Principe d'Oka-Grauert dansA ∞

Sans résumé     

A statistical approach to the solution of ill-posed problems in geophysics

The article surveys the main results of the statistical approach to the solution of ill-posed problems of mathematical physics, in application to specific ill-posed inverse problems in geophysics.Invited paper presented at the International Seminar on Mathematical Foundations of the Interpretation of Geophysical Fields, Moscow, May–June 1972.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 79, pp. 67–81, 1978.     

The components of chi-squared statistics for goodness-of-fit tests

One obtains a formula for the transformation of a vector with a given covariance matrix. The sum of the squares of the components of the transformed vector is equal to a chi-square type quadratic form, constructed with the aid of the initial vector. Taking into account this property, one finds the components of the Pearson statistic, Pearson-Fisher statistic, etc.Translated from Veroyatnostnye Raspredeleniya i Matematicheskaya Statistika, pp. 337–350, 1986.