Abstract
In this paper we study a special class of minimum distance estimators, based on nonparametric pilot estimators of the regression function, for a parameter θ ∈ Θ ⊂ R p of a linear regression model of the type Y = Xθ + ε, where X is the design matrix, Y the vector of the response variable and ε the random error vector that follows an AR(1) correlation structure. These estimators are asymptotically analyzed, by proving their strong consistency, asymptotic normality and asymptotic efficiency. In a simulation study, a better behaviour of the Mean Squared Error of the proposed estimator with respect to that of the generalized least squares estimator is observed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Akritas, M.G., (1996), On the Use of Nonparametric Regression Techniques for Fitting Parametric Regression Models, Biometrics, 52, 1342–1362.
Amemiya, T., (1973), Generalized least squares with an estimated autocovariance matrix, Econometrica 41, 713–732.
Amemiya, T., (1989), Advanced Econometrics (Oxford, Blackwell).
Cristobal, J.A., P. Faraldo and W. Gonzalez-Manteiga, (1987), A class of linear regression parameter estimators constructed by nonparametric estimation. Annals of Statistics, 15, 603–609.
Gasser, T. and H.G. Muller, (1979), Kernel estimation of regression functions, Smoothing techniques for curve estimation, Lecture Notes in Mathematics, n. 757, 23–68 (Springer-Verlag, Berlin).
Georgiev, A.A., (1988), Consistent nonparametric multiple regression: smoothing in linear regression: the fixed design case, Journal of Multivariate Analysis, 25, 100–110.
Gonzalez-Manteiga, W., (1995), Smooth linear regression using sample determined bandwidth. Sankhya, Ser. A, 57, part 1, 79–87.
Judge, G.G., R.C. Hill, W.E. Griffiths, H. Lutkepohl and T.C. Lee, (1988), Introduction to the theory and practice of Econometrics (Second edition, Wiley).
Pham, T.D. and Iran, L.T., (1985), Some mixing properties of time series models, Stochastic processes and their Applications, 19, 297–303.
Roussas, G.G., (1989), Consistent regression estimation with fixed design points under dependence conditions, Statistics & Probability Letters, 8, 41–50.
Roussas, G.G. and D. Ioannides, (1987), Moment inequalities for mixing sequences of random variables. Stochastic Analysis and Applications, 5(1), 61–120.
Seber, G.A.F., (1977), Linear Regression Analysis, Wiley, New York.
Stute, W., (1995), Bootstrap of a linear model with AR-error structure, Metrika, 42, 395–410.
Stute, W. and W. Gonzalez-Manteiga, (1990), Nearest neighbour smoothing in linear regression, Journal of Multivariate Analysis, 34, 1, 61–74.
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
About this article
Cite this article
Fernández, J.M.V., Manteiga, W.G. Generalized minimum distance estimators of a linear model with correlated errors. Statistical Papers 42, 353–373 (2001). https://doi.org/10.1007/s003620100063
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s003620100063