摘要:

A special class of change-point models, where the change is defined as a shift of observations means, is considered. We show that such models can be transformed into a nonlinear regression problem. It is proven thatM-estimators can localize the change point, and at the same time, consistently estimate the unknown parameters characterizing the change behavior. For a special class of continuous models we prove an asymptotic normality ofM-estimators simultaneously estimating the change-point and the related parameters.

ISSN:0233-1888    

DOI:10.1080/02331889708802609

出版商:Gordon & Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

To deal with heteroskedasticity of unknown form, this paper suggests to robustly estimate the regression coefficients and then to implement an heteroskedasticity consistent covariance matrix estimator. The robust regression reduces the sample bias of the heteroskedasticity consistent covariance matrix estimator, and does not require the specification of a functional form for heteroskedasticity. Indeed, it replaces each variance with the squared errors, which are in turn estimated by the squared residuals from the robust regression. A Monte-Carlo study verifies the behavior of the proposed estimator, using real data.

ISSN:0233-1888    

DOI:10.1080/02331889708802610

出版商:Gordon & Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

The consistency and the asymptotic normality of the least squares estimators are derived of the sinusoidal model under the assumption of stationary random error. It is observed that the model does not satisfy the standard sufficient conditions of Jennrich (1969), Wu (1981) or Kundu (1991). Recently the consistency and the asymptotic normality are derived for the sinusoidal signal under the assumption of normal error (Kundu; 1993) and under the assumptions of independent and identically distributed random variables in Kundu and Mitra (1996). This paper will generalize them. Hannan (1971) also considered the similar kind of model and establish the result after making the Fourier transform of the data for one parameter model. We establish the result without making the Fourier transform of the data. We give an explicit expression of the asymptotic distribution of the multiparameter case, which is not available in the literature. Our approach is different from Hannan's approach. We do some simulations study to see the small sample properties of the two types of estimators.

ISSN:0233-1888    

DOI:10.1080/02331889708802611

出版商:Gordon & Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

The sample quartiles, which are common in robust inference and nonparametric statistics, have many prevailing definitions, all with the same asymptotic distribution. In this note we examine the higher order terms in the asymptotic expansions for the bias, variance and M.S.E. of the commonly used quartiles, defined as the linear interpolant of two adjacent order statistics. The expansions are used to develop simple improvements of the interpolation based definition by removing theO(n-1) term in the bias and by minimizing the variance and M.S.E. up to orderO(n-2). It is noted that the variances of the traditional quartiles, instead of decreasing monotonically as the sample size increases, exhibit a periodic behavior. This is analogous to a property of sample medians observed by Hodges (1967), and discussed by Hodges and Lehmann (1967).

ISSN:0233-1888    

DOI:10.1080/02331889708802612

出版商:Gordon & Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

Moments of arbitrary order for the inverted Wishart distribution are obtained with the help of a factorization theorem, moments for normally distributed variables and inverse moments for chi-squared variables. Expressions are given in a recursive as well as a non-recursive manner.

ISSN:0233-1888    

DOI:10.1080/02331889708802613

出版商:Gordon & Breach Science Publishers    

年代:1997

数据来源: Taylor

ISSN:0233-1888    

DOI:10.1080/02331889708802608

出版商:Gordon & Breach Sceince Publishers    

年代:1997

数据来源: Taylor