It is shown that for every closed, convex and nowhere dense subset C of a superreflexive Banach space X there exists a Radon probability measure μ on X so that μ(C + x) = 0 for all x ∈ X. In particular, closed, convex, nowhere dense sets in separable superreflexive Banach spaces are Haar null. This is unlike the situation in separable nonreflexive Banach spaces, where there always exists a clos...

‎The problem of shrinkage testimation (test-estimation) for the Rayleigh scale‎ ‎parameter θ based on censored samples under the reflected‎ ‎gamma loss function is considered‎. We obtain the minimum risk‎ ‎estimator among a subclass and compute its risk‎. ‎A shrinkage‎ ‎testimator based on acceptance or rejection of a null hypothesis&lr...

In this paper, we propose a novel bagging null space locality preserving discriminant analysis (bagNLPDA) method for facial feature extraction and recognition. The bagNLPDA method first projects all the training samples into the range space of a so-called locality preserving total scatter matrix without losing any discriminative information. The projected training samples are then randomly samp...

Let A be a subset of the nonnegative integers ω (a real). A Martin-Löf test (relative to A) is a recursive (in A) set U ⊆ ω× 2 such that μUn ≤ 2−n, where Un denotes the nth section of U . If in addition μUn = 2−n then U is called a Schnorr test (relative to A). Then ∩nUn is called a Martin-Löf null set (relative to A) or Schnorr null set (relative to A), respectively. A is Schnorr random if for...