Sangun Park

Yonsei University · Department of Applied Statistics

In this paper, we study the Kullback–Leibler (KL) information of a censored variable, which we will simply call it censored KL information. The censored KL information is shown to have the necessary monotonicity property in addition to inherent properties of nonnegativity and characterization. We also present a representation of the censored KL inf...

The sample entropy (Vasicek, 1976) has been most widely used as a nonparametric entropy estimator due to its simplicity, but its underlying distribution function has not been known yet though its moments are required in establishing the entropy-based goodness of test statistic (Soofi et al., 1995). In this paper we derive the nonparametric distribu...

Any collection of order statistics from two different probability distributions may contain equal Fisher information about a scalar parameter. We derive a necessary and sufficient condition under which two distributions have equal Fisher information in any order statistics. Hence this condition can be used to define an equivalence relation on param...

Calculation of the entropy of a set of consecutive order statistics is relatively more complicated than that of the entropy of the individual order statistic, which has been studied by Wong and Chan (1990). We provide some fundamental relations occurring in the entropy of consecutive-order statistics, which are very useful for computations. We firs...

This article presents some powerful omnibus tests for multivariate normality based on the likelihood ratio and the characterizations of the multivariate normal distribution. The power of the proposed tests is studied against various alternatives via Monte Carlo simulations. Simulation studies show our tests compare well with other powerful tests in...

Baratpour and Rad (2012 Baratpour, S. and Rad, A. H. (2012). Testing goodness-of-fit for exponential distribution based on cumulative residual entropy, Communications in Statistics - Theory and Methods, 41, 1387–1396.[Taylor & Francis Online], [Web of Science ®] [Google Scholar]) proposed the cumulative residual Kullback-Leibler information and sug...

In this paper, we suggest an extension of the cumulative residual entropy (CRE) and call it generalized cumulative entropy. The proposed entropy not only retains attributes of the existing uncertainty measures but also possesses the absolute homogeneous property with unbounded support, which the CRE does not have. We demonstrate its mathematical pr...

We consider a linear combination of two logarithms of cumulative hazard functions and propose a general class of flexible Weibull distribution functions which includes some well-known modified Weibull distributions. We suggest a very flexible Weibull distribution, which belongs to the class, and show that its hazard function is monotone, bathtub-sh...

Mixed-mode surveys are becoming more popular recently because of their convenience for users, but different mode effects can complicate the comparability of the survey results. Motivated by the Private Education Expenditure Survey (PEES) of Korea, we propose a novel application of fractional imputation to handle mixed-mode survey data. The proposed...

A hybrid censoring is a mixture of Type I and Type II censoring where the experiment terminates when either rth failure or predetermined censoring time comes first or later. In this article, we consider order statistics of the Type I censored data and provide a simple expression for their Kullback–Leibler (KL) information. Then, we provide the expr...

We propose an extension of Kullback–Leibler information to the survival function, and generalize it to the censored case. We evaluate its performance as a goodness-of-fit test statistic with the progressively Type-II censored data. The new test is evaluated through Monte Carlo Simulations.

We propose an extension of Kullback–Leibler information to the survival function, and generalize it to the censored case. We evaluate its performance as a goodness-of-fit test statistic with the progressively Type-II censored data. The new test is evaluated through Monte Carlo Simulations.

In this paper, we first consider the entropy estimators introduced by Vasicek [A test for normality based on sample entropy. J R Statist Soc, Ser B. 1976;38:54–59], Ebrahimi et al. [Two measures of sample entropy. Stat Probab Lett. 1994;20:225–234], Yousefzadeh and Arghami [Testing exponentiality based on type II censored data and a new cdf estimat...

A calculation of the Kullback-Leibler information of consecutive order statistics is complicated because it depends on a multi-dimensional integral. Park (2014) discussed a representation of the Kullback-Leibler information of the first r order statistics in terms of the hazard function and simplified the r-fold integral to a single integral. In th...

For comparing two cumulative hazard functions, we consider an extension of the Kullback-Leibler information to the cumulative hazard function, which is concerning the ratio of cumulative hazard functions. Then we consider its estimate as a goodness of fit test with the Type II censored data. For an exponential null distribution, the proposed test s...

We provide simple computational formulas of both expected termination time and Fisher information of the flexible progressive censoring scheme proposed by Bairamov and Parsi (2011). Then, the design and planning of the flexible progressive censoring schemes are discussed with illustrative examples.

Cumulative residual entropy has been proposed by Rao et al. (2004). In this paper, we first show a representation of the cumulative residual entropy of the first rr order statistics as a single integral. Then we provide some related results including recurrence relations, identity and characterization property.

The representation of the entropy in terms of the hazard function and its extensions have been studied by many authors including Teitler et al. (IEEE Trans Reliab 35:391–395, 1986). In this paper, we consider a representation of the Kullback-Leibler information of the first r order statistics in terms of the relative risk (Park and Shin in Statisti...

Kullback-Leibler (KL) information is a measure of discrepancy between two probability density functions. However, several nonparametric density function estimators have been considered in estimating KL information because KL information is not well-defined on the empirical distribution function. In this paper, we consider the KL information of the...

The extensions of the entropy and Kullback-Leibler (KL) information to the cumulative distribution function have been recently studied because they are well defined on the empirical distribution function. In this paper, we generalize the extended KL information to the censored case and propose a censored cumulative residual KL information. We estim...

Cumulative residual Kullback-Leibler (CRKL) information is well defined on the empirical distribution function (EDF) and allows us to construct a EDF-based goodness of t test statistic. However, we need to consider a scaled CRKL because CRKL is not scale invariant. In this paper, we consider several criterions for estimating the scale parameter in...

In this paper, we propose an estimation method when sample data are incomplete. We decompose the likelihood according to missing patterns and combine the estimators based on each likelihood weighting by the Fisher information ratio. This approach provides a simple way of estimating parameters, especially for non-monotone missing data. Numerical exa...

Background: Compared to an abundance of data on surgical techniques for degenerative spine conditions and the outcomes thereof, little is available to guide optimal perioperative pain management after spinal surgery. The aim of this study was to survey patterns of perioperative pain management after spinal surgery and to investigate the effects of...

We study kernel density estimator from the ranked set samples (RSS). In the kernel density estimator, the selection of the bandwidth gives strong influence on the resulting estimate. In this article, we consider several different choices of the bandwidth and compare their asymptotic mean integrated square errors (MISE). We also propose a plug-in es...

In this paper, we propose a generalized Kullback-Leibler (KL) information for measuring the distance between two distribution functions where the extension to the censored case is immediate. The generalized KL information has the nonnegativity and characterization properties, and its censored version has the additional property of monotonic increas...

Some extensions of entropy and KL information to the survival function have been recently proposed. We first compare some extensions of KL information and provide a criterion in choosing one among those extensions. Then we study moment constraints for maximum cumulative residual entropy distribution (Rao et al., 2004) in view of the relation betwee...

It is well known that a ranked set sample under perfect ranking provides more information than an i.i.d. sample of the same size. Then it may be interesting to study how much information is lost due to imperfect ranking. In this article, we consider some ranking mechanisms and study the loss of the Fisher information according to the degree of impe...

The hybrid censoring scheme, which is a mixture of Type-I and Type-II censoring schemes, has been extended to the case of progressive censoring schemes by Kundu and Joarder [Analysis of Type-II progressively hybrid censored data, Comput. Stat. Data Anal. 50 (2006), pp. 2509–2528] and Childs et al. [Exact likelihood inference for an exponential para...

Robust panel unit root tests are developed for cross-sectionally dependent multiple time series. The tests have limiting null distributions derived from standard normal distributions. A Monte Carlo experiment shows that the tests have better finite sample robust performance than existing tests. Some Latin American real exchange rates revealing many...

A hybrid censoring scheme is a mixture of Type-I and Type-II censoring schemes. In this paper, we present two interesting results which are useful in deriving the Fisher information along with the expected censoring times and expected numbers of failures in hybrid and generalized hybrid censoring schemes. We first interpret the Type-II censoring sc...

Fisher information is a fundamental concept of statisti-cal inference and plays an important role in many areas of statistical analysis. Research in Fisher information in order statistics started around 1965 by John Tukey. Recently, the research in this area has been extended from classical order statistics and Type-I and Type-II censored data to o...

A hybrid censoring is a mixture of Type I and II censoring. Type I and Type II hybrid censoring models are considered in this work. When n items are placed on a life-test, the experiment terminates under the Type I (Type II) hybrid censoring when either the r-th failure (1<=r<=n) or the pre-determined censoring time T comes first (later). We study...

The Kulback-Leibler information has been considered for establishing goodness-of-fit test statistics, which have been shown to perform very well (Arizono & Ohta, 1989; Ebrahimi et al., 1992, etc). In this paper, we propose censored Kullback-Leibler information to generalize the discussion of the Kullback-Leibler information to the censored case. Th...

In this paper, we propose the conditional optimal spacing defined as the optimal spacing after specifying a predetermined order statistic. If we specify a censoring time, then the optimal inspection times for grouped inspection can be determined from this conditional optimal spacing. We take an example of exponential distribution, and provide a sim...

In bioassay, the logit model is the most widely used parametric model. However, the exact form of the response curve is usually unknown and even very complicated, so it is likely that the true model does not follow the logit model. Therefore, according to well-known asymptotic results, when the sample size is very large, we should probably use the...

It is known that the Fisher information in any set of order statistics can be simplified to a sum of double integrals. In this article, we show that it can be further simplified to a sum of single integrals for the scale parameter of an exponential distribution. Moreover, we use the result and provide a simple method of obtaining the optimal spacin...

This article gives a simple result for the expression of the Fisher information in order statistics. This result enables us to calculate easily the Fisher information in any set of order statistics whose details have been known to be messy and complicated. We consider here its application in the optimal spacing problem where the exact Fisher inform...

We express the joint entropy of order statistics in terms of an incomplete integral of the hazard function, and provide a simple estimate of the joint entropy of the type II censored data. Then we establish a goodness of fit test statistic based on the Kullback-Leibler information with the type II censored data, and compare its performance with som...

In bioassay, the logit model is the most widely used parametric model. However, the exact form of the response curve is usually un-known and even very complicated, so it is likely that the true model does not follow the logit model. Therefore, according to well known asymptotic results, when the sample size is very large, we should prob-ably use no...

We extend the result of Efron and Johnstone (1990), who expressed the Fisher information in terms of the hazard function, to express the Fisher information in order statistics as an expectation of the incomplete integral of the hazard function. Then we obtain the the asymptotic Fisher information in terms of the incomplete integral of the hazard fu...

The sample entropy, the estimate of the entropy per observation, has been introduced by Vasicek (1976) (A test for normality based on sample entropy, J. Royal Statist. Soc. B 38, 730–737). In this paper, we provide the sample entropy of order statistics, and present one application of the sample entropy of order statistics as a test of normality ve...

The entropy measure is considered to denote the uncertainty of order statistics filters and choose the length of consecutive order statistic filters. However, it needs much calculations to get the amount of the entropy of all possible sets of consecutive order statistics, and the results of those calculations return many numerical values. Thus we p...

In the decomposition of the score function based on all the order statistics, partial derivative/partial derivative theta log L(1...n) = partial derivative/partial derivative theta log L(1...n) + partial derivative/partial derivative theta log L(r + 1...n/r), we study the asymptotic behaviour of the maximum conditional likelihood estimator, based o...

When we have n independently and identically distributed observations, it is an interesting question how the Fisher information is distributed among order statistics. The recipe for the Fisher information in order statistics is easy, but the detailed calculation has been known to be complicated. An indirect approach, using a decomposition of the Fi...

When we have an i.i.d. sample of size n from a continuous distribution, the distribution truncated on the left at the rth order statistic plays an important role in the theoretical analysis of the Type 2 censored data. The charaterization of distributions by the average of the conditional expectation and the average of the conditional information c...