In this note we give a proof of the Wilks theorem for the empirical likelihood ratio for the right censored data, when the hypothesis are formulated in terms of p estimating equations or mean functions. In particular we show that the empirical likelihood ratio test statistic is equal to a quadratic form similar to a Hotelling’s T 2 statistic, plus a small error.

The separation of a complex mixture based solely on second-order statistics can be achieved using the Strong Uncorrelating Transform (SUT) if and only if all sources have distinct circularity coefficients. However, in most problems we do not know the circularity coefficients, and they must be estimated from observed data. In this work, we propose a detector, based on the generalized likelihood ...

Recall that a continuous function $fcolon Xto Y$ between Tychonoff spaces is proper if and only if the Stone extension $f^{beta}colon beta Xtobeta Y$ takes remainder to remainder, in the sense that $f^{beta}[beta X-X]subseteq beta Y-Y$. We introduce the notion of ``taking remainder to remainder" to frames, and, using it, we define a frame homomorphism $hcolon Lto M$ to be $beta$-proper, $lambd...

let $p(lambda)$ be an $n$-square complex matrix polynomial, and $1 leq k leq n$ be a positive integer. in this paper, some algebraic and geometrical properties of the $k$-numerical range of $p(lambda)$ are investigated. in particular, the relationship between the $k$-numerical range of $p(lambda)$ and the $k$-numerical range of its companion linearization is stated. moreover, the $k$-numerical ...

Purpose: This paper aims to determine the relationship between standard of living inhabitants selected regions European Union and scientific technological potential. Design/Methodology/Approach: The study covered 60 – NUTS 2 in 13 Member States. data concerned year 2018. Due multidimensional character analyzed categories, a canonical analysis was used as generalization multiple linear regressio...