平滑转换向量误差修正模型的非线性协整SupLM检验

本文考虑平滑转换向量误差修正模型的非线性协整检验问题,相对于传统的两步检验法,给出已知协整向量下的直接检验非线性协整的SupLM检验方法,通过定义平滑转换协整模型,给出SupLM检验统计量,在原假设下得到检验统计量的渐近分布和相关的bootstrap算法,模拟结果和实例计算表明了该方法的有效性。     

Better saddlepoint confidence intervals via bootstrap calibration

Confidence interval construction for parameters of lattice distributions is considered. By using saddlepoint formulas and bootstrap calibration, we obtain relatively short intervals and bounds with coverage errors, in contrast with and coverage errors for normal theory intervals and bounds when the population distribution is absolutely continuous. Closed form solutions are also provided for the cases of binomial and Poisson distributions. The method is illustrated by some simulation results.

     

删截分布未知的多维随机删截数据的PP拟合优度检验

文[5]在假定删截分布已知的条件下,用投影寻踪（PP）技巧讨论了多维随机删截数据的PP拟合优度检验问题．本文讨论截尾分布未知时,多维随机删截数据的拟合优度检验问题,得到了检验统计量在零假设成立时的渐近分布,并讨论了其Bootstrap逼近．     

进口铁矿砷量特征的内核密度分析与Bootstrap代表值估计

对进口铁矿中的砷量进行了总体统计分析, 在数据统计分布特征研究基础上, 使用内核密度估计对进口铁矿砷量进行数据多态性分析, 使用bootstrap对原始数据样本值重复取样以获得稳健的砷量代表值估计及标准偏差, 证明以bootstrap重新取样样本分布的均值与标准偏差作为有限单次样本代表值是合理、有效的.     

样本均值Bootstrap逼近的收敛速度

本文进一步研究Ｂｏｏｔｓｔｒａｐ逼近的收敛速度，在随机变量的（２＋δ）阶矩（０≤δ＜２）有限的情况下，讨论标准化样本均值的分布与它的Ｂｏｏｔｓｔｒａｐ逼近之间差的一致收敛速度，以及这种逼近与正态分布之间差的一致收敛速度。     

Test to compare two population logspectra

Summary  The objective of this paper is to compare time series patterns generated over two populations. A random sample of objects is chosen from each population. On each object, a stationary process with an absolutely continuous spectral distribution is observed at the same times. We assume that the logarithm of the periodogram from each time series follows a model which involves the pattern of each population. A statistical test is proposed which will compare these patterns. The probability distribution of the test under the null hypothesis is approximated by the bootstrap. The consistency of the method is analyzed using the Mallows metric. A simulation study is also carried out. This paper has been partially funded by I+D research program ref. BFM2000-0517     

Analytic smoothing of geometric maps with applications to KAM theory

We show that finitely differentiable diffeomorphisms which are either symplectic, volume-preserving, or contact can be approximated with analytic diffeomorphisms that are, respectively, symplectic, volume-preserving or contact. We prove that the approximating functions are uniformly bounded on some complex domains and that the rate of convergence, in Cr-norms, of the approximation can be estimated in terms of the size of such complex domains and the order of differentiability of the approximated function. As an application to this result, we give a proof of the existence, the local uniqueness and the bootstrap of regularity of KAM tori for finitely differentiable symplectic maps. The symplectic maps considered here are not assumed either to be written in action-angle variables or to be perturbations of integrable systems. Our main assumption is the existence of a finitely differentiable parameterization of a maximal dimensional torus that satisfies a non-degeneracy condition and that is approximately invariant. The symplectic, volume-preserving and contact forms are assumed to be analytic.     

Saddlepoint approximations to studentized bootstrap distributions based onM-estimates

Summary  Saddlepoint methods can provide extremely accurate approximations to resampling distributions. This article applies them to distributions of studentized bootstrap statistics based on robustM-estimates. As examples we consider the studentized versions of Huber’sM-estimate of location, of its initially MAD scaled version, and of Huber’s proposal 2. The studentized version of Huber’s proposal 2 seems to be a preferable measure of location. Remarks on implementation and related problems are given.     

Bandwidth choice for local polynomial estimation of smooth boundaries

Local polynomial methods hold considerable promise for boundary estimation, where they offer unmatched flexibility and adaptivity. Most rival techniques provide only a single order of approximation; local polynomial approaches allow any order desired. Their more conventional rivals, for example high-order kernel methods in the context of regression, do not have attractive versions in the case of boundary estimation. However, the adoption of local polynomial methods for boundary estimation is inhibited by lack of knowledge about their properties, in particular about the manner in which they are influenced by bandwidth; and by the absence of techniques for empirical bandwidth choice. In the present paper we detail the way in which bandwidth selection determines mean squared error of local polynomial boundary estimators, showing that it is substantially more complex than in regression settings. For example, asymptotic formulae for bias and variance contributions to mean squared error no longer decompose into monotone functions of bandwidth. Nevertheless, once these properties are understood, relatively simple empirical bandwidth selection methods can be developed. We suggest a new approach to both local and global bandwidth choice, and describe its properties.     

Approximation for bootstrapped empirical processes

We obtain an approximation for the bootstrapped empirical process with the rate of the Komlós, Major and Tusnády approximation for empirical processes. The proof of the new approximation is based on the Poisson approximation for the uniform empirical distribution function and the Gaussian approximation for randomly stopped sums.