory and statistics. These are namely, Jeffryes-Kullback-Leiber (Jeffreys, 1946 Jeffreys , H. ( 1946 ). An invariant form for the prior probability in estimation problems . Proc. Roy. Soc. Lon. Ser. A 186 : 453 – 461 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]; Kullback and Leibler, 1951 Kullback , S. , Leibler , R. A. ( 1951 ). On information and sufficiency . Ann. Math. Statist. 22 : 79 – 86 .[Crossref] , [Google Scholar]) J-divergence. Sibson-Burbea-Rao (Sibson, 1969 Sibson , R. ( 1969 ). Information radius . Z. Wahrs. und verw Geb. 14 : 149 – 160 .[Crossref], [Web of Science ®] , [Google Scholar]), Jensen-Shannon divegernce, (Burbea and Rao, 1982 Burbea , J. , Rao , C. R. ( 1982 ). On the convexity of some divergence measures based on entropy functions . IEEE Trans. Inform. Theor. IT-28 : 489 – 495 .[Crossref], [Web of Science ®] , [Google Scholar]), and Taneja (1995 Taneja , I.J. ( 1995 ). New developments in generalized information measures , In: Hawkes , P. W. , Ed., Advances in Imaging and Electron Physics . 91:37–136 . [Google Scholar]). Arithmetic-Geometric divergence. These three measures bear an interesting relationship among each other. The divergence measures like Hellinger (1909 Hellinger , H. ( 1909 ). Neue Begründung der theorie der quadratischen formen von unendlichen vielen Veränderlichen . J. Reine Aug. Math. 136 : 210 – 271 .[Crossref] , [Google Scholar]) discrimination, symmetric χ²-divergence, and triangular discrimination are also known in the literature. In this article, we have considered generalized symmetric divergence measures having the measures given above as particular cases. Bounds on the probability of error are obtained in terms of generalized symmetric divergence measures. Study of bounds on probability of error is extended for the difference of divergence measures.     

Estimation of Slope for Linear Regression Model with Uncertain Prior Information and Student-t Error

This article considers estimation of the slope parameter of the linear regression model with Student-t errors in the presence of uncertain prior information on the value of the unknown slope. Incorporating uncertain non sample prior information with the sample data the unrestricted, restricted, preliminary test, and shrinkage estimators are defined. The performances of the estimators are compared based on the criteria of unbiasedness and mean squared errors. Both analytical and graphical methods are explored. Although none of the estimators is uniformly superior to the others, if the non sample information is close to its true value, the shrinkage estimator over performs the rest of the estimators.     

Macroeconomic Factors Strike Back: A Bayesian Change-Point Model of Time-Varying Risk Exposures and Premia in the U.S. Cross-Section

This article proposes a Bayesian estimation framework for a typical multi-factor model with time-varying risk exposures to macroeconomic risk factors and corresponding premia to price U.S. publicly traded assets. The model assumes that risk exposures and idiosyncratic volatility follow a break-point latent process, allowing for changes at any point on time but not restricting them to change at all points. The empirical application to 40 years of U.S. data and 23 portfolios shows that the approach yields sensible results compared to previous two-step methods based on naive recursive estimation schemes, as well as a set of alternative model restrictions. A variance decomposition test shows that although most of the predictable variation comes from the market risk premium, a number of additional macroeconomic risks, including real output and inflation shocks, are significantly priced in the cross-section. A Bayes factor analysis massively favors the proposed change-point model. Supplementary materials for this article are available online.     

供求冲击与中国经济波动： 基于SVAR模型的甄别分析

 本文首先利用经全国经济普查信息修正后的季度数据推算得到1992年第1季度到2008年第3季度的实际GDP和GDP减缩指数,然后借鉴Blanchard和Quah（1989）提出的方法构建二元SVAR模型,对驱动中国经济波动的供求冲击进行甄别分析。结果发现：①无论是在长期还是在短期,2/3以上的产出波动可以归因于供给冲击的影响;②对于价格波动,短期内需求冲击和供给冲击的贡献几乎相当,而长期内需求冲击能够解释70％左右;③总的来说,供给冲击和需求冲击在中国经济波动中具有几乎同等的重要性。上述结论具有重要的宏观操作政策含义。     

An Exact Corrected Log-Likelihood Function for Cox's Proportional Hazards Model under Measurement Error and Some Extensions

Abstract.  This paper studies Cox's proportional hazards model under covariate measurement error. Nakamura's [ Biometrika 77 (1990) 127] methodology of corrected log-likelihood will be applied to the so-called Breslow likelihood, which is, in the absence of measurement error, equivalent to partial likelihood. For a general error model with possibly heteroscedastic and non-normal additive measurement error, corrected estimators of the regression parameter as well as of the baseline hazard rate are obtained. The estimators proposed by Nakamura [Biometrics 48 (1992) 829], Kong et al. [ Scand. J. Statist. 25 (1998) 573] and Kong & Gu [ Statistica Sinica 9 (1999) 953] are re-established in the special cases considered there. This sheds new light on these estimators and justifies them as exact corrected score estimators. Finally, the method will be extended to some variants of the Cox model.     

A Bayesian Learning Coefficient of Generalization Error and Vandermonde Matrix-Type Singularities

The coefficient of the main term of the generalization error in Bayesian estimation is called a Bayesian learning coefficient. In this article, we first introduce Vandermonde matrix type singularities and show certain orthogonality conditions of them. Recently, it has been recognized that Vandermonde matrix type singularities are related to Bayesian learning coefficients for several hierarchical learning models. By applying the orthogonality conditions of them, we show that their log canonical threshold also corresponds to the Bayesian learning coefficient for normal mixture models, and we obtain the explicit computational results in dimension one.     

中国国际收支经常账户与资本金融账户关系研究：1981-2007

 本文针对中国国际收支多年来“双顺差”的事实,利用1981～2007年度中国国际收支时序数据和我们认为与之相关的最重要的两个宏观经济变量：中国的对外开放度指标和实际GDP的增长率数据,构建了多组向量自回归（VAR）模型,通过格兰杰因果检验、脉冲响应函数和方差分解等计量方法,实证检验了中国国际收支经常账户及其子账户与资本金融账户之间,各账户与宏观经济变量之间的因果关系、动态冲击响应和变量间影响的相对重要性。     

中国公共服务投入与产出的动态关系研究——以教育和公共卫生为例

在财政实践中,公共服务投入与产出之间往往存在着动态的双向效应,而以往学者仅着重于单向效应的研究,这无助于在公共预算约束下实现公共服务供给效率最大化。利用向量自回归模型和向量误差修正模型考察了中国以教育和公共医疗卫生为代表的公共服务投入与产出长期均衡关系以及短期波动关系。研究结果表明：公共服务投入与产出在长期内存在协整关系;短期内公共服务的投入与产出之间存在动态正向关系;在受到外部随机冲击时,公共服务的投入与产出系统表现出良好的稳定性和规律性。     

Publication Decisions Revisited: The Effect of the Outcome of Statistical Tests on the Decision to Publish and Vice Versa

This article presents evidence that published results of scientific investigations are not a representative sample of results of all scientific studies. Research studies from 11 major journals demonstrate the existence of biases that favor studies that observe effects that, on statistical evaluation, have a low probability of erroneously rejecting the so-called null hypothesis (H ₀). This practice makes the probability of erroneously rejecting H ₀ different for the reader than for the investigator. It introduces two biases in the interpretation of the scientific literature: one due to multiple repetition of studies with false hypothesis, and one due to failure to publish smaller and less significant outcomes of tests of a true hypotheses. These practices distort the results of literature surveys and of meta-analyses. These results also indicate that practice leading to publication bias have not changed over a period of 30 years.     

Discrete Gamma Distributions: Properties and Parameter Estimations

A two-parameter discrete gamma distribution is derived corresponding to the continuous two parameters gamma distribution using the general approach for discretization of continuous probability distributions. One parameter discrete gamma distribution is obtained as a particular case. A few important distributional and reliability properties of the proposed distribution are examined. Parameter estimation by different methods is discussed. Performance of different estimation methods are compared through simulation. Data fitting is carried out to investigate the suitability of the proposed distribution in modeling discrete failure time data and other count data.     

An Efficiency and Protection Degree-Based Comparison Among the Quantitative Randomized Response Strategies

There have been many alternative strategies for implementing sampling survey on quantitative characteristic of sensitive issues by using randomized response (RR) technique. The efficiency of most of those strategies has been improved by choosing the suitable design parameters of model. However, the two different procedures with pre-assigned design parameter values cannot ensure that they possess the same protection degree to the respondents. Some earlier comparisons of those strategies are inadequate (as in Eichhorn and Hayre, 1983 Eichhorn , B. H. , Hayre , L. S. ( 1983 ). Scrambled randomized response methods for obtaining sensitive quantitative data . J. Statist. Plann. Infer. 7 : 307 – 316 .[Crossref], [Web of Science ®] , [Google Scholar]; Gupta et al., 2002 Gupta , S. , Gupta , B. , Singh , S. ( 2002 ). Estimation of sensitivity level of personal interview survey questions . J. Statist. Plann. Infer. 100 ( 2 ): 239 – 247 .[Crossref], [Web of Science ®] , [Google Scholar]). Some literature contains a more comprehensive comparison based on efficiency and protection degree to the respondents among the qualitative characteristic RR techniques (see Bhargava and Singh, 2002 Bhargava , M. , Singh , R. ( 2002 ). On the efficiency comparison of certain randomized response strategies . Metrika 55 : 191 – 197 .[Crossref], [Web of Science ®] , [Google Scholar]; Nayak, 1994 Nayak , T. K. ( 1994 ). On randomized response surveys for estimating a proportion . Commun. Statist. Theor. Meth. 23 ( 11 ): 3303 – 3321 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]; Zaizai and Zankan, 2004 Zaizai , Y. , Zankan , N. ( 2004 ). A fair comparison of the randomized response strategies . Acta Mathematica Scientia 24A ( 3 ): 362 – 368 . [Google Scholar]). As far as the comparisons are concerned that are based on efficiency and protection degree to the respondents among the quantitative characteristic RR techniques, very few related studies have been found so far. The purpose of this article is to give a more adequate comparison among those earlier quantitative characteristic RR strategies. It is found that several important differences between the results obtained in this article and some known results exist. Therefore, these earlier RR strategies should be reevaluated.     

Modeling and predicting IBNR reserve: extended chain ladder and heteroscedastic regression analysis

This work deals with two methodologies for predicting incurred but not reported (IBNR) actuarial reserves. The first is the traditional chain ladder, which is extended for dealing with the calendar year IBNR reserve. The second is based on heteroscedastic regression models suitable to deal with the tail effect of the runoff triangle – and to forecast calendar year IBNR reserves as well. Theoretical results regarding closed expressions for IBNR predictors and mean squared errors are established – for the case of the second methodology, a Monte Carlo study is designed and implemented for accessing finite sample performances of feasible mean squared error formulae. Finally, the methods are implemented with two real data sets. The main conclusions: (i) considering tail effects does not imply theoretical and/or computational problems; and (ii) both methodologies are interesting to design softwares for IBNR reserve prediction.     

Compositional Changes of the Labor Force and the Icrease of the Unemployment Rate: An Estimate for the United States

This article estimates how demographic changes in the composition of the labor force affect the unemployment rate in the United States. In addition to the effect from changes in the weights of the individual groups composing the total, the impact of compositional changes on the individual unemployment rates is estimated by using a dummy-variables model and incorporated into the estimate on the overall unemployment rate. The results suggest that the incorporation of the latter effect is significant. Indedd, the estimates presented in this article are almost twice as high as those provided by the fixed-weight method used in previous studies.     

Testing the equality of several multivariate normal mean vectors under heteroscedasticity: A fiducial approach and an approximate test

We consider the problem of testing the equality of several multivariate normal mean vectors under heteroscedasticity. We first construct a fiducial confidence region (FCR) for the differences between normal mean vectors and we then propose a fiducial test for comparing mean vectors by inverting the FCR. We also propose a simple approximate test that is based on a modification of the χ² approximation. This simple test avoids the complications of simulation-based inference methods. We show that the proposed fiducial test has correct type one error rate asymptotically. We compare the proposed fiducial and approximate tests with the parametric bootstrap test in terms of controlling the type one error rate via an extensive simulation study. Our simulation results show that the proposed fiducial and approximate tests control the type one error rate, while there are cases that the parametric bootstrap test is out of control. We also discuss the power performance of the tests. Finally, we illustrate with a real example how our proposed methods are applicable in analyzing repeated measure designs including a single grouping variable.     

面板数据双因素误差回归模型序列相关和随机效应的联合LM检验

对面板数据双因素误差回归模型构造了检验序列相关和随机效应的一种联合LM检验,发现该LM统计量也是检验联合假设H0：σμ^2=λ=0的Baltagi-Li LM统计量和检验假设H0：σv^2=λ=0的Breusch-Pagan-LM统计量之和。当面板数据的个体数N充分大时,该联合LM统计量的渐近分布是χ^2（3）分布;无论双因素误差面板数据回归模型的剩余误差项是AR（1）过程还是MA（1）过程,联合LM检验是相同的,即对随机效应和一阶序列相关的联合LM检验是独立于序列相关的形式。     

An Estimator of Shannon Entropy of Beta-Generated Distributions and a Goodness-of-Fit Test

The aim of this article is twofold: on the one hand to introduce and study some of the statistical properties of an estimator for the Shannon entropy and on the other hand to develop a goodness-of-fit test for beta-generated distributions and the distribution of order statistics. Beta-generated distributions are a broad class of univariate distributions which has received great attention during the last 15 years, as it obeys nice properties and it extends the distribution of order statistics. The proposed estimator of Shannon entropy of beta-generated distributions is motivated by the respective Vasicek’s estimator, as the latter one is tailored to the class of the beta-generated distributions and the distribution of order statistics. The estimator of Shannon entropy is defined and its consistency is studied. It is, moreover, exploited to build a goodness-of-fit test for the beta-generated distribution and the distribution of order statistics. Simulations are performed to examine the small- and moderate-sample properties of the proposed estimator and to compare the power of the proposed test with the power of competitors under a variety of alternatives.     

General minimum lower order confounding designs: An overview and a construction theory

For fractional factorial (FF) designs, Zhang et al. (2008) introduced a new pattern for assessing regular designs, called aliased effect-number pattern (AENP), and based on the AENP, proposed a general minimum lower order confounding (denoted by GMC for short) criterion for selecting design. In this paper, we first have an overview of the existing optimality criteria of FF designs, and then propose a construction theory for 2^n−m$2^{n-m}$ GMC designs with 33N/128≤n≤5N/16$33N/128\le n\le 5N/16$, where N=2^n−m$N=2^{n-m}$ is the run size and n is the number of factors, for all N's and n  's, via the doubling theory and SOS resolution IV designs. The doubling theory is extended with a new approach. By introducing a notion of rechanged (RC) Yates order for the regular saturated design, the construction result turns out to be quite transparent: every GMC 2^n−m$2^{n-m}$ design simply consists of the last n columns of the saturated design with a specific RC Yates order. This can be very conveniently applied in practice.