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Evaluation of the effect of stochastic explanatory variables in regression models when the underlying distribution is in the class of elliptical distributions

当基础分布属于椭圆分布类时，评估回归模型中随机解释变量的影响

基本信息

批准号：
14530036
负责人：
HODOSHIMA Jiro
金额：
$ 1.22万
依托单位：
NAGOYA CITY UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2002
资助国家：
日本
起止时间：
2002 至 2004
项目状态：
已结题

项目摘要

1. I obtained the properties of the asymptotic covariance matrix of the LSE of regression parameters, investigated its small sample properties by simulation, and studied asset pricing models as examples, when explanatory variables are random in regression models. In particular, I (1) derived the asymptotic and small sample properties of the covariance matrix of the LSE when the joint distribution of explanatory and dependent variables is elliptical, (2) showed how the asymptotic variances of the LSE of alpha and beta depend on skewness and kurtosis of the joint distribution in the market model in finance without assuming any specific distribution, (3) found there is no effect of nonnormality on the unconditional LSE inference of expected asset returns in K-factor asset pricing models when factors and returns are i.i.d., and (4) studied the small sample properties of the covariance matrix of the LSE when explanatory variables and error term are uncorrelated but not independent and compared them to those when there is heteroskedasticity.2. I proposed a new definition of weak exogeneity when the underlying distribution is nonnormal in the class of elliptical distributions. Based on the new definition, I compared by simulation the joint and conditional MLEs of parameters for the student's t linear heteroskedastic regression model studied by Spanos (1994). The conditional MLE was found to work fine for regression parameters of the conditional model but not for other parameters.

1.得到了回归参数的最小二乘估计的渐近协方差矩阵的性质，通过模拟研究了它的小样本性质，并以资产定价模型为例，研究了回归模型中解释变量为随机变量时的情形。特别地，我（1）推导了当解释变量和因变量的联合分布为椭圆时，LSE协方差矩阵的渐近和小样本性质，（2）在金融市场模型中，在不假设任何特定分布的情况下，证明了alpha和beta的LSE的渐近方差如何依赖于联合分布的偏度和峰度，（3）发现当因子和收益均独立同分布时，K因子资产定价模型中预期资产收益的无条件LSE推断不受非正态性的影响，（4）研究了解释变量和误差项不相关但不独立时LSE协方差矩阵的小样本性质，并与异方差时的性质进行了比较.在椭圆分布类中，当底层分布为非正态分布时，提出了弱外生性的一个新定义。在此基础上，通过模拟比较了Spanos（1994）研究的t-线性异方差回归模型参数的联合极大似然估计和条件极大似然估计。条件极大似然估计被发现对条件模型的回归参数工作良好，但对其他参数则不然。

项目成果

期刊论文数量（29）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Comparison of the joint and conditional maximum likelihood estimators in the student's t linear heteroskedastic regression model

学生 t 线性异方差回归模型中联合和条件最大似然估计量的比较

DOI：
发表时间：
2004
期刊：
Discussion papers in Economics, Nagoya City University 386
影响因子：
0
作者：
Hodoshima;J.;Ando;M.;Jiro Hodoshima;Jiro Hodoshima;Jiro Hodoshima;Jiro Hodoshima
通讯作者：
Jiro Hodoshima

The effect of nonnormality on the market model: quantitative evaluation

非正态性对市场模型的影响：定量评估

DOI：
发表时间：
2003
期刊：
Discussion papers in Economics 359
影响因子：
0
作者：
Masakazu Ando;Jiro Hodoshima;Jiro Hodoshima;Jiro Hodoshima;Jiro Hodoshima
通讯作者：
Jiro Hodoshima

Comparison of the joint and conditional maximum likelihood estimators for the student's t linear heteroskedastic regression model

学生 t 线性异方差回归模型的联合和条件最大似然估计量的比较

DOI：
发表时间：
2004
期刊：
Discussion papers in Economics 386
影响因子：
0
作者：
Hodoshima;J.;Ando;M.;Jiro Hodoshima;Jiro Hodoshima;Jiro Hodoshima;Jiro Hodoshima;Jiro Hodoshima;Jiro Hodoshima;Jiro Hodoshima;Jiro Hodoshima;Jiro Hodoshima
通讯作者：
Jiro Hodoshima

HODOSHIMA, Jiro: "The effect of nonnormality on the stochastic regression model"Discussion papers, Faculty of Economics, Nagoya City University. 342. 24 (2003)

HODOSHIMA，Jiro：“非正态性对随机回归模型的影响”讨论论文，名古屋市立大学经济学院。