基于贝叶斯偏态线性混合模型的费率厘定

线性混合模型是非寿险费率厘定的主要方法之一。通常的线性混合模型假设随机误差项服从正态分布,而保险损失数据往往具有右偏特征,这使得该模型在非寿险费率厘定中的应用受到一定影响。在通常的线性混合模型基础上,假设随机误差项服从偏态分布,即可建立偏态线性混合模型,从而改善费率厘定结果的合理性。基于一组实际的保险损失数据,应用贝叶斯MCMC方法建立几个不同的偏态线性混合模型,并与正态分布假设下的线性混合模型进行对比,实证检验偏态线性混合模型在非寿险费率厘定中的优越性。     

STAR模型的滞后阶数选择与稳健性研究

本文讨论了六种信息准则在STAR模型滞后阶数选择中的适应性及稳健性问题。Monte Carlo模拟结果显示,在多数情况下,数据生成过程中的误差项分布并不影响信息准则正确识别模型最大滞后阶数的能力;对于短STAR模型,ACC准则具有较高的正确识别率,并且对不同平滑转移系数及不同门限值具有很好的稳健性;而对于长STAR模型,SC准则及ACC准则具有更高的正确率及良好的稳健性。     

基于ARFIMA(p, d, q)过程的半参数估计量分布特征及其有偏性研究7737976300

 本文运用蒙特卡罗模拟的方法对小样本下长记忆性的三种半参数估计量的分布特征尤其是有偏性问题进行了深入分析,结果发现,当长记忆和短记忆同时存在时,在大多数情况下,各参数估计量仍然服从正态分布,因此在小样本下仍可以构造t统计量判别参数的显著性,但由于受到短期参数的影响,估计量的分布是有偏的,因此导致参数的估计和检验出现偏差。而当真实数据过程接近非平稳或过度差分时,半参数估计量的分布也会发生改变。     

基于逆γ偏正态分布的Tobit回归模型

Tobit模型是一种应用很广泛的截尾回归模型,并假定其误差项服从正态分布.相对于对称分布,偏态分布能获得更全面准确、及时有效的信息.基于此,文章提出了基于逆尺度因子偏正态分布的Tobit回归模型,并给出了该模型参数的极大似然估计,通过数值模拟与正态假设下的Tobit模型进行比较,结果表明该模型和方法是有用和有效的.     

基于蒙特卡罗模拟的几种VaR模型度量效果比较

文章通过蒙特卡罗模拟产生误差项服从标准正态分布、t分布的GARCH过程敷据,在其基础上利用真实分位数和估计分位敷之间的误差评价了几种VaR模型的度量效果.结果显示,基于这两个过程,误差项服从t分布的GARCH模型优于误差项服从标准正态分布的GAARCH模型,而相对复杂的极值理论略微优于效果最差的历史模拟法:从而实证研究中,由于极值理论的度量效果不一定较好,应该尝试多种VaR模型,从中选择最适合的模型.     

ESTAR模型单位根检验的性质研究

文章以转移函数为指数形式的平滑转移自回归模型(ESTAR)作为典型代表,通过模拟实验考察了非线性单位根检验(包括ADF检验和PP检验)的小样本性质;以MA(1)和GARCH(1,1)过程为代表,研究了误差项服从序列相关和异方差时,非线性参数和滞后阶数对两类检验统计量实际水平和功效的影响,从而为非平稳STAR族模型的应用研究提供一定的理论支持.     

偏斜参数对GARCH族模型估计与预测绩效的影响

本文先运用蒙特卡洛模拟考察了偏斜参数对GARCH族模型估计结果的影响并发现,若标准化扰动项偏斜且厚尾,基于对称厚尾分布的极大似然估计量渐近有偏.以上证指数收益为样本,利用SPA检验,实证考察了10种常见的GARCH族结构分别在正态分布、Student-t、GED以及Skew-t分布假设下的波动率预测绩效.结果发现:①Skew-t分布假设下的GARCH族结构能够获得优越的预测绩效;②10种GARCH族结构中,有8种模型在Student-t分布假设下的预测绩效不及正态分布,而GED分布假设下也有4种模型不及正态分布;③样本外观测值的多少以及GARCH-m结构的有无不改变主要结论.     

关于样本均值的抽样分布能否作正态近似的探讨

一、引言当我们对总体均值进行统计推断时,常常需要假定样本均值服从或近似服从正态分布。我们知道,当样本来自于正态总体时,样本①均值服从正态分布;当样本来自于非正态总体时,根据中心极限定理对于足够大的样本容量n,样本均值将近似服从正态分布。对于非正态总体,问题的关键是样本容量n的“足够大”到底指多少?这很难一概而论。人们通常以30为界,将n≥30的样本称为大样本,并认为样本均值-x的抽样分布可作正态近似;而将n<30的样本称为小样本,认为此时不宜将-x的抽样分布作正态近似。许多统计应用者都是按这样的工作规则来做的,但在许多实际…     

基于偏正态随机效应模型的信度保费

信度模型是非寿险经验费率厘定的主要方法。传统的Buhlmann-Straub信度模型可以表示为随机截距模型,而随机截距模型假设随机效应服从正态分布。在实际的保险损失数据中,部分个体风险的损失可能远远高于总体平均水平,从而使得不同个体风险之间的风险差异呈现右偏特征。在这种情况下,Buhlmann-Straub模型有可能低估高风险的信度保费。本文在随机截距模型中假设随机效应服从偏正态分布,求得了偏正态随机效应假设下的信度保费。可以证明,Buhlmann-Straub信度保费是其特例。模拟分析和实证研究的结果都表明,偏正态随机效应假设下的信度模型可以更好地预测高风险的信度保费,从而改进传统信度模型的保费估计结果。     

广义线性模型的性质及其在非寿险中的应用

广义线性模型的误差项服从指数分布族，通常的指数分布族包括正态分布、泊松分布、二项分布、伽玛分布、逆高斯分布等，这些分布模型在非寿险精算中都有广泛的应用。在对上述常见模型特点分析的同时，用实际数据进行了拟合，为精算师在实务工作中提供了些建议。     

Effects of model misspecification on tests of no randomized treatment effect arising from Cox's proportional hazards model

We examine the asymptotic and small sample properties of model-based and robust tests of the null hypothesis of no randomized treatment effect based on the partial likelihood arising from an arbitrarily misspecified Cox proportional hazards model. When the distribution of the censoring variable is either conditionally independent of the treatment group given covariates or conditionally independent of covariates given the treatment group, the numerators of the partial likelihood treatment score and Wald tests have asymptotic mean equal to 0 under the null hypothesis, regardless of whether or how the Cox model is misspecified. We show that the model-based variance estimators used in the calculation of the model-based tests are not, in general, consistent under model misspecification, yet using analytic considerations and simulations we show that their true sizes can be as close to the nominal value as tests calculated with robust variance estimators. As a special case, we show that the model-based log-rank test is asymptotically valid. When the Cox model is misspecified and the distribution of censoring depends on both treatment group and covariates, the asymptotic distributions of the resulting partial likelihood treatment score statistic and maximum partial likelihood estimator do not, in general, have a zero mean under the null hypothesis. Here neither the fully model-based tests, including the log-rank test, nor the robust tests will be asymptotically valid, and we show through simulations that the distortion to test size can be substantial.     

Bootstrapping analogs of the one way MANOVA test

Abstract

Analogs of the classical one way MANOVA model have recently been suggested that do not assume that population covariance matrices are equal or that the error vector distribution is known. These tests are based on the sample mean and sample covariance matrix corresponding to each of the p populations. We show how to extend these tests using other measures of location such as the trimmed mean or coordinatewise median. These new bootstrap tests can have some outlier resistance, and can perform better than the tests based on the sample mean if the error vector distribution is heavy tailed.     

Correlated random effects regression analysis for a log-normally distributed variable

In regression analysis, it is assumed that the response (or dependent variable) distribution is Normal, and errors are homoscedastic and uncorrelated. However, in practice, these assumptions are rarely satisfied by a real data set. To stabilize the heteroscedastic response variance, generally, log-transformation is suggested. Consequently, the response variable distribution approaches nearer to the Normal distribution. As a result, the model fit of the data is improved. Practically, a proper (seems to be suitable) transformation may not always stabilize the variance, and the response distribution may not reduce to Normal distribution. The present article assumes that the response distribution is log-normal with compound autocorrelated errors. Under these situations, estimation and testing of hypotheses regarding regression parameters have been derived. From a set of reduced data, we have derived the best linear unbiased estimators of all the regression coefficients, except the intercept which is often unimportant in practice. Unknown correlation parameters have been estimated. In this connection, we have derived a test rule for testing any set of linear hypotheses of the unknown regression coefficients. In addition, we have developed the confidence ellipsoids of a set of estimable functions of regression coefficients. For the fitted regression equation, an index of fit has been proposed. A simulated study illustrates the results derived in this report.     

基于STAR模型的中国货币政策对产出影响的非对称性研究

对中国GDP增长率建立以可预期到的货币冲击、未预期到的正向货币冲击和未预期到的负向货币冲击滞后三期为转移变量的LSTAR模型,拟合效果良好,分析不同类型的货币冲击对产出的非线性和非对称性影响,给出可预期到的货币冲击、未预期到的正向货币冲击和未预期到的负向货币冲击的阀值,分别为20.03%、2%和1.58%,说明不同类型的货币冲击对产出呈现不同的非对称性影响,强弱机制的转换区间存在差异,且负向货币冲击的阀值小于正向货币冲击的阀值。研究结果表明中国的货币政策存在显著的非线性和非对称性特征,且紧缩性货币政策比扩张性货币政策更有效。     

A nonparametric Bayesian prediction interval for a finite population mean

ABSTRACT

Given a sample from a finite population, we provide a nonparametric Bayesian prediction interval for a finite population mean when a standard normal assumption may be tenuous. We will do so using a Dirichlet process (DP), a nonparametric Bayesian procedure which is currently receiving much attention. An asymptotic Bayesian prediction interval is well known but it does not incorporate all the features of the DP. We show how to compute the exact prediction interval under the full Bayesian DP model. However, under the DP, when the population size is much larger than the sample size, the computational task becomes expensive. Therefore, for simplicity one might still want to consider useful and accurate approximations to the prediction interval. For this purpose, we provide a Bayesian procedure which approximates the distribution using the exchangeability property (correlation) of the DP together with normality. We compare the exact interval and our approximate interval with three standard intervals, namely the design-based interval under simple random sampling, an empirical Bayes interval and a moment-based interval which uses the mean and variance under the DP. However, these latter three intervals do not fully utilize the posterior distribution of the finite population mean under the DP. Using several numerical examples and a simulation study we show that our approximate Bayesian interval is a good competitor to the exact Bayesian interval for different combinations of sample sizes and population sizes.     

When is n large enough? Looking for the right sample size to estimate proportions

The central limit theorem indicates that when the sample size goes to infinite, the sampling distribution of means tends to follow a normal distribution; it is the basis for the most usual confidence interval and sample size formulas. This study analyzes what sample size is large enough to assume that the distribution of the estimator of a proportion follows a Normal distribution. Also, we propose the use of a correction factor in sample size formulas to ensure a confidence level even when the central limit theorem does not apply for these distributions.     

基于g-h分布的极值风险度量研究

依据ARMA-GJR模型构造标准残差序列,利用EVT模型拟合标准残差序列的尾部特征,进而确定样本阀值,最后结合g-h分布建立一种新的金融风险度量模型———基于ARMA-GJR-EVT-g-h的动态VaR模型。用该模型对上证综指进行实证分析,结果表明,该模型能够更合理有效地管理上证综指收益的风险,并且在高的置信水平上表现更好。     

A note on the most powerful invariant test of Rayleigh against exponential distribution

Abstract

The problem of testing Rayleigh distribution against exponentiality, based on a random sample of observations is considered. This problem arises in survival analysis, when testing a linearly increasing hazard function against a constant hazard function. It is shown that for this problem the most powerful invariant test is equivalent to the “ratio of maximized likelihoods” (RML) test. However, since the two families are separate, the RML test statistic does not have the usual asymptotic chi-square distribution. Normal and saddlepoint approximations to the distribution of the RML test statistic are derived. Simulations show that saddlepoint approximation is more accurate than the normal approximation, especially for tail probabilities that are the main values of interest in hypothesis testing.