Bootstrap approach to test the homogeneity of order restricted mean vectors when the covariance matrices are unknown

Testing homogeneity of multivariate normal mean vectors under an order restriction when the covariance matrices are unknown, arbitrary positive definite and unequal are considered. This problem of testing has been studied to some extent, for example, by Kulatunga and Sasabuchi (1984 Kulatunga, D. D. S., Sasabuchi, S. (1984). A test of homogeneity of mean vectors against multivariate isotonic alternatives. Mem Fac Sci, Kyushu Univ Ser A Mathemat 38:151–161. [Google Scholar]) when the covariance matrices are known and also Sasabuchi et al. (2003 Sasabuchi, S., Tanaka, K., Tsukamodo, T. (2003). Testing homogeneity of multivariate normal mean vectors under an order restriction when the covariance matrices are common but unknown. Annals of Statistics. 31(5):1517–1536.[Web of Science ®] , [Google Scholar]) and Sasabuchi (2007 Sasabuchi, S. (2007). More powerful tests for homogeneity of multivariate normal mean vectors under an order restriction. Sankhya 69(4):700–716. [Google Scholar]) when the covariance matrices are unknown but common. In this paper, a test statistic is proposed and because of the main advantage of the bootstrap test is that it avoids the derivation of the complex null distribution analytically, a bootstrap test statistic is derived and since the proposed test statistic is location invariance the bootstrap p-value defined logical and some steps are presented to estimate it. Our numerical studies via Monte Carlo simulation show that the proposed bootstrap test can correctly control the type I error rates. The power of the test for some of the p-dimensional normal distributions is computed by Monte Carlo simulation. Also, the null distribution of test statistic is estimated using kernel density. Finally, the bootstrap test is illustrated using a real data.     

VIF-based adaptive matrix perturbation method for heteroskedasticity-robust covariance estimators in the presence of multicollinearity

In this study, we investigate linear regression having both heteroskedasticity and collinearity problems. We discuss the properties related to the perturbation method. Important observations are summarized as theorems. We then prove the main result that states the heteroskedasticity-robust variances can be improved and that the resulting bias is minimized by using the matrix perturbation method. We analyze a practical example for validation of the method.     

Tests for compound periodicities and estimating a non linear function

We propose two tests for testing compound periodicities which are the uniformly most powerful invariant decision procedures against simple periodicities. The second test can provide an excellent estimation of a compound periodic non linear function from observed data. These tests were compared with the tests proposed by Fisher and Siegel by Monte Carlo studies and we found that all the tests showed high power and high probability of a correct decision when all the amplitudes of underlying periods were the same. However, if there are at least several different periods with unequal amplitudes, then the second test proposed always showed high power and high probability of a correct decision, whereas the tests proposed by Fisher and Siegel gave 0 for the power and 0 for the probability of a correct decision, whatever the standard deviation of pseudo normal random numbers. Overall, the second test proposed is the best of all in view of the probability of a correct decision and power.     

M-estimation for functional linear regression

This paper studies M-estimation in functional linear regression in which the dependent variable is scalar while the covariate is a function. An estimator for the slope function is obtained based on the functional principal component basis. The global convergence rate of the M-estimator of unknown slope function is established. The convergence rate of the mean-squared prediction error for the proposed estimators is also established. Monte Carlo simulation studies are conducted to examine the finite-sample performance of the proposed procedure. Finally, the proposed method is applied to analyze the Berkeley growth data.     

Bayesian expectile regression with asymmetric normal distribution

In this paper, we adopt the Bayesian approach to expectile regression employing a likelihood function that is based on an asymmetric normal distribution. We demonstrate that improper uniform priors for the unknown model parameters yield a proper joint posterior. Three simulated data sets were generated to evaluate the proposed method which show that Bayesian expectile regression performs well and has different characteristics comparing with Bayesian quantile regression. We also apply this approach into two real data analysis.     

Finite-sample distributions of the Wald,likelihood ratio,and Lagrange multiplier test statistics in the classical linear model

In this note, it is shown that the finite-sample distributions of the Wald, likelihood ratio, and Lagrange multiplier statistics in the classical linear regression model are members of the generalized beta model introduced by McDonald and Xu (1995a McDonald, J.B., Xu, Y.J. (1995a). A generalization of the beta distribution with applications. J. Econom. 66:133–152.[Crossref], [Web of Science ®] , [Google Scholar]). This is useful for examining the properties of these test statistics. For example, this characterization makes it easy to find distribution, quantile, and density functions for each test statistic, makes it clear why Wald tests may overreject the null hypothesis using asymptotic critical values, and formalizes the fact that the Lagrange multiplier statistic follows a distribution with bounded support.     

Progressively Type-II censored conditionally N-ordered statistics from a unified elliptically contoured copula

Progressively Type-II censored conditionally N-ordered statistics (PCCOS-N) arising from iid random vectors X_i = (X¹_i, X²_i, …, X_i^p), i = 1, 2…, n, were investigated by Bairamov (2006 Bairamov, I. (2006). Progressive Type II censored order statistics for multivariate observations. J. Mult. Anal. 97:797–809.[Crossref], [Web of Science ®] , [Google Scholar]), with respect to the magnitudes of N(X_i), i = 1, 2, …, n, where N( · ) is a p-variate measurable function defined on the support set of X₁ satisfying certain regularity conditions and N(X_i) denotes the lifetime of the random vector X_i, i = 1, …, n. Under the PCCOS-N sampling scheme, n independent units are placed on a life-test and after the ith failure, R_i (i = 1, …, m) of the surviving units are removed at random from the remaining observations. In this article, we consider PCCOS-N arising from a vector with identical as well as non identical dependent components, jointly distributed according to a unified elliptically contoured copula (PCCOSDUECC-N). Results established here contain the previous results as particular cases. Illustrative examples and simulation studies show that PCCOSDUECC-N enables us to analyze the lifetime of several systems, including repairable systems and systems with standby components, more efficiently than PCCOS-N.     

Prevalence of and risk factors associated with cesarean section in Lebanon — A retrospective study based on a sample of 29,270 women

Background

During the last decades, there has been an alarming and dramatic increase in the number of cesarean births in both developed and undeveloped countries. This increase has not been clinically justified but, nevertheless, has raised an important number of issues.

一种新的金融动态横截面估计方法——基于中国股票市场条件定价模型评估的应用与扩展

大多数资产定价模型常常用静态横截面回归(the static cross-sectional regression)进行定价表现评估,从而投资组合回报率的时间变化性并不能被时变的风险承载或者(和)时变的风险溢价所解释.本文从经济学的角度,运用一种新的金融动态横截面回归(the dynamic cross-sectional regression),首次考察了基于中国股票市场和美国股票市场的条件资产定价模型的定价表现:股票市场投资组合回报率的时变性是否能被时变的风险溢价所解释.本文发现,短期收益反转和流通市值加权市场换手率为条件变量的条件资本资产定价模型和基于消费的条件资本资产定价模型,能更好的解释中国股票投资组合的回报时变性,其时变性主要来自于时变的风险溢价.另外,本文发现一些拥有持续(persistence)和缓慢变化(slow-moving)特性的条件变量更能够解释横截面投资组合的时变回报.     

金融发展与区域经济增长研究——基于重庆市的实证分析

金融对经济的促进作用往往会受到其他因素的影响,而使得结果大打折扣,其主要原因是因为目前资金的流动受到很多制度和人为因素的影响,导致资源不能及时从低效率部门流入高效率部门。本研究从现有理论出发,通过收集重庆市1986—2010年有关经济增长和金融发展的数据,利用计量经济学软件,通过误差修正模型,得出二者之间的协整关系。在此基础之上,结合重庆现状分析回归结果并提出有关政策建议。