We establish global rates of convergence of the Maximum Likelihood Estimator (MLE) of a multivariate distribution function on ℝ d in the case of (one type of) "interval censored" data. The main finding is that the rate of convergence of the MLE in the Hellinger metric is no worse than n-1/3(log n)γ for γ = (5d - 4)/6.

We propose a classical (nonBayesian) Laplace estimator alternative for a large class of 3 p n–consistent estimators, including isotonic density and regression estimators, inverse density and regression estimators, the maximum score and mode regression estimators, and interval censoring and monotone hazard rate estimators. The proposed alternative provides a unified method of smoothing that appl...

the present study aimed to assess changes in resting and maximum heart rates as primary indicators of cardiac autonomic function in metabolic syndrome (mets) patients and to determine their value for discriminating mets from non-mets. 468 participants were enrolled in this cross-sectional study and assessed according to the updated adult treatment panel iii (atp-iii) definition of mets. resting...

Bounds for the bracketing entropy of the classes of bounded k-monotone functions on [0, A] are obtained under both the Hellinger distance and the L(p)(Q) distance, where 1 ≤ p < ∞ and Q is a probability measure on [0, A]. The result is then applied to obtain the rate of convergence of the maximum likelihood estimator of a k-monotone density.

The distribution of an inhomogeneous Wiener process is determined by the mean function m(t) ss EW(t) and the variance function b(t) = V^(W(t)) which depend on unknown parameter d _ 0 . Observations are assumed to be in discrete time points where the sample size tends to infinity. Using the general theory of Ibragimow, Hasminskij [2] sufficient conditions for consistency of MLE i?n are establish...

This paper presents improved relaxed stabilization conditions and design procedures of state observer based controllers for continuous nonlinear systems in T-S model representation. First, the T-S model approach for nonlinear systems and some stabilization results are recalled. New stabilization conditions are obtained by relaxing those derived in previous works in this field. The asymptotic an...

Two maximization problems of Rényi entropy rate are investigated: the maximization over all stochastic processes whose marginals satisfy a linear constraint, and the Burg-like maximization over all stochastic processes whose autocovariance function begins with some given values. The solutions are related to the solutions to the analogous maximization problems of Shannon entropy rate.