Stability of invariant linearly sufficient statistics in the general Gauss-Markov model

Andrzej Kornacki

Displaying similar documents to “Stability of invariant linearly sufficient statistics in the general Gauss-Markov model”

Some limit behavior for linear combinations of order statistics

Yu Miao, Mengyao Ma (2021)

Kybernetika

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In the present paper, we establish the moderate and large deviations for the linear combinations of uniform order statistics. As applications, the moderate and large deviations for the $k$ -th order statistics from uniform distribution, Gini mean difference statistics and the $k$ -th order statistics from general continuous distribution are obtained.

Stress-strength based on $m$ -generalized order statistics and concomitant for dependent families

Filippo Domma, Abbas Eftekharian, Mostafa Razmkhah (2019)

Applications of Mathematics

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The stress-strength model is proposed based on the $m$ -generalized order statistics and the corresponding concomitant. For the dependency between $m$ -generalized order statistics and its concomitant, a bivariate copula expansion is considered and the stress-strength model is obtained for two special cases of order statistics and upper record values. In the particular case of copula function, the generalized Farlie-Gumbel-Morgenstern bivariate distribution function is considered with proportional...

Characterization of the multivariate Gauss-Markoff model with singular covariance matrix and missing values

Wiktor Oktaba (1998)

Applications of Mathematics

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The aim of this paper is to characterize the Multivariate Gauss-Markoff model $(M G M)$ as in () with singular covariance matrix and missing values. $M G M D P 2$ model and completed $M G M D P 2 Q$ model are obtained by three transformations $D$ , $P$ and $Q$ (cf. ()) of $M G M$ . The unified theory of estimation (Rao, 1973) which is of interest with respect to $M G M$ has been used. The characterization is reached by estimation of parameters: scalar $σ^{2}$ and linear combination $λ^{'} \bar{B}$ ( $\bar{B} = v e c B)$ as in (), (), () as well as by the model of the form ()...

A spatial individual-based contact model with age structure

Dominika Jasińska (2017)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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The Markov dynamics of an infinite continuum birth-and-death system of point particles with age is studied. Each particle is characterized by its location $x \in ℝ^{d}$ and age $a_{x} \geq 0$ . The birth and death rates of a particle are age dependent. The states of the system are described in terms of probability measures on the corresponding configuration space. The exact solution of the evolution equation for the correlation functions of first and second orders is found.

Asymptotically normal confidence intervals for a determinant in a generalized multivariate Gauss-Markoff model

Wiktor Oktaba (1995)

Applications of Mathematics

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By using three theorems (Oktaba and Kieloch [3]) and Theorem 2.2 (Srivastava and Khatri [4]) three results are given in formulas (2.1), (2.8) and (2.11). They present asymptotically normal confidence intervals for the determinant $| σ^{2} \sum |$ in the MGM model $(U, X B, σ^{2} \sum \otimes V)$ , $\sum > 0$ , scalar $σ^{2} > 0$ , with a matrix $V \geq 0$ . A known $n \times p$ random matrix $U$ has the expected value $E (U) = X B$ , where the $n \times d$ matrix $X$ is a known matrix of an experimental design, $B$ is an unknown $d \times p$ matrix of parameters and $σ^{2} \sum \otimes V$ is the covariance matrix of $U, \otimes$ being the symbol...

Tangential Markov inequality in $L^{p}$ norms

Agnieszka Kowalska (2015)

Banach Center Publications

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In 1889 A. Markov proved that for every polynomial p in one variable the inequality $| | p^{'} {| |}_{[- 1, 1]} {\leq (d e g p) ² | | p | |}_{[- 1, 1]}$ is true. Moreover, the exponent 2 in this inequality is the best possible one. A tangential Markov inequality is a generalization of the Markov inequality to tangential derivatives of certain sets in higher-dimensional Euclidean spaces. We give some motivational examples of sets that admit the tangential Markov inequality with the sharp exponent. The main theorems show that the results on certain arcs...

Displaying similar documents to “Stability of invariant linearly sufficient statistics in the general Gauss-Markov model”

Some limit behavior for linear combinations of order statistics

Stress-strength based on m -generalized order statistics and concomitant for dependent families

Characterization of the multivariate Gauss-Markoff model with singular covariance matrix and missing values

A spatial individual-based contact model with age structure

Asymptotically normal confidence intervals for a determinant in a generalized multivariate Gauss-Markoff model

Tangential Markov inequality in L p norms

Stress-strength based on $m$ -generalized order statistics and concomitant for dependent families

Tangential Markov inequality in $L^{p}$ norms