The leading term in the normal approximation to the distribution of Student’s t statistic is derived in a general setting, with the sole assumption being that the sampled distribution is in the domain of attraction of a normal law. The form of the leading term is shown to have its origin in the way in which extreme data influence properties of the Studentized sum. The leading-term approximation...

The method of alternating projections is a classical tool to solve feasibility problems. Here we prove local convergence of alternating projections between subanalytic sets A,B under a mild regularity hypothesis on one of the sets. We show that the speed of convergence is O(k−ρ) for some ρ ∈ (0,∞).

We consider Bayesian density estimation for compactly supported densities using Bernstein mixtures of beta-densities equipped with a Dirichlet prior on the distribution function. We derive the rate of convergence for α-smooth densities for 0 < α ≤ 2 and show that a faster rate of convergence can be obtained by using fewer terms in the mixtures than proposed before. The Bayesian procedure adapts...

Solution: Since {xn} ∞ n=1 is a bounded sequence in R, the Bolzano-Weierstrass Theorem ensures that there is at least one convergent subsequence: let L be its limit. If the entire sequence does not converge to L, then for some > 0 there must be infinitely many terms of the sequence outside the ball B = (L− , L+ ). This infinite but bounded collection of terms likewise by Bolzano-Weierstrass has...

the complete convergence is investigated for moving-average processes of doubly infinite sequence of negative dependence sub-gaussian random variables with zero means, finite variances and absolutely summable coefficients. as a corollary, the rate of complete convergence is obtained under some suitable conditions on the coefficients.

the complete convergence is investigated for moving-average processes of doubly infinite sequence of negative dependence sub-gaussian random variables with zero means, finite variances and absolutely summable coefficients. as a corollary, the rate of complete convergence is obtained under some suitable conditions on the coefficients.

In this paper we study the concepts of I-Cauchy and I∗-Cauchy for double sequences in a linear metric space. Also, we give the relation between I-convergence and I∗-convergence of double sequences of functions defined between linear metric spaces.

For the Lotka-Sharpe-McKendrick demographic model the rate of convergence to the persistent age distribution is estimated in terms of the age-dependent mortality and fertility. In an abstract setting the problems amounts to estimating the second largest spectral bound of a linear operator. The convergence rate is indeed characterized as the difference between the first and second spectral bound...

The generalized quasilinearization method for second-order boundary value problem has been extended when the forcing function is the sum of two functions without require that any of the two functions involved to be 2-hyperconvex or 2-hyperconcave. Two sequences are developed under suitable conditions which converge to the unique solution of the boundary value problem. Furthermore, the convergen...

We give bounds on the rate of convergence to equilibrium of the symmetric simple exclusion process in Z d. Our results include the existent results in the literature. We get better bounds and larger class of initial states via a unified approach. The method includes a comparison of the evolution of n interacting particles with n independent ones along the whole time trajectory.