Abstract: b value in the relation between magnitude and frequency is calculated by using robust regression of M estimation and choosing function j as normal density type function. The difference between the results obtained by the methods of robust estimation and least square estimation is also discussed in the paper. It is considered that the b value obtained by robust estimation is more suitable for the dimension proportion in the relation between magnitude and frequency, and it can be used as a reliable background value. As an appli-cation ex ample, the b value of Xinjiang region has been scanned spatially and temporally, and the difference between b value of least square estimation and robust estimation is de-fined and used as a discriminant index for precursors of moderate and strong earthquakes. Through discussion on anomalies appeared before earthquakes with M≥ 6 which have oc-curred in Karshi-Barchu area since 1980, we think that the index indirectly reflects the di-mension-declining process and has certain practical meaning.

Key words: Relation between magnitude and frequency, Ro bust estimation, Devia-tion degree of b value