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A Computationally Efficient Algorithm to Solve Generalized Method of Moments Estimating Equations Based on Secant Procedure
Naushad Ali Mamode Khan, M. Heenaye
Pages - 28 - 33     |    Revised - 01-07-2011     |    Published - 05-08-2011
Volume - 2   Issue - 1    |    Publication Date - July / August 2011  Table of Contents
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KEYWORDS
Newton-Raphson, Jacobian, Quadratic Inference Function
ABSTRACT
Generalized method of moment estimating function enables one to estimate regression parameters consistently and efficiently. However, it involves one major computational problem: in complex data settings, solving generalized method of moments estimating function via Newton-Raphson technique gives rise often to non-invertible Jacobian matrices. Thus, parameter estimation becomes unreliable and computationally inefficient. To overcome this problem, we propose to use secant method based on vector divisions instead of the usual Newton-Raphson technique to estimate the regression parameters. This new method of estimation demonstrates a decrease in the number of non-convergence iterations as compared to the Newton-Raphson technique and provides reliable estimates.
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1 Makkar, S. R., Williamson, A., Turner, T., Redman, S., & Louviere, J. (2015). Using conjoint analysis to develop a system to score research engagement actions by health decision makers. Health Research Policy and Systems, 13(1), 22.
2 Zhaoming Tao, & Xu Xiaoli. (2014). Quadratic function of longitudinal data to infer semi parametric model estimates. Statistics and Decision, (7), 8-10.
3 Zhaoming Tao, & Xu Xiaoli. (2014). Penalty semiparametric longitudinal model of quadratic inference function estimation. Statistics and Information Forum, 29 (8), 3-8.
4 Zhaoming Tao, & Xiao group. (2013). Longitudinal data non-punitive model parameters correction quadratic inference function estimation. Mathematics in Practice and Theory, 5, 031.
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Dr. Naushad Ali Mamode Khan
University of Mauritius - Mauritius
n.mamodekhan@uom.ac.mu
Dr. M. Heenaye
- Mauritius