Asymptotic behavior of tails and quantiles of quadratic forms of Gaussian vectors

We derive results on the asymptotic behavior of tails and quantiles of quadratic forms of Gaussian vectors. They appear in particular in delta–gamma models in financial risk management approximating portfolio returns. Quantile estimation corresponds to the estimation of the Value-at-Risk, which is a serious problem in high dimension.     

用不变速度推导卢瑟福散射公式

通过横向速度变换得到两种不变速度，由此推出卢瑟福散射公式。     

Sequential Estimation of the Parameters in a Trigonometric Regression Model with the Gaussian Coloured Noise

This paper considers the estimation problem for a trigonometric regression model with the noise specified by the Ornstein–Uhlenbeck process with unknown parameter. We propose a sequential procedure which ensures a prescribed mean square precision uniformly in the nuisance parameter. The asymptotic behaviour of the procedure duration mean has been studied. This revised version was published online in August 2006 with corrections to the Cover Date.     

Regression quantiles for unstable autoregressive models

This paper investigates regression quantiles (RQ) for unstable autoregressive models. The uniform Bahadur representation of the RQ process is obtained. The joint asymptotic distribution of the RQ process is derived in a unified manner for all types of characteristic roots on or outside the unit circle. It involves stochastic integrals in terms of a sequence of independent and identically distributed multivariate Brownian motions with correlated components. The related L-estimator is also discussed. The asymptotic distributions of the RQ and the L-estimator corresponding to the nonstationary componentwise arguments can be transformed into a function of a normal random variable and a sequence of i.i.d. univariate Brownian motions. This is different from the analysis based on the LSE in the literature. As an auxiliary theorem, a weak convergence of a randomly weighted residual empirical process to the stochastic integral of a Kiefer process is established. The results obtained in this paper provide an asymptotic theory for nonstationary time series processes, which can be used to construct robust unit root tests.     

合理垂直烧结速度的研究

通过考查气流速度的变化研究垂直烧结速度随烧结过程的变化规律。结果表明:垂直烧结速度并非固定不变,而是随着烧结过程的逐步进行发生显著变化;点火保温后,随烧结物理化学反应的进行,燃烧带逐渐形成并变宽且产生过湿现象,导致料层的透气性显著变差,烧结速度显著下降,直至约25 min后过湿层完全消失,透气性变好,烧结速度迅速上升。根据垂直烧结速度变化规律,通过改变负压烧结,进行烧结速度优化实验,结果表明:在保持转鼓强度及成品率基本不变的情况下,将垂直烧结速度由20.08 mm/min提高到21.82 mm/min,利用系数由1.401 t/(m2-h)提高到1.587 t/(m2-h)。     

Nonparametric estimation of distributions with categorical and continuous data

In this paper we consider the problem of estimating an unknown joint distribution which is defined over mixed discrete and continuous variables. A nonparametric kernel approach is proposed with smoothing parameters obtained from the cross-validated minimization of the estimator's integrated squared error. We derive the rate of convergence of the cross-validated smoothing parameters to their ‘benchmark’ optimal values, and we also establish the asymptotic normality of the resulting nonparametric kernel density estimator. Monte Carlo simulations illustrate that the proposed estimator performs substantially better than the conventional nonparametric frequency estimator in a range of settings. The simulations also demonstrate that the proposed approach does not suffer from known limitations of the likelihood cross-validation method which breaks down with commonly used kernels when the continuous variables are drawn from fat-tailed distributions. An empirical application demonstrates that the proposed method can yield superior predictions relative to commonly used parametric models.     

一种求解刚体3D运动参数的鲁棒算法

提出一种基于鲁棒统计学中位数的３Ｄ运动参数估计方法，能够有效地克服由于出格点造成的粗差，并且不需任何参数初始值，整个算法计算简便，计算机模拟显示，其估计精度是令人满意的。     

奇摄动非线性微分方程周期边值问题解的估计

本文考虑一类二阶非线性微分方程奇摄动周期边值问题。利用微分不等式技巧,不仅研究了解的存在性,而且还给出解及其导数的估计,从而提供了研究解的导数估计的一种方法。     

可闻声波检测与空气中声速的测定

描述了用改进的声波探测器在空气中测定声速的方法。