Properties of integral least squares method

Abstract

A new modification of the least squares method (LSM) is proposed. The main idea is to consider the fitting parameters β i as independent random variables with a certain distribution density F(β1, β2, ..., β k ; φ1, ..., φ m ), which depends on a set of m experimental points φ j . Within this approach, the estimates of the parameters β^i minimize squared deviations and are equivalent to means of the probability distribution β^i = β¯i = ∫β i F(β1, β2, ..., β k ; φ1, ..., φ m )dβ1 dβ2...dβ k .