We study the structure and smoothness of non-homogeneous convex conservation laws. The question regarding the number of smoothness pieces is addressed. It is shown that under certain conditions on the initial data the entropy solution has only a finite number of discontinuous curves. We also obtain some global estimates on derivatives of the piecewise smooth entropy solution along the generaliz...

This paper suggests an estimator of the number of jumps of the jump regression functions. The estimator is based on the diierence between right and left one-sided kernel smoothers. It is proved to be a.s. consistent. Some results about its rate of convergence are also provided.

With s n (z) denoting the n-th partial sum of e z , the exact rate of convergence of the zeros of the normalized partial sums, s n (nz), to the Szeg} o curve D 0;1 was recently studied by Carpenter et al. (1991), where D 0;1 is deened by

We provide tight bounds on the rate of convergence of the equilibrium payo sets for repeated games under both perfect and imperfect public monitoring. The distance between the equilibrium payo set and its limit vanishes at rate (1− δ)1/2 under perfect monitoring, and at rate (1− δ)1/4 under imperfect monitoring. For strictly individually rational payo vectors, these rates improve to 0 (i.e., al...

Let (Xn)n≥1 be a sequence of random variables on a probability space (Ω, ,P) and p ≥ 1 a fixed real number. We say that (Xn)n≥1 is Lp-bounded if it has finite pth moments, that is, ‖Xn‖p ≤ C for some C > 0 and any n ≥ 1. Let ε > 0; finding the rate of convergence of the moderate deviations probabilities P[|∑k=1Xk| > εan] with an = (n logn)1/2 or (n loglogn)1/2 is known in the literature as Davi...

We investigate the estimation of a multiplicative separable regression function from a bi-dimensional nonparametric regression model with random design. We present a general estimator for this problem and study its mean integrated squared error (MISE) properties. A wavelet version of this estimator is developed. In some situations, we prove that it attains the standard unidimensional rate of co...

We split [0,1] in a uniform manner, take the largest of the two intervals thus obtained, split this interval again uniformly, and continue in this fashion ad infinitum. We show that the extremes of this interval converge almost surely to a beta (2,2) random variable.

We introduce a one parameter family of hybrid operators and study quantitative convergence theorems for these operators e.g. local and weighted approximation results and simultaneous approximation of derivatives. Further, we discuss the statistical convergence of these operators. Lastly, we show the rate of convergence of these operators to a certain function by illustrative graphics in Matlab....

In this paper, we address the problem of deriving bounds for the moments of nearest neighbor distributions. The bounds are formulated for the general case and specifically applied to the problem of noise variance estimation with the Delta test and the Gamma test. For this problem, we focus on the rate of convergence and the bias of the estimators and validate the theoretical achievements with e...