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GARCH模型中的R估计量：渐近理论与应用AI 解读

Summary The quasi-maximum likelihood estimation is a commonly-used method for estimating the generalized autoregressive conditional heteroscedastic parameters. However, such estimators are sensitive to outliers and their asymptotic normality is proved under the finite fourth moment assumption on the underlying error distribution. In this paper, we propose a novel class of estimators of the generalized autoregressive conditional heteroscedastic parameters based on ranks of…

GARCH 模型中的 M 估计AI 解读

This paper derives asymptotic normality of a class of M -estimators in the generalized autoregressive conditional heteroskedastic (GARCH) model. The class of estimators includes least absolute deviation and Huber's estimator in addition to the well-known quasi maximum likelihood estimator. For some estimators, the asymptotic normality results are obtained only under the existence of fractional unconditional moment assumption on the error distribution and some mild smoothness…

条件异方差下的广义秩估计量AI 解读

In this paper, we extend the classical idea of Rank-estimation of parameters from homoscedastic problems to heteroscedastic problems. In particular, we define a class of rank estimators of the parameters associated with the conditional mean function of an autoregressive model through a three-steps procedure and then derive their asymp- totic distributions. The class of models considered includes Engel’s ARCH model and the threshold heteroscedastic model. The class of…

有限总体抽样中层级贝叶斯估计量的设计一致性AI 解读

We obtain a limit of a hierarchical Bayes estimator of a finite population mean when the sample size is large. The limit is in the sense of ordinary calculus, where the sample observations are treated as fixed quantities. Our result suggests a simple way to correct the hierarchical Bayes estimator to achieve design-consistency, a well-known property in the traditional randomization approach to finite population sampling. We also suggest three different measures of…

长程依赖下随机加权经验过程的线性化及非线性回归分位数应用AI 解读

This paper discusses some asymptotic uniform linearity results of randomly weighted empirical processes based on long range dependent random variables. These results are subsequently used to linearize nonlinear regression quantiles in a nonlinear regression model with long range dependent errors, where the design variables can be either random or nonrandom. These, in turn, yield the limiting behavior of the nonlinear regression quantiles. As a corollary, we obtain the…

复杂调查中有限总体均值的经验贝叶斯估计AI 解读

Estimation of finite population means is considered when samples are collected using a stratified sampling design. Finite populations for different strata are assumed to be realizations from different superpopulations. The true means of the observations lie on a regression surface with random intercepts for different strata. The true sampling variances are also different and random for different strata. The strata are connected through two common prior distributions, one for…

复杂调查中有限总体均值的经验贝叶斯估计AI 解读

Estimation of finite population means is considered when samples are collected using a stratified sampling design. Finite populations for different strata are assumed to be realizations from different superpopulations. The true means of the observations lie on a regression surface with random intercepts for different strata. The true sampling variances are also different and random for different strata. The strata are connected through two common prior distributions, one for…