噪声因子存在下的多响应参数设计的优化

采用多元损失函数法,对噪声因子存在下的多响应稳健性参数设计进行了优化.该方法考虑了噪声因子的影响,结合响应期望值和响应方差,其中响应方差结合了噪声因子产生的方差和拟合模型的预测方差,给出了综合方差的无偏估计,使解决方案对噪声因子和参数估计的不确定性都具有稳健性,避免了方差出现非正定的可能性.采用该方法对实例进行分析,得到较好的优化结果.     

Local polynomial regression smoothers with AR-error structure

Consider the fixed regression model with random observation error that follows an AR(1) correlation structure. In this paper, we study the nonparametric estimation of the regression function and its derivatives using a modified version of estimators obtained by weighted local polynomial fitting. The asymptotic properties of the proposed estimators are studied: expressions for the bias and the variance/covariance matrix of the estimators are obtained and the joint asymptotic normality is established. In a simulation study, a better behavior of the Mean Integrated Squared Error of the proposed regression estimator with respect to that of the classical local polynomial estimator is observed when the correlation of the observations is large. This work has been partially supported by grants PB98-0182-C02-01, PGIDT01PXI10505PR and MCyT Grant BFM2002-00265 (European FEDER support included).     

具有随机回归子的不完全信息和随机截尾的广义线性模型的重对数律

在可靠性研究中,带有不完全信息随机截尾的线性模型经常受到关注.本文将带有不完全信息随机截尾的线性模型推广到带有随机回归子的不完全信息的随机截尾广义线性模型,并运用概率极限理论对后者的极大似然估计的收敛速度进行了研究,得到了两个重对数律.从渐近的意义看,第一个重对数律给出了未知参数的最小100％置信区间,而第二个重对数律给出了估计量能够达到的精确下界.     

Interval estimation of the tail index of a GARCH(1,1) model

It is known that the tail index of a GARCH model is determined by a moment equation, which involves the underlying unknown parameters of the model. A?tail index estimator can therefore be constructed by solving the sample moment equation with the unknown parameters being replaced by its quasi-maximum likelihood estimates (QMLE). To construct a confidence interval for the tail index, one needs to estimate the non-trivial asymptotic variance of the QMLE. In this paper, an empirical likelihood method is proposed for interval estimation of the tail index. One advantage of the proposed method is that interval estimation can still be achieved without having to estimate the complicated asymptotic variance. A?simulation study confirms the advantage of the proposed method.     

Weiss-Hill estimator

In this paper the asymptotic distributional behaviour is derived for a new estimator for the extreme value index γ of distribution, which is a combination of two estimators proposed by Weiss and Hill (Weiss, 1971, and Hill, 1975). For |γ|>1/2, the estimator outperforms the Moment estimator (Dekkers and al., 1989). in the sense that it has a smaller asymptotic variance than the latter; moreover, for γ>1/2 (γ<0, resp.) the estimator behaves asymptoticaly like the Hillresp. Weiss—estimator; for |γ|<1/2 the estimator does not achieve the same rate of convergence as the Moment estimator. Simulation results concerning the comparison of the mentioned estimators are also presented. This research project was partially supported by FCT/PRAXIS XXI/FEDER and POCTI.     

Convergence of the optimal M-estimator over a parametric family of M-estimators

We consider a method to select an optimal M-estimator over a family of M-estimators of a parameter. Assuming that there exists an estimate of the mean square error for each element of this family of estimators, a natural estimator to consider is the M-estimator in the class which minimizes the considered estimates of the mean square errors. It is shown that under regularity conditions, this M-estimator is asymptotically normal and its asymptotic mean square error is equal to the infimum of the asymptotic mean square errors of the M-estimators in the class. We see how this method works in two different situations. In order to tackle the former problem, we present sufficient conditions for the weak convergence of a class of M-estimators.     

A Short-Cut Method for Estimation in Renewal Processes

This article proposes a simple, noniterative estimator of the lifetime distribution from stationary renewal processes data, which is a variation of the Kaplan-Meier estimator. The method is compared with the nonparametric maximum likelihood estimator using real and simulated data, and the results show that as long as the censoring level is not too high the two estimates are remarkably close. A heuristic asymptotic argument is given to support the simulation results and to justify the rationale behind the estimator. The estimator's connection with the Kaplan–Meier estimator is exploited to suggest a variance estimate and associated confidence interval, which, through a simulation study, are found to be conservative.     

Some Complete and Censored Sampling Results for the Weibull or Extreme-Value Distribution

A simple, unbiased estimator, based on a censored sample, has been proposed by Rain [1] for the scale parameter of the Extreme-value distribution. This estimator was shown to have high efficiency and to be approximately distributed as a chi-square variable if substantial censoring occurs. Further small sample and asymptotic properties of this estimator are considered in this paper. The estimator is modified so that it is more applicable to the complete sample case and a close chi-square approximation is established for all cases. The estimator is also shown to be related to the maximum likelihood estimator.     

A smooth simultaneous confidence band for correlation curve

A plug-in estimator is proposed for a local measure of variance explained by regression, termed correlation curve in Doksum et al. (J Am Stat Assoc 89:571–582, 1994), consisting of a two-step spline–kernel estimator of the conditional variance function and local quadratic estimator of first derivative of the mean function. The estimator is oracally efficient in the sense that it is as efficient as an infeasible correlation estimator with the variance function known. As a consequence of the oracle efficiency, a smooth simultaneous confidence band (SCB) is constructed around the proposed correlation curve estimator and shown to be asymptotically correct. Simulated examples illustrate the versatility of the proposed oracle SCB which confirms the asymptotic theory. Application to a 1995 British Family Expenditure Survey data has found marginally significant evidence for a local version of Engel’s law, i.e., food budget share and household real income are inversely related (Hamilton in Am Econ Rev 91:619–630, 2001).     

Bias-reduced estimators of the Weibull tail-coefficient

In this paper, we consider the problem of the estimation of the Weibull tail-coefficient θ. In particular, we propose a regression model, from which we derive a bias-reduced estimator of θ. This estimator is based on a least-squares approach. The asymptotic normality of this estimator is established. We also introduce an adaptive selection procedure to determine the number of upper order statistics to be used in the estimator. A simulation study as well as an application to a real data set are provided in order to prove the efficiency of the above mentioned methods.