Robust Model for the Quadratic Production Function in Presence of High Leverage Points

Rizwan Yousuf¹ , Manish Sharma² , M. Iqbal Jeelani Bhat³ , S.E.H. Rizvi⁴

Section:Research Paper, Product Type: Journal-Paper
Vol.8 , Issue.2 , pp.8-13, Apr-2021

Online published on Apr 30, 2021

Copyright © Rizwan Yousuf, Manish Sharma, M. Iqbal Jeelani Bhat , S.E.H. Rizvi . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

View this paper at   Google Scholar | DPI Digital Library

XML View     PDF Download

How to Cite this Paper

Abstract :
As in the presence of High leverage points (HLP) i.e. outliers, the ordinary least square (OLS) method does not provide the precise and true estimates of production function. In this study, we have used the simulation data to study the behaviour of estimates of quadratic production function in presence of HLP. The HLP were identified through different techniques like Mahanablios distance, Robust minimum covariance determinant (MCD)Distance, Standard robust residuals, Cook’s distance, studentized residual, WSSDI, Hat Diagonals and deleted residuals. The data set is influenced by the influential observations. The Robust techniques viz M estimation, MM estimation, S estimation, LTS estimation and OLS after resolving the issue of HLP have been used. The estimates of the quadratic function have been compared and observed that the influential observations have affected the size, sign and significance of the parameter(s).The LTS estimation found to be the best as compared to the others on the basis of AIC, SBIC and R2.

Key-Words / Index Term :
Outliers, Residuals, , Cook’s distance , OLS, Robust M estimation and LTS estimation

References :
[1] C. Ackello-Ogutu, Q. Paris, W.A. Williams, “Testing a von Liebig Crop Response Function against Polynomial Specifications”. American Journal of Agricultural Economics, Vol.67, pp.873–880, 1985.
[2] R. L. Anderson, L. A. Nelson, “A Family of Models Involving Intersecting Straight Lines and Concomitant Experimental Designs Useful in Evaluating Response to Fertilizer Nutrients”. Biometrics, Vol.31, pp.303–318, 1975.
[3] G.Bélanger, J. R.Walsh, J. E. Richards, P. H. Milburn, N. Ziadi, “Comparison of Three Statistical Models Describing Potato Yield Response to Nitrogen Fertilizer”. Agronomy Journal, Vol.92, pp.902–908,2000
[4] P. Berck, G.Helfand, “Reconciling the von Liebig and Differentiable Crop Production Functions”. American Journal of Agricultural Economics, Vol.72, pp.985–996,1990.
[5] C. Chen (2002), Robust Regression and Outlier Detection with the ROBUSTREG Procedure. Statistics and Data Analysis. Conference paper.
[6] P.J.Huber, “Robust Regression: Asymptotics, Conjectures and Monte Carlo”. The Annals of Statistics, Vol,1,pp.799–821,1973.
[7] P.J.Huber, “Robust Statistical Procedures”.Philadelphia: Society for Industrial and Applied Mathematics.Vol.3,pp.231-241,1996.
[8] Rousseeuw, “Least median of squares Regression”, Journal of the American Statistical Association, Vol.79,871-880,1984
[9] J.E.Sturm, J.De Haan, “How Robust is the Relationship between Economic Freedom and Economic Growth” .In Applied Economics .Vol.33,pp.834-44. 2001.
[10] V J. Yohai, “High breakdown-point and high efficiency robust estimates for regression”. The Annals of Statistics. Vol.pp.15:642-656. 1987.