• Title, Summary, Keyword: penalized likelihood

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Bayesian Confidence Intervals in Penalized Likelihood Regression

  • Kim Young-Ju
    • Communications for Statistical Applications and Methods
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    • v.13 no.1
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    • pp.141-150
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    • 2006
  • Penalized likelihood regression for exponential families have been considered by Kim (2005) through smoothing parameter selection and asymptotically efficient low dimensional approximations. We derive approximate Bayesian confidence intervals based on Bayes model associated with lower dimensional approximations to provide interval estimates in penalized likelihood regression and conduct empirical studies to access their properties.

A correction of SE from penalized partial likelihood in frailty models

  • Ha, Il-Do
    • Journal of the Korean Data and Information Science Society
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    • v.20 no.5
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    • pp.895-903
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    • 2009
  • The penalized partial likelihood based on restricted maximum likelihood method has been widely used for the inference of frailty models. However, the standard-error estimate for frailty parameter estimator can be downwardly biased. In this paper we show that such underestimation can be corrected by using hierarchical likelihood. In particular, the hierarchical likelihood gives a statistically efficient procedure for various random-effect models including frailty models. The proposed method is illustrated via a numerical example and simulation study. The simulation results demonstrate that the corrected standard-error estimate largely improves such bias.

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Penalized Likelihood Regression with Negative Binomial Data with Unknown Shape Parameter

  • Kim, Young-Ju
    • Communications for Statistical Applications and Methods
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    • v.14 no.1
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    • pp.23-32
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    • 2007
  • We consider penalized likelihood regression with data from the negative binomial distribution with unknown shape parameter. Smoothing parameter selection and asymptotically efficient low dimensional approximations are employed for negative binomial data along with shape parameter estimation through several different algorithms.

Estimating Parameters in Muitivariate Normal Mixtures

  • Ahn, Sung-Mahn;Baik, Sung-Wook
    • Communications for Statistical Applications and Methods
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    • v.18 no.3
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    • pp.357-365
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    • 2011
  • This paper investigates a penalized likelihood method for estimating the parameter of normal mixtures in multivariate settings with full covariance matrices. The proposed model estimates the number of components through the addition of a penalty term to the usual likelihood function and the construction of a penalized likelihood function. We prove the consistency of the estimator and present the simulation results on the multi-dimensional nor-mal mixtures up to the 8-dimension.

Maximum penalized likelihood estimation for a stress-strength reliability model using complete and incomplete data

  • Hassan, Marwa Khalil
    • Communications for Statistical Applications and Methods
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    • v.25 no.4
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    • pp.355-371
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    • 2018
  • The two parameter negative exponential distribution has many practical applications in queuing theory such as the service times of agents in system, the time it takes before your next telephone call, the time until a radioactive practical decays, the distance between mutations on a DNA strand, and the extreme values of annual snowfall or rainfall; consequently, has many applications in reliability systems. This paper considers an estimation problem of stress-strength model with two parameter negative parameter exponential distribution. We introduce a maximum penalized likelihood method, Bayes estimator using Lindley approximation to estimate stress-strength model and compare the proposed estimators with regular maximum likelihood estimator for complete data. We also introduce a maximum penalized likelihood method, Bayes estimator using a Markov chain Mote Carlo technique for incomplete data. A Monte Carlo simulation study is performed to compare stress-strength model estimates. Real data is used as a practical application of the proposed model.

A Penalized Principal Components using Probabilistic PCA

  • Park, Chong-Sun;Wang, Morgan
    • Proceedings of the Korean Statistical Society Conference
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    • pp.151-156
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    • 2003
  • Variable selection algorithm for principal component analysis using penalized likelihood method is proposed. We will adopt a probabilistic principal component idea to utilize likelihood function for the problem and use HARD penalty function to force coefficients of any irrelevant variables for each component to zero. Consistency and sparsity of coefficient estimates will be provided with results of small simulated and illustrative real examples.

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Penalized Likelihood Regression: Fast Computation and Direct Cross-Validation

  • Kim, Young-Ju;Gu, Chong
    • Proceedings of the Korean Statistical Society Conference
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    • pp.215-219
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    • 2005
  • We consider penalized likelihood regression with exponential family responses. Parallel to recent development in Gaussian regression, the fast computation through asymptotically efficient low-dimensional approximations is explored, yielding algorithm that scales much better than the O($n^3$) algorithm for the exact solution. Also customizations of the direct cross-validation strategy for smoothing parameter selection in various distribution families are explored and evaluated.

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Computation and Smoothing Parameter Selection In Penalized Likelihood Regression

  • Kim Young-Ju
    • Communications for Statistical Applications and Methods
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    • v.12 no.3
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    • pp.743-758
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    • 2005
  • This paper consider penalized likelihood regression with data from exponential family. The fast computation method applied to Gaussian data(Kim and Gu, 2004) is extended to non Gaussian data through asymptotically efficient low dimensional approximations and corresponding algorithm is proposed. Also smoothing parameter selection is explored for various exponential families, which extends the existing cross validation method of Xiang and Wahba evaluated only with Bernoulli data.

Tests of Hypotheses in Multiple Samples based on Penalized Disparities

  • Park, Chanseok;Ayanendranath Basu;Ian R. Harris
    • Journal of the Korean Statistical Society
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    • v.30 no.3
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    • pp.347-366
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    • 2001
  • Robust analogues of the likelihood ratio test are considered for testing of hypotheses involving multiple discrete distributions. The test statistics are generalizations of the Hellinger deviance test of Simpson(1989) and disparity tests of Lindsay(1994), obtained by looking at a 'penalized' version of the distances; harris and Basu (1994) suggest that the penalty be based on reweighting the empty cells. The results show that often the tests based on the ordinary and penalized distances enjoy better robustness properties than the likelihood ratio test. Also, the tests based on the penalized distances are improvements over those based on the ordinary distances in that they are much closer to the likelihood ratio tests at the null and their convergence to the x$^2$ distribution appears to be dramatically faster; extensive simulation results show that the improvement in performance of the tests due to the penalty is often substantial in small samples.

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H-likelihood approach for variable selection in gamma frailty models

  • Ha, Il-Do;Cho, Geon-Ho
    • Journal of the Korean Data and Information Science Society
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    • v.23 no.1
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    • pp.199-207
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    • 2012
  • Recently, variable selection methods using penalized likelihood with a shrink penalty function have been widely studied in various statistical models including generalized linear models and survival models. In particular, they select important variables and estimate coefficients of covariates simultaneously. In this paper, we develop a penalize h-likelihood method for variable selection in gamma frailty models. For this we use the smoothly clipped absolute deviation (SCAD) penalty function, which satisfies a good property in variable selection. The proposed method is illustrated using simulation study and a practical data set.