×
Kucuk, Serenay; Asikgil, Baris

A novel hybrid robust tapering approach for nonlinear regression in the presence of autocorrelation and outliers. (English) Zbl 07793004

Commun. Stat., Simulation Comput. 52, No. 11, 5550-5566 (2023).
Summary: Nonlinear models are commonly used for analyzing real-life data such as in medicine, engineering, and economics. To make efficient inferences about model parameter estimations and statistical results in nonlinear regression, assumptions related to error term are needed to be satisfied. Ordinary least squares and some modified least squares methods fail to give efficient parameter estimates when there are the problems of autocorrelation and outlier together in nonlinear regression. In this study, a novel hybrid robust tapering approach called as robust modified two-stage least squares is proposed to overcome the problems for obtaining more efficient parameter estimates in nonlinear regression. Two numerical examples and a comprehensive Monte-Carlo simulation study are given in order to examine the performance of robust modified two-stage least squares.

MSC:

62-XX Statistics

Keywords:

autocorrelation; nonlinear regression; outlier; robust modified two-stage least squares; tapering

Software:

nlmdl
Cite Review PDF
Full Text: DOI

References:

[1] Aşıkgil, B.; Erar, A., Polynomial tapered two-stage least squares method in nonlinear regression, Applied Mathematics and Computation, 219, 18, 9743-54 (2013) · Zbl 1290.62048 · doi:10.1016/j.amc.2013.03.088
[2] Bates, D. M.; Watts, D. G., Nonlinear regression analysis and its applications (1988), New York: John Wiley and Sons, New York · Zbl 0728.62062
[3] Brockwell, P. J.; Dahlhaus, R., Generalized Levinson-Durbin and Burg algorithms, Journal of Econometrics, 118, 1-2, 129-49 (2004) · Zbl 1033.62091 · doi:10.1016/S0304-4076(03)00138-6
[4] Gallant, A. R., Nonlinear statistical models (1987), New York: Wiley, New York · Zbl 0611.62071
[5] Gallant, A. R.; Goebel, J. J., Nonlinear regression with autocorrelated errors, Journal of the American Statistical Association, 71, 356, 961-7 (1976) · Zbl 0337.62046 · doi:10.2307/2286869
[6] Grynovicki, J.; Thomas, J., Robust regression: A diagnostic tool (2013), Maryland: Aberdeen Proving Ground, Maryland
[7] Hampel, F. R., The influence curve and its role in robust estimation, Journal of the American Statistical Association, 69, 346, 383-93 (1974) · Zbl 0305.62031 · doi:10.1080/01621459.1974.10482962
[8] Hampel, F. R.; Ronchetti, E. M.; Rousseeuw, P. J.; Stahel, W. A., Robust statistics: The approach based on influence functions (1986), New York: John Wiley and Sons, New York · Zbl 0593.62027
[9] Huber, P. J., Robust statistical procedures (1977), Philadelphia: Society for Industrial and Applied Mathematics, Philadelphia · Zbl 0367.62057
[10] Kucuk, S., Robust estimation methods in nonlinear regression in presence of autocorrelation and outlier (2020)
[11] Montgomery, D. C.; Peck, E. A.; Vining, G. G., Introduction to linear regression analysis (2012), New York: John Wiley and Sons, New York · Zbl 1274.62016
[12] Riazoshams, H.; Midi, H.; Sharipov, O., The performance of robust two-stage estimator in nonlinear regression with autocorrelated error, Communications in Statistics - Simulation and Computation, 39, 6, 1251-68 (2010) · Zbl 1195.62112 · doi:10.1080/03610918.2010.490316
[13] Rousseuw, P. J.; Yohai, V. J.; Franke, J.; Härdle, W.; Martin, vol., D., Robust and nonlinear time series analysis, lecture notes in statistics, 26, Robust regression by means of S-estimator, 256-72 (1984), New York: Springer-Verlag, New York · Zbl 0567.62027 · doi:10.1007/978-1-4615-7821-5_15
[14] Seber, G. A. F.; Wild, C. J., Nonlinear regression (1989), New York: John Wiley and Sons, New York · Zbl 0721.62062
[15] Yohai, V. J., High breakdown point and high efficiency robust estimator regression, The Annals of Statistics, 15, 2, 642-56 (1987) · Zbl 0624.62037 · doi:10.1214/aos/1176350366
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.