Properties of integral least squares method

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 minimize squared deviations and are equivalent to means of the probability distribution = = ∫β _i F(β₁, β₂, ..., β _k ; φ₁, ..., φ _m )dβ₁ dβ₂...dβ _k . Original Russian Text ? I.D. Gorlachev, B.B. Knyazev, A. Kuketayev, F.M. Pen’kov, 2009, published in Izvestiya Rossiiskoi Akademii Nauk. Seriya Fizicheskaya, 2009, Vol. 73, No. 2, pp. 257–260.