Trigonometric regression estimation for observations with additive and multiplicative errors
Waldemar Popiński · Communication in Statistics- Theory and Methods · 2015
The problem of non parametric function fitting using the complete orthogonal system of trigonometric functions em, m = 0, ±1, ±2, …, for the observation model yj = djf(xjn) + ηj, j = 0, 1, …, n − 1, is considered, where , ηj are uncorrelated random variables with zero mean value and finite variance, dj are uncorrelated random variables with mean value d ≠ 0 and finite variance, independent of ηj, and the observation points xjn ∈ [0, 2π] are equidistant. Conditions for convergence of the integrated mean-square error and the pointwise mean-square error of the estimator for f ∈ BV[0, 2π] and coefficients obtained by the least squares method are studied.