摘要:

Abstract.Any of the Cramér‐von Mises, Anderson‐Darling, and Kolmogorov‐Smirnov statistics can be used to test the null hypothesis that the standardized spectral distribution of a stationary stochastic process is a specified one. The asymptotic distributions of the criteria have been characterized (Anderson, 1993). They are the same as for probability distributions if the observations are independent (all autocorrelations zero), but are different when there is dependence. In this paper simulation with 10000 replications has been used to determine the distributions of the criteria for samples of size 6, 10, 30 and 100 when the observations are independent. These empirical distributions have been compared with the asymptotic distributions in order to ascertain the sample sizes necessary for using the asymptotic tables. For practical purposes they are 30 for the Cramér‐von Mises and Kolmogorov statistics and over 100 for Anderso

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1996.tb00292.x

出版商:Blackwell Publishing Ltd    

年代:1996

数据来源: WILEY

摘要:

Abstract.The recursive least squares (RLS) estimation algorithm with exponential forgetting is commonly used to estimate time‐varying parameters in stochastic systems. The statistical properties of the RLS estimator are often hard to find, since they depend in a non‐linear way on the time‐varying characteristics. In this paper the RLS estimator with exponential forgetting factor is applied to stationary Gaussian vector autoregres‐sions and the asymptotic bias and covariance function of the parameter estimates are

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1996.tb00293.x

出版商:Blackwell Publishing Ltd    

年代:1996

数据来源: WILEY

摘要:

Abstract.Local high‐order polynomial fitting is employed for the estimation of the multivariate regression functionm(x1,…xd) =E{φ(Yd)φX1=x1,…,Xd=xd}, and of its partial derivatives, for stationary random processes {Yi,Xi}. The functionφmay be selected to yield estimates of the conditional mean, conditional moments and conditional distributions. Uniform strong consistency over compact subsets ofRd, along with rates, are established for the regression function and its partial derivatives for strongly mixing p

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1996.tb00294.x

出版商:Blackwell Publishing Ltd    

年代:1996

数据来源: WILEY

摘要:

Abstract.In the present paper we consider nonlinear wavelet estimators of the spectral densityfof a zero mean, not necessarily Gaussian, stochastic process, which is stationary in the wide sense. It is known in the case of Gaussian regression that these estimators outperform traditional linear methods if the degree of smoothness of the regression function varies considerably over the interval of interest. Such methods are based on a nonlinear treatment of empirical coefficients that arise from an orthonormal series expansion according to a wavelet basis.The main goal of this paper is to transfer these methods to spectral density estimation. This is done by showing the asymptotic normality of certain empirical coefficients based on the tapered periodogram. Using these results we can show the risk equivalence to the Gaussian case for monotone estimators based on such empirical coefficients. The resulting estimator offkeeps all interesting properties such as high spatial adaptivity that are already known for wavelet estimators in the case of Gaussian regression.It turns out that appropriately tuned versions of this estimator attain the optimal uniform rate of convergence of theirL2risk in a wide variety of Besov smoothness classes, including classes where linear estimators (kernel, spline) are not able to attain this rate. Some simulations indicate the usefulness of the new method in cases of high spatial inhomogeneity.

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1996.tb00295.x

出版商:Blackwell Publishing Ltd    

年代:1996

数据来源: WILEY