Adaptive Estimation of Periodic Regression Model in Short Panel Data


Abstract


This paper proposes the use of the adaptive estimation method for estimating the periodic regression parameters in short panel data. This will go through three phases. The first phase aims to show that the periodic regression model verifies the Uniform Local Asymptotic Normality (ULAN), the second phase focuses on constructing the local asymptotically Minimax (LAM) estimators, and the last phase deals with constructing the Adaptive Estimators (AE) of the periodic regression model using the results of phase one and phase two. The results obtained in the simulation show that the Adaptive Estimator is always better than the Least Squares Estimator. The AE is more efficient in the case of an asymmetric score function. Real data are used to compare the two methods and show that the periodic coefficient regression model outperforms both traditional regression and random regression models.

Keywords: Periodic regression model; Panel data; Locally asymptotically minimax estimators; Uniform local asymptotic normality; Adaptive estimators

References


Akharif, A., Fihri, M., Hallin, M., and Mellouk, A. (2020). Optimal pseudo-gaussian and rank-based random coefficient detection in multiple regression.

Allal, J. and El Melhaoui, S. (2006). Tests de rangs adaptatifs pour les modèles de régression linéaire avec erreurs arma. In Annales des sciences mathématiques du Québec, volume 30, pages 29–54.

Bentarzi, M., Guerbyenne, H., and Merzougui, M. (2009). Adaptive estimation of causal periodic autoregressive model. Communications in Statistics-Simulation and Computation, 38(8):1592–1609.

Beran, R., Feuerverger, A., and Hall, P. (1996). On nonparametric estimation of intercept and slope distributions in random coefficient regression. The Annals of Statistics, 24(6):2569–2592.

Fabian, V. and Hannan, J. (1982). On estimation and adaptive estimation for locally asymptotically normal families. Zeitschrift fur Wahrscheinlichkeitstheorie und verwandte Gebiete, 59(4):459–478.

Fihri, M., Akharif, A., Mellouk, A., and Hallin, M. (2020). Efficient pseudo-gaussian and rank-based detection of random regression coefficients. Journal of Nonparametric Statistics, 32(2):367–402.

Franses, P. H. and Paap, R. (1994). Model selection in periodic autoregressions. Oxford Bulletin of Economics and Statistics, 56(4):421–439.

Ghysels, E. (1994). On the periodic structure of the business cycle. Journal of Business & Economic Statistics, 12(3):289–298.

Goto, Y., Suzuki, K., Xu, X., and Taniguchi, M. (2023). Tests for the existence of group effects and interactions for two-way models with dependent errors. Annals of the Institute of Statistical Mathematics, 75(3):511–532.

Kreiss, J.-P. (1987). On adaptive estimation in stationary arma processes. The Annals of Statistics, pages 112–133.

LeCam, L. (1960). Locally asymptotically normal families of distributions. Univ. California Publ. Statist., 3:37–98.

Ling, S. (2003). Adaptive estimators and tests of stationary and nonstationary short and long-memory ARFIMA-GARCH models. Journal of the American Statistical Association, 98(464):955–967.

Linton, O. (1993). Adaptive estimation in ARCH models. Econometric Theory, 9(4):539–569.

Lmakri, A., Akharif, A., and Mellouk, A. (2020). Optimal detection of bilinear dependence in short panels of regression data. Revista Colombiana de Estad´ıstica, 43(2):143–171.

Newbold, P. and Bos, T. (1985). Stochastic parameter regression models, beverly hills, ca: Sage publications.

Ou Larbi, Y., El Halimi, R., Akharif, A., and Mellouk, A. (2021). Optimal tests for random effects in linear mixed models. Hacettepe Journal of Mathematics and Statistics, 50(4):1185–1211.

Regui, S., Akharif, A., and Mellouk, A. (2024). Locally optimal tests against periodic linear regression in short panels. Communications in Statistics-Simulation and Computation, pages 1–15.

Zhu, S., Nyarko, E. K., and Hadzima-Nyarko, M. (2018). Modelling daily water temperature from air temperature for the missouri river. PeerJ, 6:e4894.


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