A suboptimal filter to estimate a signal corrupted by a white noise, derived from the approximative Karhunen-Lo6ve expansion of the signal, is given. The convergence of the suboptimal filter is showed and a bound on the truncation error is found.

a class of new methods based on a septic non-polynomial spline function for the numerical solution one-dimensional bratu's problem are presented. the local truncation errors and the methods of order 2th, 4th, 6th, 8th, 10th, and 12th, are obtained. the inverse of some band matrixes are obtained which are required in proving the convergence analysis of the presented method. associated bound...

We investigate the parametric maximum likelihood estimator for truncated data when the truncation value is different according to the observed individual or item. We extend Lehmann’s proof (1983) of the asymptotic properties of the parametric maximum likelihood estimator in the case of independent non-identically distributed observations. Two cases are considered: either the number of distinct ...