Generalized Measures of Divergence in Survival Analysis and Reliability

The cumulative Kullback–Leibler information has been proposed recently as a suitable extension of Kullback–Leibler information to the cumulative distribution function. In this paper, we obtain various results on such a measure, with reference to its relation with other information measures and notions of reliability theory. We also provide some lower and upper bounds. A dynamic version of the cumulative Kullback–Leibler information is then proposed for past lifetimes. Furthermore, we investigate its monotonicity property, which is related to some new concepts of relative aging. Moreover, we propose an application to the failure of nanocomponents. Finally, in order to provide an application in image analysis, we introduce the empirical cumulative Kullback–Leibler information and prove an asymptotic result

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“…In the following counterexample, we show that the assumption X ⩾ rh Y is necessary to obtain inequalities expressed in (28) and (29).…”

Section: A Dynamic Measure For Past Lifetimesmentioning

confidence: 97%

“…respectively. See Sunoj et al [27], Vonta and Karagrigoriou [28], and Sachlas and Papaioannou [29] for various results and applications of past lifetimes.…”

Section: A Dynamic Measure For Past Lifetimesmentioning

confidence: 99%

Some properties and applications of cumulative Kullback–Leibler information

Crescenzo

Longobardi

2015

Appl Stoch Models Bus & Ind

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Robust Portfolio Optimization Using Pseudodistances

Toma¹,

Leoni-Aubin²

2015

PLoS ONE

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The presence of outliers in financial asset returns is a frequently occurring phenomenon which may lead to unreliable mean-variance optimized portfolios. This fact is due to the unbounded influence that outliers can have on the mean returns and covariance estimators that are inputs in the optimization procedure. In this paper we present robust estimators of mean and covariance matrix obtained by minimizing an empirical version of a pseudodistance between the assumed model and the true model underlying the data. We prove and discuss theoretical properties of these estimators, such as affine equivariance, B-robustness, asymptotic normality and asymptotic relative efficiency. These estimators can be easily used in place of the classical estimators, thereby providing robust optimized portfolios. A Monte Carlo simulation study and applications to real data show the advantages of the proposed approach. We study both in-sample and out-of-sample performance of the proposed robust portfolios comparing them with some other portfolios known in literature.

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