Nonlinear regression in the presence of autocorrelated errors

Goebel, J. Jeffery

doi:10.31274/rtd-180813-614

Cited by 1 publication

(1 citation statement)

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“…The most difficult issue is that of the estimation of P. In the aforementioned paper of Grossman (1979), this was dealt with, in the case that the errors follow an autoregressive process, by using a stepwise procedure which involved estimating the parameters and spectral density iteratively. Hannan (1971) and Goebel (1974) use a circular symmetric matrix to approximate P, and estimate the approximating matrix by first estimating the spectral density of the generating series.…”

Section: Construction and Asymptotic Properties Of The Estimatormentioning

confidence: 99%

One‐step M‐estimators in the linear model, with dependent errors

Field

Wiens

1994

Can J Statistics

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We consider the problem of robust M-estimation of a vector of regression parameters, when the errors are dependent. We assume a weakly stationary, but otherwise quite general dependence structure. Our model allows for the representation of the correlations of any time series of finite length.We first construct initial estimates of the regression, scale, and autocorrelation parameters. The initial autocorrelation estimates are used to transform the model to one of approximate independence. In this transformed model, final one-step M-estimates are calculated.Under appropriate assumptions, the regression estimates so obtained are asymptotically normal, with a variance-covariance structure identical to that in the case in which the autocorrelations are known (I priori. The results of a simulation study are given. Two versions of our estimator are compared with the L,-estimator and several Huber-type M-estimators. In terms of bias and mean squared error, the estimators are generally very close. In terms of the coverage probabilities of confidence intervals, our estimators appear to be quite superior to both the 151-estimator and the other estimators. The simulations also indicate that the approach to normality is quite fast. RESUMENous considirons le probkme de M-estimation robuste pour un vecteur de parambtres de rtgression, lorsque les erreurs sont dependantes. Nous supposons une stationnaritt faible, rnais autrement une structure de dtpendance plut6t gtntrale. Notre modde permet la representation des corrtlations de n'importe quelle sine chronologique de longueur finie.Tout d'abord, nous construisons des estimateurs initiaux des paramkres de rtgression, d'tchelle et d'autocorrelation. Les estimateurs initiaux d'autocorr6lation sont utilists afin de transformer le modkle en un modtle avex indtpendance approximative. Les M-estimateurs finaux son1 calculks avec ce modsle transform&.Sous des hypothbses approprikes, les estimateurs de rkgression ainsi obtenus son1 asymptotiquement normaux, avec une structure de variance/covariance identique B celle lorsque les autocorrtlations sont connues a priori. Nous donnons les rtsultats d'une ttude de simulation. Nous comparons deux versions de notre estimateur avec I'estimateur L , et plusieurs M-estimateurs de type Huber. Les estimateurs sont gkneralement trks proches sur le plan du biais et de l'erreur quadratique moyenne. Nos estimateurs sont sup6rieurs B I'estimateur LI et aux autres estimateurs sur le plan des probabilites de couverture des intervalles de confiance. Nos simulations indiquent aussi que la convergence vers la normale est trks rapide.

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Section: Construction and Asymptotic Properties Of The Estimatormentioning

confidence: 99%