The Almon Liu-Type M-Estimator for the Distributed Lag Models in the Presence of Multicollinearity and Outliers

Nasir Ali; Muhammad Aslam; Abdul Majid; Muhammad Imdad Ullah

doi:10.64060/JASR.v1i3.3

Authors

Nasir Ali Higher Education Department, Lahore, Pakistan Author https://orcid.org/0009-0000-9233-569X
Muhammad Aslam Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan Author https://orcid.org/0000-0003-2290-2307
Abdul Majid Pakistan Bureau of Statistics, Regional Office Multan, Pakistan. Author https://orcid.org/0000-0002-3071-2610
Muhammad Imdad Ullah Department of Statistics, Ghazi University Dera Ghazi Khan, Pakistan Author https://orcid.org/0000-0002-1315-491X

DOI:

https://doi.org/10.64060/JASR.v1i3.3

Keywords:

Ordinary Least squares, distributed lag models, Almon Estimator, Robust Estimation

Abstract

The Almon method is widely used for the estimation of the distributed lag models (DLM). The advantage of using the Almon technique lies in its capability to avoid some serious problems that may arise from the direct application of ordinary least squares (OLS). In the Almon technique, the OLS procedure is applied on transformed regressors, and these regressors correlate themselves leading to the problem of multicollinearity. Moreover, in the presence of outliers in the y-direction, the Almon estimator (AE) may become sensitive. The presence of multicollinearity and outliers jointly in the dataset can strongly distort the AE, leading to the unreliable estimation of the lagged coefficients. We propose the Almon Liu-type M-estimator (ALTME) to address the joint issue of multicollinearity and outliers in y-direction. To show that the proposed estimator has an advantage over the AE, the Almon M-estimator (AME), and the Almon ridge M-estimator (ARME), the Monte Carlo Simulation and two real-life numerical examples are given.

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References

Almon, S. (1965). The distributed lag between capital appropriations and expenditures. Econometrica: Journal of the Econometric Society, 178-196.

Ertaş, H. (2017). A modified ridge m-estimator for linear regression model with multicollinearity and outliers. Communications in Statistics - Simulation and Computation, 47(4), 1240-1250. https://doi.org/10.1080/03610918.2017.1310231

Ertaş, H., Kaçıranlar, S., & Güler, H. (2017). Robust Liu-type estimator for regression based on M-estimator. Communications in Statistics-Simulation and Computation, 46(5), 3907-3932.

Ertaş, H., Toker, S., & Kaçıranlar, S. (2015). Robust two parameter ridge M-estimator for linear regression. Jour-nal of Applied Sta-tistics, 42(7), 1490-1502. https://doi.org/10.1080/02664763.2014.1000577

Fair, R. C., & Jaffee, M. (1971). A note on the estimation of polynomial distributed lags. Princeton University.

Frost, P. A. (1975). Some properties of the Almon lag technique when one searches for degree of polynomial and lag. Journal of the American Statistical Association, 70(351a), 606-612.

Güler, H., Gültay, B., & Kaçiranlar, S. (2017). Comparisons of the alternative biased estimators for the distributed lag models. Communications in Statistics-Simulation and Computation, 46(4), 3306-3318.

Gültay, B., & Kaçiranlar, S. (2015). Mean square error comparisons of the alternative estimators for the distribut-ed lag models. Hacettepe Journal of Mathematics and Statistics, 44(5), 1215-1233.

Hoerl, A. E., & Kennard, R. W. (1970). Ridge regression: Biased estimation for nonorthogonal problems. Tech-nometrics, 12(1), 55-67. https://doi.org/10.1080/00401706.1970.10488634

Huber, P. (1981). Robust statistics. John Wiley and Sons.

Judge, G. G., Griffiths, W. E., Hill, R. C., & Lutkepohl, H. (1980). Lee, Tsoung-Chao. The Theory and Practice of Econometrics. New York: John Wiley and Sons.

Kibria, B. M. G. (2003). Performance of some new ridge regression estimators. Communications in Statistics-Simulation and Com-putation, 32(2), 419-435.

Kibria, B. M. G. (2022). More than hundred (100) estimators for estimating the shrinkage parameter in a linear and generalized linear ridge regression models. Journal of Econometrics and Statistics, 2(2), 233-252.

Liu, K. (2003). Using Liu-type estimator to combat collinearity. Communications in Statistics-Theory and Meth-ods, 32(5), 1009-1020.

Lukman, A, and Kibria, B. M. G. (2021). Almon-KL estimator for the Distributed Lag Model. Arab Journal of Basic and Ap-plied Sciences, 28(1), 406-412.

Maddala, G. S. 1977. Econometrics. New York: McGraw-Hill.

Majid, A., & Aslam, M. (2023). The Almon M-estimator for the distributed lag model in the presence of outli-ers. Communications in Statistics-Simulation and Computation, 52(7), 3273-3285.

Majid, A., Aslam, M., Ahmad, S., Altaf, S., & Afzal, S. (2024). Robust estimation of the distributed lag model with multicolline-arity and outliers. Communications in Statistics-Simulation and Computation, 53(8), 3933-3947.

Månsson, K., Shukur, G., & Kibria, B. M. G. (2010). A simulation study of some ridge regression estimators un-der different distri-butional assumptions. Communications in Statistics - Simulation and Computation, 39(8), 1639-1670. https://doi.org/10.1080/03610918.2010.508862

Özbay, N. (2019). Two-parameter ridge estimation for the coefficients of Almon distributed lag model. Iranian Journal of Science and Technology, Transactions A: Science, 43, 1819-1828.

Özbay, N., & Kaçıranlar, S. (2016). The Almon two parameter estimator for the distributed lag models. Journal of Statistical Compu-tation and Simulation, 87(4), 834-843. https://doi.org/10.1080/00949655.2016.1229317

Özbay, N., & Kaçıranlar, S. (2017). The Almon two parameter estimator for the distributed lag models. Journal of Statistical Compu-tation and Simulation, 87(4), 834-843.

Qasim, M., Amin, M., & Omer, T. (2020). Performance of some new Liu parameters for the linear regression model. Communica-tions in Statistics-Theory and Methods, 49(17), 4178-4196.

Silvapulle, M. J. (1991). Robust ridge regression based on an M‐estimator. Australian Journal of Statistics, 33(3), 319-333.