Barycentre canonique pour un espace métrique à courbure négative
Bayesian like R- and M- estimators of change points
The purpose of this paper is to study Bayesian like R- and M-estimators of change point(s). These estimators have smaller variance than the related argmax type estimators. Confidence intervals for the change point based on the exchangeability arguments are constructed. Finally, theoretical results are illustrated on the real data set.
Behavior of a second class particle in Hammersley's process.
Bernstein inequality for the parameter of the pth order autoregressive process AR(p)
The autoregressive process takes an important part in predicting problems leading to decision making. In practice, we use the least squares method to estimate the parameter θ̃ of the first-order autoregressive process taking values in a real separable Banach space B (ARB(1)), if it satisfies the following relation: . In this paper we study the convergence in distribution of the linear operator for ||θ̃|| > 1 and so we construct inequalities of Bernstein type for this operator.
Berry-Esseen bounds for projections of coordinate symmetric random vectors.
Berry-Esseen bounds for the number of maxima in planar regions.
Berry–Esseen theorem and local limit theorem for non uniformly expanding maps
Berry-Esseen type estimations for multi-sample -statistics.
Berry-Esseen-Type Inequality for a Special Class of Distributions.
Best possible sufficient conditions for strong law of large numbers for multi-indexed orthogonal random elements.
Betti numbers of random real hypersurfaces and determinants of random symmetric matrices
We asymptotically estimate from above the expected Betti numbers of random real hypersurfaces in smooth real projective manifolds. Our upper bounds grow as the square root of the degree of the hypersurfaces as the latter grows to infinity, with a coefficient involving the Kählerian volume of the real locus of the manifold as well as the expected determinant of random real symmetric matrices of given index. In particular, for large dimensions, these coefficients get exponentially small away from...
Billingsley-type tightness criteria for multiparameter stochastic processes
Block distribution in random strings
For almost all infinite binary sequences of Bernoulli trials the frequency of blocks of length in the first terms tends asymptotically to the probability of the blocks, if increases like (for ) where tends to . This generalizes a result due to P. Flajolet, P. Kirschenhofer and R.F. Tichy concerning the case .
Borel methods of summability and ergodic theorems
Passing from Cesàro means to Borel-type methods of summability we prove some ergodic theorem for operators (acting in a Banach space) with spectrum contained in ℂ∖(1,∞).
Bornes pour la distribution limite de la statistique de Shepp
Bounded Laws of the Iterated Logarithm for Quadratic Forms in Gaussian Random Variables.
Bounds on random infinite urn model.
Bounds on regeneration times and limit theorems for subgeometric Markov chains
This paper studies limit theorems for Markov chains with general state space under conditions which imply subgeometric ergodicity. We obtain a central limit theorem and moderate deviation principles for additive not necessarily bounded functional of the Markov chains under drift and minorization conditions which are weaker than the Foster–Lyapunov conditions. The regeneration-split chain method and a precise control of the modulated moment of the hitting time to small sets are employed in the proof....
Bounds on tail probabilities for negative binomial distributions
In this paper we derive various bounds on tail probabilities of distributions for which the generated exponential family has a linear or quadratic variance function. The main result is an inequality relating the signed log-likelihood of a negative binomial distribution with the signed log-likelihood of a Gamma distribution. This bound leads to a new bound on the signed log-likelihood of a binomial distribution compared with a Poisson distribution that can be used to prove an intersection property...
Branching and interacting particle systems. Approximations of Feynman-Kac formulae with applications to non-linear filtering