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71.
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. 相似文献
72.
N[a,b]类中边界Nevanlinna-Pick插值(I) 总被引:1,自引:1,他引:0
用所谓的Hankel向量方法求解N[a,b]函数类中带边界插值数据的Nevanlina-Pick插值(BNP(N[a,b]))问题,并建立BNP(N[a,b])问题与[a,b]上的某种带约束条件的Hausdorff矩量问题之间等价的可解条件以及解之间明确的一一对应关系.这使得当BNP(N[a,b])问题有多解时,能通过带约束条件的矩量问题的可解性准则和解获得BNP(N[a,b])问题的可解性准则和解的参数化描述,而在唯一解的情况下,通过BNP(N[a,b])问题解的存在唯一性准则和唯一解来获得带约束条件的 相似文献
73.
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. 相似文献
74.
高阶非线性波动方程的有限差分方法 总被引:2,自引:0,他引:2
本文研究一类广泛的高阶非线性波动方程组初边值问题的有限差分格式,用离散泛函分析方法和先验估计的技巧得到了有限差分格式的收敛性。 相似文献
75.
无失效数据的Bayes和多层Bayes分析 总被引:3,自引:0,他引:3
本文推广了文献[6]的结果,对指数分布无失效数据的失效率,给出了Bayes估计、Bayes置信上限以及多层Bayes估计,从而可以得到无失效数据可靠度的估计,最后,结合实际问题进行了计算。 相似文献
76.
Let X1, X2, …, Xn be random vectors that take values in a compact set in Rd, d ≥ 1. Let Y1, Y2, …, Yn be random variables (“the responses”) which conditionally on X1 = x1, …, Xn = xn are independent with densities f(y | xi, θ(xi)), i = 1, …, n. Assuming that θ lives in a sup-norm compact space Θq,d of real valued functions, an optimal L1-consistent estimator
of θ is constructed via empirical measures. The rate of convergence of the estimator to the true parameter θ depends on Kolmogorov's entropy of Θq,d. 相似文献
77.
78.
AN ESTIMATE ON THE DISTRIBUTION AND MOMENTS OF THE LAST EXIT TIME OF AN ELLIPTIC DIFFUSION PROCESS 总被引:1,自引:0,他引:1
Let LB be the last exit time from a compact set B of an elliptic diffusion process X. A moderate estimate for the distribution of LB is obtained, and the sufficient and necessary condition for Ex(LBk)<∞is proved. 相似文献
79.
80.
A. Meister 《Mathematical Methods of Statistics》2007,16(1):63-76
This paper addresses the statistical problem of density deconvolution under the condition that the density to be estimated
has compact support. We introduce a new estimation procedure, which establishes faster rates of convergence for smooth densities
as compared to the optimal rates for smooth densities with unbounded support. This framework also allows us to relax the usual
condition of known error density with non-vanishing Fourier transform, so that a nonparametric class of densities is valid;
therefore, even the shape of the noise density need not be assumed. These results can also be generalized for fast decaying
densities with unbounded support. We prove optimality of the rates in the underlying experiment and study the practical performance
of our estimator by numerical simulations.
相似文献