• Communications for Statistical Applications and Methods
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• v.10 no.2
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• pp.525-534
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• 2003

If a restriction is imposed only to a (proper) subset of parameters of interest, we call it a local restriction. Statistical inference under a local restriction in multinomial setting is studied. The maximum likelihood estimation under a local restriction and likelihood ratio tests for and against a local restriction are discussed. A real data is analyzed for illustrative purpose.

• Journal of the Korean Data and Information Science Society
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• v.10 no.2
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• pp.465-472
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• 1999

We considered a bootstrap method for constructing confidenc intervals for a one parameter model using multinomial sampling. The convergence rates or the proposed bootstrap method are calculated for model-based maximum likelihood estimators(MLE) using multinomial sampling. Monte Carlo simulation was used to compare the performance of bootstrap methods with normal approximations in terms of the average coverage probability criterion.

• Journal of Korean Society for Quality Management
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• v.29 no.1
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• pp.11-23
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• 2001

This paper is concerned with suggesting a Bayesian method for variable selection in multinomial logit model. It is based upon an optimal rule suggested by use of Bayes rule which minimizes a risk induced by selecting the multinomial logit model. The rule is to find a subset of variables that maximizes the marginal likelihood of the model. We also propose a Laplace-Metropolis algorithm intended to suggest a simple method forestimating the marginal likelihood of the model. Based upon two examples, artificial data and empirical data examples, the Bayesian method is illustrated and its efficiency is examined.

• Journal of the Korean Data and Information Science Society
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• v.14 no.2
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• pp.413-428
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• 2003

If a restriction is imposed only to a (proper) subset of parameters of interest, we call it a local restriction. Statistical inference under a local restriction in multinomial setting is studied. The maximum likelihood estimation under a local restriction and likelihood ratio tests for and against a local restriction are discussed. A real data is analyzed for illustrative purpose.

• Journal of the Korean Data and Information Science Society
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• v.23 no.2
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• pp.411-417
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• 2012

In this paper, we consider the estimation of multinomial proportions. Multinomial distribution is the most important multivaritate distribution. Estimation of multinomial parameters for multinomial distribution is widely applicable to many practical research areas including genetics. We investigated the properties of several frequency substitution estimates and derived the maximum likelihood estimate of multinomial proportions of Hardy Weinberg proportions. Phenotype and genotype frequencies of allele are used to the estimation of multinomial proportions. These estimates are then analyzed via numerical data. Small sample Monte Carlo simulation is conducted to compare considered estimates of multinomial proportions.

• Communications for Statistical Applications and Methods
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• v.14 no.1
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• pp.121-131
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• 2007

In this paper, we examine the problem of estimating the sensitive characteristics and behaviors in a multinomial randomized response model using Bayesian approach. We derived a posterior distribution for parameter of interest for multinomial randomized response model. Based on the posterior distribution, we also calculated a credible intervals and mean squared error (MSE). We finally compare the maximum likelihood estimator and the Bayes estimator in terms of MSE.

• Journal of the Korean Statistical Society
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• v.26 no.4
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• pp.453-465
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• 1997

The family of power-divergence statistics conditional on margins is considered for testing homogeneity of .tau. multinomial populations with equal sample size and the exact Bahadur slope is obtained. It is shown that the likelihood ratio test conditional on margins is the most Bahadur efficient among the family of power-divergence statistics.

• Journal of the Korean Statistical Society
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• v.33 no.3
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• pp.313-321
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• 2004

We consider the problem of testing cell probabilities in sparse multinomial data. Aerts et al. (2000) presented T=${{\Sigma}_{i=1}}^{k}{[{p_i}^{*}-E{(p_{i}}^{*})]^2$ as a test statistic with the local least square polynomial estimator ${{p}_{i}}^{*}$, and derived its asymptotic distribution. The local least square estimator may produce negative estimates for cell probabilities. The local maximum likelihood polynomial estimator ${{\hat{p}}_{i}}$, however, guarantees positive estimates for cell probabilities and has the same asymptotic performance as the local least square estimator (Baek and Park, 2003). When there are cell probabilities with relatively much different sizes, the same contribution of the difference between the estimator and the hypothetical probability at each cell in their test statistic would not be proper to measure the total goodness-of-fit. We consider a Pearson type of goodness-of-fit test statistic, $T_1={{\Sigma}_{i=1}}^{k}{[{p_i}^{*}-E{(p_{i}}^{*})]^2/p_{i}$ instead, and show it follows an asymptotic normal distribution. Also we investigate the asymptotic normality of $T_2={{\Sigma}_{i=1}}^{k}{[{p_i}^{*}-E{(p_{i}}^{*})]^2/p_{i}$ where the minimum expected cell frequency is very small.

• Proceedings of the Korean Association for Survey Research Conference
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• 2006.06a
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• pp.131-159
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• 2006

This paper consider multinomial group testing which is concerned with classification each of N given units into one of k disjoint categories. In this paper, we propose exact Bayesian, approximate Bayesian, bootstrap methods for estimating individual category proportions using the multinomial group testing model proposed by Bar-Lev et al (2005). By the comparison of Mcan Squre Error (MSE), it is shown that the exact Bayesian method has a bettor efficiency and consistency than maximum likelihood method. We suggest an approximate Bayesian approach using Markov Chain Monte Carlo (MCMC) for posterior computation. We derive exact credible intervals based on the exact Bayesian estimators and present confidence intervals using the bootstrap and MCMC. These intervals arc shown to often have better coverage properties and similar mean lengths to maximum likelihood method already available. Furthermore the proposed models are illustrated using data from a HIV blooding test study throughout California, 2000.

• Communications for Statistical Applications and Methods
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• v.17 no.1
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• pp.67-77
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• 2010

In multinomial scheme with step-wise sampling, maximum likelihood estimates of multinomial probabilities are improved when some frequencies are merged. In this study, for cell probabilities in a I by J independent contingency tables, exact MLE and step-wise estimation methods are applied and the results are compared using MSE and Bias.