• Journal of the Korean Statistical Society
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• v.26 no.3
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• pp.397-405
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• 1997

Recently maximum likelihood estimators using unconditional likelihood function are used for testing unit roots. When one wants to use this method the determinant term of initial values in the multivariate unconditional likelihood function produces a complicated function of the elements in the coefficient matrix and variance matrix. In this paper an approximation of the determinant term is calculated and based on this aproximation an approximated unconditional likelihood function is calculated. The approximated unconditional maximum likelihood estimators can be used to test for unit roots. When multivariate process has one unit root the limiting distribution obtained by this method and the limiting distribution using exact unconditional likelihood function are the same.

• Journal of the Korean Data and Information Science Society
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• v.25 no.1
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• pp.169-176
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• 2014

Counting processes are widely used in many fields, whose properties are determined by the intensity function. For estimation of the parameters of the intensity functions when the process is observed continuously over a fixed interval, the likelihood function is of interest. However in the literature there are only heuristic derivations and some results are not coincident. We thus in this note derive the likelihood function of the counting process in a rigorous way. So this note fill up a hole in derivation of the likelihood function.

• Communications for Statistical Applications and Methods
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• v.14 no.1
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• pp.229-239
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• 2007

We present a diagnostic method for the quasi-likelihood estimators in generalized linear models. Since these estimators can be usually obtained by iteratively reweighted least squares which are well known to be very sensitive to unusual data, a diagnostic step is indispensable to analysis of data. We extend the local influence approach based on the maximum likelihood function to that on the quasi-likelihood function. Under several perturbation schemes local influence diagnostics are derived. An illustrative example is given and we compare the results provided by local influence and deletion.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.1133-1138
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• 2008

A general method of detecting outliers based on a change of likelihood by using the influence function is suggested. It can be applied to all kinds of distributions that are specified by parameters. For the multivariate normal case, specific computations are made to get the corresponding conditional influence function. A numerical example is provided for illustration.

• Journal of the military operations research society of Korea
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• v.9 no.2
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• pp.39-43
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• 1983

In this paper, we derive the likelihood function for the independent random order statistic whose underlying lifetime distribution is a two parameter Weibull form. For this purpose we first discuss the order statistic which represent a characteristic feature of most life and fatigue tests that they give rise to ordered observations. And, we describe the properties of the underlying Weibull model. The derived likelihood function is essential for establishing the statistical life test plans in the case of Weibull distribution using a likelihood ratio method.

• Communications for Statistical Applications and Methods
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• v.10 no.2
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• pp.607-617
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• 2003

This paper offers a practical comparison of efficiency between local likelihood approach and conventional kernel approach in density estimation. The local likelihood estimation procedure maximizes a kernel smoothed log-likelihood function with respect to a polynomial approximation of the log likelihood function. We use two types of data driven bandwidths for each method and compare the mean integrated squares for several densities. Numerical results reveal that local log-linear approach with simple plug-in bandwidth shows better performance comparing to the standard kernel approach in heavy tailed distribution. For normal mixture density cases, standard kernel estimator with the bandwidth in Sheather and Jones(1991) dominates the others in moderately large sample size.

• Journal of the Korean Data and Information Science Society
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• v.16 no.3
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• pp.651-656
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• 2005

In this paper the quasi-likelihood function was proposed and the estimators which are the solutions of the estimating equations for estimation of a class of nonlinear time series models. We compare the performances of the proposed estimators with those of the ML estimators under the heavy-railed distributions by simulation.

• 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.

• Journal of the Korean Statistical Society
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• v.32 no.4
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• pp.385-399
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• 2003

We first introduce the quasi-score estimating function and applied the quasi-score estimating function to nonlinear time series models. We proposed the M quasi-score estimating functions bounded functions for the quasi-score estimating functions. Also, we investigated the asymptotic properties of quasi-likelihood estimators and M quasi-likelihood estimators. Simulation results show that the M quasi-likelihood estimators work better than the least squares estimators under the heavy-tailed distributions

• Communications for Statistical Applications and Methods
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• v.27 no.1
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• pp.47-64
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• 2020

In this paper, we derive some estimators of the scale parameter of the exponentiated half-logistic distribution based on the multiply Type-I hybrid censoring scheme. We assume that the shape parameter λ is known. We obtain the maximum likelihood estimator of the scale parameter σ. The scale parameter is estimated by approximating the given likelihood function using two different Taylor series expansions since the likelihood equation is not explicitly solved. We also obtain Bayes estimators using prior distribution. To obtain the Bayes estimators, we use the squared error loss function and general entropy loss function (shape parameter q = -0.5, 1.0). We also derive interval estimation such as the asymptotic confidence interval, the credible interval, and the highest posterior density interval. Finally, we compare the proposed estimators in the sense of the mean squared error through Monte Carlo simulation. The average length of 95% intervals and the corresponding coverage probability are also obtained.