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Central limit theorems for eigenvalues in a spiked population model

Zhidong Bai, Jian-Feng Yao (2008)

Annales de l'I.H.P. Probabilités et statistiques

In a spiked population model, the population covariance matrix has all its eigenvalues equal to units except for a few fixed eigenvalues (spikes). This model is proposed by Johnstone to cope with empirical findings on various data sets. The question is to quantify the effect of the perturbation caused by the spike eigenvalues. A recent work by Baik and Silverstein establishes the almost sure limits of the extreme sample eigenvalues associated to the spike eigenvalues when the population and the...

Change point detection in vector autoregression

Zuzana Prášková (2018)

Kybernetika

In the paper a sequential monitoring scheme is proposed to detect instability of parameters in a multivariate autoregressive process. The proposed monitoring procedure is based on the quasi-likelihood scores and the quasi-maximum likelihood estimators of the respective parameters computed from a training sample, and it is designed so that the sequential test has a small probability of a false alarm and asymptotic power one as the size of the training sample is sufficiently large. The asymptotic...

Change-point estimator in continuous quadratic regression

Daniela Jarušková (2001)

Commentationes Mathematicae Universitatis Carolinae

The paper deals with the asymptotic distribution of the least squares estimator of a change point in a regression model where the regression function has two phases --- the first linear and the second quadratic. In the case when the linear coefficient after change is non-zero the limit distribution of the change point estimator is normal whereas it is non-normal if the linear coefficient is zero.

Change-point estimator in gradually changing sequences

Daniela Jarušková (1998)

Commentationes Mathematicae Universitatis Carolinae

Recently Hušková (1998) has studied the least squares estimator of a change-point in gradually changing sequence supposing that the sequence increases (or decreases) linearly after the change-point. The present paper shows that the limit behavior of the change-point estimator for more complicated gradual changes is similar. The limit variance of the estimator can be easily calculated from the covariance function of a limit process.

Characterizacion of the bivariate discrete distributions defined by a partial difference equations system.

Ramón Gutiérrez Jáimez, Miguel Angel Fajardo Caldera (1988)

Trabajos de Estadística

Conditions under which the solutions of a partial difference equations system can be probability functions are examined.When the coefficients of the system are polynomials then the partial difference equations system satisfied by generating functions associated to these distributions are easily obtained; they give useful recurrence relations for the moments. Three examples are given as well.

Characterizations based on length-biased weighted measure of inaccuracy for truncated random variables

Chanchal Kundu (2014)

Applications of Mathematics

In survival studies and life testing, the data are generally truncated. Recently, authors have studied a weighted version of Kerridge inaccuracy measure for truncated distributions. In the present paper we consider weighted residual and weighted past inaccuracy measure and study various aspects of their bounds. Characterizations of several important continuous distributions are provided based on weighted residual (past) inaccuracy measure.

Characterizations of continuous distributions through inequalities involving the expected values of selected functions

Faranak Goodarzi, Mohammad Amini, Gholam Reza Mohtashami Borzadaran (2017)

Applications of Mathematics

Nanda (2010) and Bhattacharjee et al. (2013) characterized a few distributions with help of the failure rate, mean residual, log-odds rate and aging intensity functions. In this paper, we generalize their results and characterize some distributions through functions used by them and Glaser’s function. Kundu and Ghosh (2016) obtained similar results using reversed hazard rate, expected inactivity time and reversed aging intensity functions. We also, via w ( · ) -function defined by Cacoullos and Papathanasiou...

Characterizations of the exponential distribution based on certain properties of its characteristic function

Simos G. Meintanis, George Iliopoulos (2003)

Kybernetika

Two characterizations of the exponential distribution among distributions with support the nonnegative real axis are presented. The characterizations are based on certain properties of the characteristic function of the exponential random variable. Counterexamples concerning more general possible versions of the characterizations are given.

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