The Predictive Least Squares (PLS) model selection criterion is known to be consistent in the context of linear regression. For small sample sizes, however, it can exhibit erratic behavior. We show that this shortcoming can be amended by incorporating a Student’s t-distribution into PLS. The resulting criterion is shown to be asymptotically equivalent to PLS but significantly more robust for sm...

Abstract Let $(Z_n)_{n\geq 0}$ be a critical branching process in random environment defined by Markov chain $(X_n)_{n\geq with values finite state space $\mathbb{X}$ . $ S_n = \sum_{k=1}^n \ln f_{X_k}^{\prime}(1)$ the walk associated to , where $f_i$ is offspring generating function when $i \in \mathbb{X}$ Conditioned on event $\{ Z_n>0\}$ we show nondegeneracy of limit law normalized numbe...

We give two simple algorithms for the exact evaluation of the sum S(x) = 0≤n<x;n≡0(mod3) (−1) σ(n) , where σ(n) is the binary digit sum of n and obtain the sharp estimates for x −λ S(x), λ = ln 3 ln 4 .

In this paper a loop condition is defined which generalizes the cellularity criterion and applies to compacta with nontrivial shape. It is shown that if A", fc E", n > 5, are compacta which satisfy this loop condition and whose shape classes include a space having dimension in the trivial range with respect to n, then Sh(A") = Sh( Y) is equivalent to E" — X « E" — Y. An application is given to ...

The Riemann hypothesis is equivalent to the Li criterion governing a sequence of real constants {λk}k=1, that are certain logarithmic derivatives of the Riemann xi function evaluated at unity. We investigate a related set of constants cn, n = 1, 2, . . ., showing in detail that the leading behaviour (1/2) ln n of λn/n is absent in cn. Additional results are presented, including a novel explicit...

A criterion of joint ergodicity of several sequences of transformations of a probability measure space X of the form T φi(n) i is given for the case where Ti are commuting measure preserving transformations of X and φi are integer valued generalized linear functions, that is, the functions formed from conventional linear functions by an iterated use of addition, multiplication by constants, and...

In recent time the critique of whole brain death as criterion human death, that was introduced in 1968, has been growing. The paper aims to show systematically there are good reasons based on empirical findings combined with Thomistic Christian anthropology accept traditional cardiopulmonary death. This will be shown through a systematic other criteria death: higher stem and controlled cardiac/...

The paper belongs to the studies that deal with the effectiveness of the particular event-based sampling scheme compared to the conventional periodic sampling as a reference. In the present study, the event-based sampling according to a constant energy of sampling error is analyzed. This criterion is suitable for applications where the energy of sampling error should be bounded (i.e., in buildi...

Let {X,Xn; n ≥ 1} be a sequence of i.i.d. random variables with distribution function F (x). For each positive integer n, let X1:n ≤ X2:n ≤ · · · ≤ Xn:n be the order statistics of X1, X2, · · · , Xn. Let H(·) be a real Borel-measurable function defined on R such that E|H(X)| < ∞ and let J(·) be a Lipschitz function of order one defined on [0, 1]. Write μ = μ(F, J,H) = E(J(U)H(F←(U))) and Ln(F, ...