Linearized Rank Estimates and Signed-Rank Estimates for the General Linear Hypothesis

High Breakdown Rank-Based Estimates for Linear Models

–estimates for the Linearized Monge–ampère Equation

Let Ω ⊆ Rn be a strictly convex domain and let φ ∈ C2(Ω) be a convex function such that λ ≤ detD2φ ≤ Λ in Ω. The linearized Monge– Ampère equation is LΦu = trace(ΦD u) = f, where Φ = (detD2φ)(D2φ)−1 is the matrix of cofactors of D2φ. We prove that there exist p > 0 and C > 0 depending only on n, λ,Λ, and dist(Ω′,Ω) such that ‖Du‖Lp(Ω′) ≤ C(‖u‖L∞(Ω) + ‖f‖Ln(Ω)) for all solutions u ∈ C2(Ω) to the...

Robust Signed-Rank Variable Selection in Linear Regression

The growing need for dealing with big data has made it necessary to find computationally efficient methods for identifying important factors to be considered in statistical modeling. In the linear model, the Lasso is an effective way of selecting variables using penalized regression. It has spawned substantial research in the area of variable selection for models that depend on a linear combina...

Wilcoxon signed rank test for imprecise observations

This article extends the Wilcoxon signed rank test for testing whether the median of a population is a specified constant by treating the observations as imprecise values. The test procedure is developed by using the concepts of “Credibility Theory” for studying the behavior of fuzzy phenomena. Numerical illustration of the proposed test is provided by representing the observations as trapezoid...

Freud, Rank and, the problem of anxiety

Anxiety has always been a phenomenon of great importance among psychoanalysts. Freud, as the founder of psychoanalysis, took much notice of this phenomenon from the beginning of his career, and he was always trying to give a comprehensive explanation for this problem. Therefore, throughout his career, he modified his theories about anxiety frequently, and even one time, he changed his whole the...