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Rank method of parameter estimation for regression models

Student: Efim Botvinkin

Supervisor: Elena R. Goryainova

Faculty: School of Applied Mathematics and Information Science

Educational Programme: Bachelor

Final Grade: 9

Year of Graduation: 2014

<p>This paper considers the rank method of parameter estimation for linear regression models. This method is compared with two main alternative techniques of parameter estimation, namely the method of least squares and the method of least absolute deviations, in terms of estimation efficiency in regression models with different distributions of errors. Tasks that are carried out in this paper are as follows: to describe the rank method of parameter estimation in regression models and to offer the technique of approximate calculation of rank parameter estimations; to consider different distributions of random variables and techniques of their simulation; to perform numerical experiments on accuracy of rank parameter estimations, LS-estimations and LAD-estimations in simulated linear regression models with defined parameters and distributions of noises; to calculate asymptotical relative efficiencies of rank estimations in comparison with LS-estimations and LAD-estimations; to give an example of applying the rank method of parameter estimation to a linear regression model based on real data and to compare resistances of the rank parameter estimation, the LS- and the LAD-estimations to an outlier in data. Numerical experiments allow us to make conclusions about efficiency of estimations, provided by aforementioned methods, for regression models with relatively small number of observations. Calculations of asymptotic relative efficiency allow us to make such conclusions for models with quite large number of observations. There are given some recommendations, based on these conclusions, about application of compared methods of parameter estimation. Basic research methods are as follows: methods of the probability theory and the mathematical statistics, methods of computer simulation and optimization methods. This paper provides conclusions on what distributions of noises in models make the rank method of parameter estimation superior for both the case with relatively small number of observations in models and the case with quite large number of observations. There is also made a general conclusion on applicability of the rank method in tasks of estimation of unknown parameters of models.</p>

Full text (added June 5, 2014) (376.93 Kb)

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