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Polynomial tapered two-stage least squares method in nonlinear regression. (English) Zbl 1290.62048
Summary: Nonlinear models play an important role in various scientific disciplines and engineering. The parameter estimation of these models should be efficient to make better decisions. Ordinary least squares (OLS) method is used for estimating the parameters of nonlinear regression models when all regression assumptions are satisfied. If there is a problem with these assumptions, OLS fails to give efficient results. This paper examines the efficiency of parameter estimation under the problem of autocorrelated errors. Some methods have been proposed in order to overcome the problem and obtain efficient parameter estimates especially for autoregressive (AR) processes. One of the most commonly used method is two-stage least squares (2SLS). This method is based on generalized least squares. In this paper, a novel approach is proposed for 2SLS method by evaluating a polynomial tapering procedure on autocorrelated errors. This new method is called tapered two-stage least squares (T2SLS). The finite sample properties and improvements of T2SLS are explored by means of some real life examples and a Monte Carlo simulation study. Both numerical and experimental results reveal that T2SLS can give more efficient parameter estimates especially in small samples under the autocorrelation problem when compared to OLS and 2SLS.

MSC:
62J02 General nonlinear regression
62J12 Generalized linear models (logistic models)
62L12 Sequential estimation
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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