Accurate confidence intervals in regression analyses of non-normal data

A linear model in which random errors are distributed independently and identically according to an arbitrary continuous distribution is assumed. Second- and third-order accurate confidence intervals for regression parameters are constructed from Charlier differential series expansions of approximately pivotal quantities around Student’s t distribution. Simulation verifies that small sample performance of the intervals surpasses that of conventional asymptotic intervals and equals or surpasses that of bootstrap percentile-t and bootstrap percentile-|t| intervals under mild to marked departure from normality.     

ARCH(0,1)系数中位无偏估计分布的渐近展开(英文)

This paper is concerned with the distributional properties of a median unbiased estimator of ARCH(0,1)coefficient.The exact distribution of the estimator can be easily derived,however its practical calculations are too heavy to implement, even though the middle range of sample sizes.Since the estimator is shown to have asymptotic normality,asymptotic expansions for the distribution and the percentiles of the estimator are derived as the refinements.Accuracies of expansion formulas are evaluated numerically,and the results of which show that we can effectively use the expansion as a fine approximation of the distribution with rapid calculations.Derived expansion are applied to testing hypothesis of stationarity,and an implementation for a real data set is illustrated.     

(对数)逻辑斯谛克分布下可靠性抽样检验

对于寿命遵从逻辑斯谛克分布或对数逻辑斯谛克分布的产品,本文在完全样本情形给出了制定可靠性抽样检验方案的统计方法.数值模拟结果表明该方法是可行的.本文还指出,这种方法可用于位置一刻度参数分布族.     

ARCH(0,1)系数中位无偏估计分布的渐近展开

This paper is concerned with the distributional properties of a median unbiased estimator of ARCH（0,1） coefficient. The exact distribution of the estimator can be easily derived, however its practical calculations are too heavy to implement, even though the middle range of sample sizes. Since the estimator is shown to have asymptotic normality, asymptotic expansions for the distribution and the percentiles of the estimator are derived as the refinements. Accuracies of expansion formulas are evaluated numerically, and the results of which show that we can effectively use the expansion as a fine approximation of the distribution with rapid calculations. Derived expansion are applied to testing hypothesis of stationarity, and an implementation for a real data set is illustrated.     

On the distribution of sample mean in finite populations. I

We obtain Bergström-type [2] asymptotic expansions for sample mean in finite population [8]. Analogues of the Cornish-Fisher transformation are obtained in the cases of limit distributions from class $\mathcal{L}$ and distributions of sums of independent identically distributed random variables (in [2], the Bergström equality is used).     

Gram-Charlier展开在动态金融高阶矩建模中的近似误差

Gram-Charlier展开(GCE)在动态条件高阶矩GARCH模型中得到了广泛应用。相比于常见的分布,GCE的高阶矩形式更加直观,能更直接地刻画条件高阶矩的动态特征。此展开函数并不非负,在实际应用时需要平方并归一化,但已有文献大多忽略此处理后高阶矩所发生的变化。本文研究了平方处理方法对展开函数高阶矩的影响,推导了正确的高阶矩形式。实证研究表明,用原始参数作为近似高阶矩会产生显著偏误,在VaR预测时会严重低估风险。     

Nonparametric confidence intervals for functions of several distributions

Let F=(F₁...F_k) denote k unknown distribution functions and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmOrayaaja% Gaeyypa0ZaaeWaaeaaceWGgbGbaKaadaWgaaWcbaGaaGymaaqabaGc% caGGUaGaaiOlaiaac6caceWGgbGbaKaadaWgaaWcbaGaam4Aaaqaba% aakiaawIcacaGLPaaaaaa!3E24!\[\hat F = \left( {\hat F_1 ...\hat F_k } \right)\] their sample (empirical) functions based on random samples from them of sizes n ₁, ..., n _k. Let T(F) be a real functional of F. The cumulants of T(% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmOrayaaja% aaaa!35B2!\[\hat F\]) are expanded in powers of the inverse of n, the minimum sample size. The Edgeworth and Cornish-Fisher expansions for both the standardized and Studentized forms of T(% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmOrayaaja% aaaa!35B2!\[\hat F\]) are then given together with confidence intervals for T(F) of level 1–+O(n^-j/2) for any given in (0, 1) and any given j. In particular, confidence intervals are given for linear combinations and ratios of the means and variances of different populations without assuming any parametric form for their distributions.     

应用EWMA-GARCH(1,1)-M模型对沪深300股指期货最小VaR套期保值效果研究

VaR是目前国际上应用最广泛的度量金融风险的指标之一,其核心在于波动率,也就是方差的参数估计.采用EWMA模型估计方差,并且结合风险溢价特征的GARCH(1,1)-M模型计算出沪深300股指及其期货的最优衰减因子为0.933 25,摒弃了以往采用0.940 0作为衰减因子的一贯做法,并且运用Cornish-Fisher方程对正态分布的分位数进行了修正,得到修正后的套期保值比率以及资产组合的VaR,与传统的套期保值模型相比,该模型的风险价值VaR降低的程度明显,并且对投资组合未来的VaR具有很好的预测效果,表明EWMA-GARCH(1,1)-M模型对沪深300股指期货的套期保值效果较好.     

Asymptotic expansions for the distribution of quadratic forms in normal variables

Higher order asymptotic expansions for the distribution of quadratic forms in normal variables are obtained. The Cornish-Fisher inverse expansions for the percentiles of the distribution are also given. The resulting formula for a definite quadratic form guarantees accuracy almost up to fourth decimal place if the distribution is not very skew. The normalizing transformation investigated by Jensen and Solomon (1972, J. Amer. Statist. Assoc., 67, 898–902) is reconsidered based on the rate of convergence to the normal distribution.Faculty of Science, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka 812 Japan     

Gamma分布环境因子的统计分析

证明了Gamma分布环境因子的最大似然估计是有偏估计,且其偏差为正,进而导出了Gamma分布环境因子的近似无偏估计.利用Cornish-Fisher展开导出了Gamma分布环境因子的广义置信区间,另外也给了Gamma分布环境因子的Bootstrap-t置信区间.利用模拟方法研究了所给近似无偏估计和区间估计的精度,模拟结果显示所给近似无偏估计和区间估计的精度是相当好的.