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一元平滑估计中的方差降低AI 解读

A variance reduction technique in nonparametric smoothing is proposed: at each point of estimation, form a linear combination of a preliminary estimator evaluated at nearby points with the coefficients specified so that the asymptotic bias remains unchanged. The nearby points are chosen to maximize the variance reduction. We study in detail the case of univariate local linear regression. While the new estimator retains many advantages of the local linear estimator, it has…

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多参数似然模型中的方差缩减AI 解读

Local likelihood modeling is a unified and effective approach to establishing the dependence of a response variable, which can be of various types, on independent variables. Therefore, these models have become popular in a wide range of applications. There is an increasing interest in employing multiparameter local likelihood models to investigate trends of sample extremes in environmental statistics. When sample maxima are modeled by a generalized extreme value…

重尾分布高分位数的置信域AI 解读

Estimating high quantiles plays an important role in the context of risk management. This involves extrapolation of an unknown distribution function. In this paper we propose three methods, namely, the normal approximation method, the likelihood ratio method and the data tilting method, to construct confidence regions for high quantiles of a heavy tailed distribution. A simulation study prefers the data tilting method.

ARCH(1) 误差下 AR(1) 过程的加权最小绝对偏差估计AI 解读

The weighted least absolute deviations estimator is studied for an AR(1) process with ARCH(1) errors εt. Unlike for the quasi maximum likelihood estimator, the estimator's, limiting distribution is shown to be normal even when E(εt4) = ∞. Furthermore, the estimator can be applied to examine the symmetry of the density of εt and to estimate the quantity E(log |α + λ½ εt|), which are of crucial importance for conducting asymptotic inference for quasi maximum likelihood…

重尾分布均值的经验似然置信区间AI 解读

Empirical-likelihood-based confidence intervals for a mean were introduced by Owen [Biometrika 75 (1988) 237–249], where at least a finite second moment is required. This excludes some important distributions, for example, those in the domain of attraction of a stable law with index between 1 and 2. In this article we use a method similar to Qin and Wong [Scand. J. Statist. 23 (1996) 209–219] to derive an empirical-likelihood-based confidence interval for the mean when the…

利用局部似然追踪断裂线与边界AI 解读

Summary We suggest locally parametric methods for estimating curves, such as boundaries of density supports or fault lines in response surfaces, in a variety of spatial problems. The methods are based on spatial approximations to the local likelihood that the curve passes through a given point in the plane, as a function of that point. The local likelihood might be a regular likelihood computed locally, with kernel weights (e.g. in the case of support boundary estimation) or…