Estimation of regression model parameter under heteroskedasticity of an unknown form
The paper considers the problem of estimating linear regression model parameters under heteroscedasticity conditions. Constructing the model assumes that the variance of a random error depends on several factors (e.g. one of the model input factors or some external factor). It is assumed that all the source data can be split into sections of equal dispersion. The proposed approach permits us to reduce the regression model with these assumptions to a structured error model. Constructing the model assumes that the covariance matrix of an error is a linear combination of known matrices with unknown coefficients. These known matrices are diagonal matrices and are formed based on the structure of the input data. The estimation of the model parameters is proposed using the minimum norm quadratic estimates. An algorithm for determining the boundaries of the area of the source data intervals with equal variance is proposed. In this algorithm the test of hypotheses of variance differences at different areas is carried out by using the variance analysis criterion (ANOVA-criterion). Computational experiments showing the efficiency of the algorithm have been conducted by statistical simulation methods. Advice on selecting the best algorithm parameters is given.