This paper develops a logistic approximation to the cumulative normal distribution. Although the literature contains a vast collection of approximate functions for the normal distribution, they are very complicated, not very accurate, or valid for only a limited range. This paper proposes an...

Estimation of the signal function defined on the unit sphere of the Euclidean space is considered. Gaussian continuous time white noise model is supposed. Uniform norm is chosen as a loss function and exact asymptotic minimax risk is derived extending the result of Korostelev (1993. The exact...

This paper develops a logistic approximation to the cumulative normal distribution. Although the literature contains a vast collection of approximate functions for the normal distribution, they are very complicated, not very accurate, or valid for only a limited range. This paper proposes an...

The Minimax criterion is considered as an alternative to the least-squares method in determination of principal components Estimated coefficients are formulated as linear programming problem The offered approach was experimentally checked using well known test data sets On these data sets the...

We study the Bayes estimation of an infinite dimensional parameter from a Sobolev smoothness class. We propose a family of sieve priors whose resulting Bayes estimators are adaptive optimal, both in posterior concentration rate and in risk convergence for the inherent distance of the model,...