Robust Estimation of Engineering Parameters

Abstract eng:
In the estimation of various engineering parameters as well as in establishing empirical relationships among them the least squares regression analysis is widely used. In certain cases maximum likelihood (ML) method is also utilized. The estimation of the parameters of Richter's magnitude-frequency relationship, development of magnitude conversion equations, relationship between compression index and void ratio of soils, relationship between modulus of elasticity and strength of timber are some examples for such applications. However, in implementing these statistical methods, engineers very seldom check the validity of the underlying assumptions with respect to the available data. This may lead to serious errors if the normality assumption, which is an underlying assumption of classical regression, is not valid. Under non-normality, least squares estimators (LSEs) are neither efficient nor robust (Akkaya and Tiku, 2008). On the other hand, the likelihood equations obtained in the ML method involve nonlinear functions and are very difficult to solve even iteratively due to some convergence problems. Here we propose the use of the modified maximum likelihood (MML) method for the estimation of parameters in cases where least squares and/or maximum likelihood estimation methods are commonly used. In order to demonstrate the application of the MML method, the parameters of the quadratic magnitude-frequency relationship are derived when the error distribution is non-normal. Here the preference of the quadratic magnitude-frequency relationship is due to the fact that it is more realistic and can easily be reduced to the linear one. For the numerical application of the MML method the most active segment of the North Anatolian Fault Zone is analyzed.

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