A canonical process for estimation of convex functions: The "invelope" of integrated Brownian motion +t4

A process associated with integrated Brownian motion is introduced that characterizes the limit behavior of nonparametric least squares and maximum likelihood estimators of convex functions and convex densities, respectively. We call this process “the invelope” and show that it is an almost surely uniquely defined function of integrated Brownian...

Isotonic inverse estimators for nonparametric deconvolution

A new nonparametric estimation procedure is introduced for the distribution function in a class of deconvolution problems, where the convolution density has one discontinuity. The estimator is shown to be consistent and its cube root asymptotic distribution theory is established. Known results on the minimax risk for the estimation problem...

Isotonic estimation and rates of convergence in Wicksell's problem

Metric Properties of Denjoy's Canonical Continued Fraction Expansion

Metric properties of Denjoy's canonical continued fraction expansion are studied, and the natural extension of the underlying ergodic system is given. This natural extension is used to give simple proofs of results on mediant convergents obtained by W. Bosma in 1990.

Maximal functions, factorization, and the R-boundedness of integral operators

We generalize a recent result on the ℓs-boundedness of a family of integral operators from the weighted vector-valued Lp(Rd,w;Lq(Ω)) setting to the weighted vector-valued Lp(Rd,w;X) setting for a large class of Banach function spaces X. For this we first extensively study the first part of an unpublished manuscript on the factorization of ℓ2...

The Weight and Hopcount of the Shortest Path in the Complete Graph with Exponential Weights

Both the hopcount HN (the number of links) and the weight WN (the sum of the weights on links) of the shortest path between two arbitrary nodes in the complete graph KN with i.i.d. exponential link weights is computed. We consider the joint distribution of the pair (HN,WN) and derive, after proper scaling, the joint limiting distribution. One of...

Development and validation of the cylindrical Mass Conserving Level Set method