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Change-point estimation from indirect observations. 1. Minimax complexity

A. Goldenshluger, A. Juditsky, A. B. Tsybakov, A. Zeevi (2008)

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

We consider the problem of nonparametric estimation of signal singularities from indirect and noisy observations. Here by singularity, we mean a discontinuity (change-point) of the signal or of its derivative. The model of indirect observations we consider is that of a linear transform of the signal, observed in white noise. The estimation problem is analyzed in a minimax framework. We provide lower bounds for minimax risks and propose rate-optimal estimation procedures.

Change-point estimation from indirect observations. 2. Adaptation

A. Goldenshluger, A. Juditsky, A. Tsybakov, A. Zeevi (2008)

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

We focus on the problem of adaptive estimation of signal singularities from indirect and noisy observations. A typical example of such a singularity is a discontinuity (change-point) of the signal or of its derivative. We develop a change-point estimator which adapts to the unknown smoothness of a nuisance deterministic component and to an unknown jump amplitude. We show that the proposed estimator attains optimal adaptive rates of convergence. A simulation study demonstrates reasonable practical...

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.

Change-point problems: A Bayesian nonparametric approach

Pietro Muliere, Marco Scarsini (1985)

Aplikace matematiky

A change-point problem is examined from a Bayesian viewpoint, under nonparametric hypotheses. A Ferguson-Dirichlet prior is chosen and the posterior distribution is computed for the change-point and for the unknown distribution functions.

Change-Point problems: approaches and applications.

Adrian F. M. Smith (1980)

Trabajos de Estadística e Investigación Operativa

Problems of making inferences about abrupt changes in the mechanism underlying a sequence of observations are considered in both retrospective and on-line contexts. Among the topics considered are the Lindisfarne scribes problem; switching straight lines; manoeuvering targets, and shifts of level or slope in linear time series models. Summary analyses of data obtained in studies of schizophrenic and kidney transplant patients are presented.

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.

Characterization of admissible linear estimators under extended balanced loss function

Buatikan Mirezi, Selahattin Kaçıranlar (2021)

Kybernetika

In this paper, we study the admissibility of linear estimator of regression coefficient in linear model under the extended balanced loss function (EBLF). The sufficient and necessary condition for linear estimators to be admissible are obtained respectively in homogeneous and non-homogeneous classes. Furthermore, we show that admissible linear estimator under the EBLF is a convex combination of the admissible linear estimator under the sum of square residuals and quadratic loss function.

Characterization of lung tumor subtypes through gene expression cluster validity assessment

Giorgio Valentini, Francesca Ruffino (2006)

RAIRO - Theoretical Informatics and Applications

The problem of assessing the reliability of clusters patients identified by clustering algorithms is crucial to estimate the significance of subclasses of diseases detectable at bio-molecular level, and more in general to support bio-medical discovery of patterns in gene expression data. In this paper we present an experimental analysis of the reliability of clusters discovered in lung tumor patients using DNA microarray data. In particular we investigate if subclasses of lung adenocarcinoma...

Characterization of the first operating period of a two-unit standby redundant system with three states of units

Antonín Lešanovský (1982)

Aplikace matematiky

A two-unit cold-standby redundant system with one repair facility is considered. Each unit can be in three states: good (I), degraded (II), and failed (III). We suppose that only the following state-transitions af a unit are possible: I → I I , I I → I I I , I I → I , I I I → I . The paper is devoted to the problems which arise only provided that the units of the redundant system can be in more than two states (i.e. in operating and failed states). The following characteristics dealing with a single operating period of the system are studied...

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

Wiktor Oktaba (1998)

Applications of Mathematics

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 ' B ¯ ( B ¯ = v e c B ) as in (), (), () as well as by the model of the form () (cf. Th. )....

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.

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