• Title/Summary/Keyword: Nonparametric Class

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Empirical Bayes Nonparametric Estimation with Beta Processes Based on Censored Observations

  • Hong, Jee-Chang;Kim, Yongdai;Inha Jung
    • Journal of the Korean Statistical Society
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    • v.30 no.3
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    • pp.481-498
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    • 2001
  • Empirical Bayes procedure of nonparametric estiamtion of cumulative hazard rates based on censored data is considered using the beta process priors of Hjort(1990). Beta process priors with unknown parameters are used for cumulative hazard rates. Empirical Bayes estimators are suggested and asymptotic optimality is proved. Our result generalizes that of Susarla and Van Ryzin(1978) in the sensor that (i) the cumulative hazard rate induced by a Dirichlet process is a beta process, (ii) our empirical Bayes estimator does not depend on the censoring distribution while that of Susarla and Van Ryzin(1978) does, (iii) a class of estimators of the hyperprameters is suggested in the prior distribution which is assumed known in advance in Susarla and Van Ryzin(1978). This extension makes the proposed empirical Bayes procedure more applicable to real dta sets.

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Testing unknown age classes of life distributions based on TTT-transform

  • El-Din, M.M. Mohie;Abu-Youssef, S.E.;Ali, Nahed S.A.
    • International Journal of Reliability and Applications
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    • v.14 no.1
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    • pp.1-9
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    • 2013
  • A nonparametric procedure for testing exponentially against used better than aged in expectation (UBAE) class of life distributions is presented. We construct a test statistics based on scaled total time on test (TTT)-transformation, to test exponentiality against UBAE class of life distributions. The distribution of the statistic is investigated via simulation. Practical applications of the proposed test are presented.

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ON CONSISTENCY OF SOME NONPARAMETRIC BAYES ESTIMATORS WITH RESPECT TO A BETA PROCESS BASED ON INCOMPLETE DATA

  • Hong, Jee-Chang;Jung, In-Ha
    • The Pure and Applied Mathematics
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    • v.5 no.2
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    • pp.123-132
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    • 1998
  • Let F and G denote the distribution functions of the failure times and the censoring variables in a random censorship model. Susarla and Van Ryzin(1978) verified consistency of $F_{\alpha}$, he NPBE of F with respect to the Dirichlet process prior D($\alpha$), in which they assumed F and G are continuous. Assuming that A, the cumulative hazard function, is distributed according to a beta process with parameters c, $\alpha$, Hjort(1990) obtained the Bayes estimator $A_{c,\alpha}$ of A under a squared error loss function. By the theory of product-integral developed by Gill and Johansen(1990), the Bayes estimator $F_{c,\alpha}$ is recovered from $A_{c,\alpha}$. Continuity assumption on F and G is removed in our proof of the consistency of $A_{c,\alpha}$ and $F_{c,\alpha}$. Our result extends Susarla and Van Ryzin(1978) since a particular transform of a beta process is a Dirichlet process and the class of beta processes forms a much larger class than the class of Dirichlet processes.

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Nonparametric Test for Used Better Than Aged in Convex Ordering Class(UBAC) of Life Distributions with Hypothesis Testing Applications

  • Abu-Youssef, S.E.
    • International Journal of Reliability and Applications
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    • v.10 no.2
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    • pp.81-88
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    • 2009
  • A non-parametric procedure is presented for testing exponentially against used better than aged in convex ordering class (UBAC) of life distributions based on u-test. Convergence of the proposed statistic to the normal distribution is proved. Selected critical values are tabulated for sample sizes 5(5)40. The Pitman asymptotic relative efficiency of my proposed test to tests of other classes is studied. An example of 40 patients suffering from blood cancer disease demonstrates practical application of the proposed test.

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Weighted Estimation of Survival Curves for NBU Class Based on Censored Data

  • Lee, Sang-Bock
    • Journal of the Korean Data and Information Science Society
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    • v.7 no.1
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    • pp.59-68
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    • 1996
  • In this paper, we consider how to estimate New Better Than Used (NBU) survival curves from randomly right censored data. We propose several possible NBU estimators and study their properties. Numerical studies indicate that the proposed estimators are appropriate in practical use. Some useful examples are presented.

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An Improvement of LVQ3 Learning Using SVM (SVM을 이용한 LVQ3 학습의 성능개선)

  • 김상운
    • Proceedings of the IEEK Conference
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    • 2001.06c
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    • pp.9-12
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    • 2001
  • Learning vector quantization (LVQ) is a supervised learning technique that uses class information to move the vector quantizer slightly, so as to improve the quality of the classifier decision regions. In this paper we propose a selection method of initial codebook vectors for a teaming vector quantization (LVQ3) using support vector machines (SVM). The method is experimented with artificial and real design data sets and compared with conventional methods of the condensed nearest neighbor (CNN) and its modifications (mCNN). From the experiments, it is discovered that the proposed method produces higher performance than the conventional ones and then it could be used efficiently for designing nonparametric classifiers.

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A Nonparametric Method for Random Signal Detection in Signal-Dependent Noise : Two-Sample Case (신호 의존성 잡음에서 확률 신호 검파를 위한 비모수 방법 : 두 표본을 쓰는 경우)

  • Kim, Chang-Bae;Song, Ik-Ho;Bae, Jin-Su
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.28 no.4C
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    • pp.374-378
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    • 2003
  • The asymptotic performance of the two-sample locally optimum rank detector for random signals buried in signal-dependent noise and additive noise is consigered in this paper. It is shown that the locally optimum rank detector, a nonparametric detector, has reasonable asymptotic performance for a class of correlated random signals, compared with the locally optimum detector. It is noteworthy that the the two-sample locally optimum rank detector perform almost the same with the one-sample locally optimum rank detector.

Nonparametric Estimation of the Survival Function under Progressively Random Censorship (점진적(漸進的) 임의중단법(任意中斷法)에서 생존함수(生存函數)의 비모수적(非母數的) 추정(推定)에 관한 연구(硏究))

  • Park, Byung-Gu;Lee, Kwang-Ho
    • Journal of the Korean Data and Information Science Society
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    • v.2
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    • pp.45-62
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    • 1991
  • In this paper we propose new nonparametric estimators of the survival function using spline function under the progressively random censoring scheme. This sampling scheme is applied in many practical situations such as clinical trials or the life testing problems. We also investigate the behaviors for some estimators in the proposed class and the performance of progressively random censoring scheme through the numerical examples and Monte Carlo simulation.

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Mixtures of Beta Processes Priors for Right Censored Survival Data

  • Kim, Yongdai
    • Journal of the Korean Statistical Society
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    • v.30 no.1
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    • pp.127-138
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    • 2001
  • In order to combine parametric and nonparametric approaches together for survival analysis with censored observations, a new class of priors called mixtures of the beta processes is introduced. It is shown that mixtures of beta processes priors generalized the well known priors - mixtures of Dirichlet processes, and they are conjugate with right censored observations. Formulas for computing the posterior distribution are derived. Finally, a real data set is analyzed for illustrational purpose.

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Locating the Change Point of Mean Residual Life of Certain Life Distributions

  • Li, Xiaohu
    • International Journal of Reliability and Applications
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    • v.3 no.2
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    • pp.91-98
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    • 2002
  • A class of life distributions, whose mean residual life keeps stable at its earlier phase and then starts to decrease in time, is proposed to model the life of an element haying survived its burn-in. A strongly consistent estimator and a nonparametric testing procedure are developed to locate the occurrence of the change-point of the mean residual life. Finally, some numerical simulations are employed to be an illustration as well.

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