Estimation of rational transfer function models

In the estimation of rational transfer function models, it has been recommended that starting values of a transfer function component be assumed to be zero (or a constant) in the recursive computation of the transfer function response. It is demonstrated that such algorithms may lead to serious bias in the estimation of moving average parameters. This paper discusses several other algorithms that may rectify this problem. It is found that the starting-value-free (SVF) method is a more reliable algorithm. For computer programs using the traditional algorithm, i.e., the zero-starting-value (ZSV) method, the bias problem can be easily remedied using a short-cut method that omits appropriate number of values at the beginning of the residual series.     

Small-Sample Quantile Estimators in a Large Nonparametric Model

The large nonparametric model in this note is a statistical model with the family ? of all continuous and strictly increasing distribution functions. In the abundant literature of the subject, there are many proposals for nonparametric estimators that are applicable in the model. Typically the kth order statistic X _k:n is taken as a simplest estimator, with k = [nq], or k = [(n + 1)q], or k = [nq] + 1, etc. Often a linear combination of two consecutive order statistics is considered. In more sophisticated constructions, different L-statistics (e.g., Harrel–Davis, Kaigh–Lachenbruch, Bernstein, kernel estimators) are proposed. Asymptotically the estimators do not differ substantially, but if the sample size n is fixed, which is the case of our concern, differences may be serious. A unified treatment of quantile estimators in the large, nonparametric statistical model is developed.     

On Asymptotic Normality of the Local Polynomial Regression Estimator with Stochastic Bandwidths

Nonparametric density and regression estimators commonly depend on a bandwidth. The asymptotic properties of these estimators have been widely studied when bandwidths are non stochastic. In practice, however, in order to improve finite sample performance of these estimators, bandwidths are selected by data driven methods, such as cross-validation or plug-in procedures. As a result, nonparametric estimators are usually constructed using stochastic bandwidths. In this article, we establish the asymptotic equivalence in probability of local polynomial regression estimators under stochastic and nonstochastic bandwidths. Our result extends previous work by Boente and Fraiman (1995 Boente , G. , Fraiman , R. ( 1995 ). Asymptotic distribution of data-driven smoothers in density and regression estimation under dependence . Can. J. Statist. 23 : 383 – 397 .[Crossref], [Web of Science ®] , [Google Scholar]) and Ziegler (2004 Ziegler , K. ( 2004 ). Adaptive kernel estimation of the mode in nonparametric random design regression model . Probab. Mathemat. Statist. 24 : 213 – 235 . [Google Scholar]).     

Consistency and Normality of M-Estimators in Partly Linear Models with Stochastic Adapted Errors

The robust M-estimators for the partly linear model under stochastic adapted errors are considered. It is shown that the M-estimator of parameter is asymptotically normal and the M-estimator of the nonparametric function achieves the optimal rate of convergence for nonparametric regression. Some known results are improved and generalized. Some simulations and a real data example are conducted to illustrate the proposed method.     

Measuring the Discrepancy of a Parametric Model via Local Polynomial Smoothing

Abstract. In the context of multivariate mean regression, we propose a new method to measure and estimate the inadequacy of a given parametric model. The measure is basically the missed fraction of variation after adjusting the best possible parametric model from a given family. The proposed approach is based on the minimum L ² ‐distance between the true but unknown regression curve and a given model. The estimation method is based on local polynomial averaging of residuals with a polynomial degree that increases with the dimension d of the covariate. For any d ≥ 1 and under some weak assumptions we give a Bahadur‐type representation of the estimator from which ‐consistency and asymptotic normality are derived for strongly mixing variables. We report the outcomes of a simulation study that aims at checking the finite sample properties of these techniques. We present the analysis of a dataset on ultrasonic calibration for illustration.     

Estimation of k-Factor GIGARCH Process: A Monte Carlo Study

In this article, we discuss the parameter estimation for a k-factor generalized long-memory process with conditionally heteroskedastic noise. Two estimation methods are proposed. The first method is based on the conditional distribution of the process and the second is obtained as an extension of Whittle's estimation approach. For comparison purposes, Monte Carlo simulations are used to evaluate the finite sample performance of these estimation techniques, using four different conditional distribution functions.     

Estimating Prediction Error: Cross-Validation vs. Accumulated Prediction Error

We study the validation of prediction rules such as regression models and classification algorithms through two out-of-sample strategies, cross-validation and accumulated prediction error. We use the framework of Efron (1983 Efron , B. ( 1983 ). Estimating the error rate of a prediction rule: improvement on cross-validation . Journal of the American Statistical Association 78 : 316 – 331 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) where measures of prediction errors are defined as sample averages of expected errors and show through exact finite sample calculations that cross-validation and accumulated prediction error yield different smoothing parameter choices in nonparametric regression. The difference in choice does not vanish as sample size increases.     

Statistical methods in optimal curve fitting

Many optimal curve fitting and approximation problems have the same structure as certain estimation problems involving random processes. This structural correspondence has many useful consequences for curve fitting problems, including recursive algorithms and computable error bounds. The basic facts of this correspondence are reviewed and some new results on error bounds and optimal sampling are presented.     

涉及微分多项式的亚纯函数正规性

研究了涉及微分多项式的亚纯函数的正规性.继承Schwick的思想将正规族与分担值联系起来,对一族亚纯函数中函数与该函数微分多项式分担值的情况进行研究,得出亚纯函数的正规性.已知定理:设F为区域D上的全纯函数族,k为正整数,a,b,c和d为有穷复数,b≠0,c≠0且b≠a,若对f∈F,f-d的零点重级至少为k,f=0f(k)=a且f(k)=bf=c. 则F在D上正规.本文将这个定理推广到亚纯函数情形,并且将f(k)用f的微分多项式来代替,结论仍成立.     

校正高频天波雷达电离层频率调制的级联方法(英文)

电离层频率调制导致地表面杂波的多谱勒展宽,极大地限制了高频天波雷达的目标探测性能。本文针对这种电离层频率调制,给出了一种级联的两步校正处理的方法。在第一步校正中,首先分析这种时变信号的时频分布,并设计了一种谱峰追踪方法从时频分布中获得粗糙的电离层频率调制估计。然后采用基于分段多项式相位模型的参数化方法作二次校正处理,消除残余调制污染。模拟结果表明,即使对Bragg峰发生混叠的重污染的情形,这种级联的校正方法都具有非常好的效果。