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Journal of Systems Science & Complexity 2017年第6期30卷 1350-1363页

作者： CHEN Wangxue TIAN Yi XIE Minyu Department of Mathematics and Statistics Jishou University Department of Mathematics and Statistics Central China Normal University

This paper studies a maximum likelihood estimator(MLE) of the parameter for a continuous one-parameter exponential family under ranked set sampling(RSS). The authors first find the optimal RSS according to the character of the family, viz, arrange the RSS based on quasi complete and sufficient statistic of independent and identically distributed(iid) samples. Then under this RSS, some sufficient conditions for the existence and uniqueness of the MLE, which are easily used in practice,are obtained. Using these conditions, the existence and uniqueness of the MLEs of the parameters for some usual distributions in this family are proved. Numerical simulations for these distributions fully support the result from the above two step optimizations of the sampling and the estimation method.

关键词： Complete sufficient statistic continuous one-parameter exponential family maximum likelihood estimator ranked set sampling

maximum likelihood estimator of the Location Parameter under Moving Extremes Ranked Set Sampling Design

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Acta Mathematicae Applicatae Sinica 2021年第1期37卷 101-108页

作者： Wang-xue CHEN Chun-xian LONG Rui YANG Dong-sen YAO Department of Mathematics and Statistics Jishou UniversityJishou 416000China

Cost effective sampling design is a problem of major concern in some experiments especially when the measurement of the characteristic of interest is costly or painful or time consuming.In the current paper,a modification of ranked set sampling(RSS)called moving extremes RSS(MERSS)is considered for the estimation of the location parameter for location family.A maximum likelihood estimator(MLE)of the location parameter for this family is studied and its properties are obtained.We prove that the MLE is an equivariant estimator under location transformation.In order to give more insight into the performance of MERSS with respect to(w.r.t.)simple random sampling(SRS),the asymptotic efficiency of the MLE using MERSS w.***.t.that using SRS is computed for some usual location distributions.The relative results show that the MLE using MERSS can be real competitors to the MLE using SRS.

关键词： ranked set sampling moving extremes ranked set sampling maximum likelihood estimator equivariant estimator fisher information number

EXACT maximum likelihood estimator FOR DRIFT FRACTIONAL BROWNIAN MOTION AT DISCRETE OBSERVATION

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Acta Mathematica Scientia 2011年第5期31卷 1851-1859页

作者：胡耀忠 Nualart David 肖炜麟张卫国 Department of Mathematics University of Kansas 405 Snow Hall Lawrence Kansas 66045-2142 USA School of Business and Administration South China University of Technology

This paper deals with the problems of consistency and strong consistency of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. Both the central limit theorem and the Berry-Ess′een bounds for these estimators are obtained by using the Stein’s method via Malliavin calculus.

关键词： maximum likelihood estimator fractional Brownian motions strong consistency central limit theorem Berry-Ess′een bounds Stein’s method Malliavin calculus

Fuzzy maximum likelihood estimator

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Fuzzy Maximum Likelihood Estimator

A novel nonparametric mixture model for the detection pattern of COVID-19 on Diamond Princess cruise

第三届中国智能计算大会

作者： Jicai Liu,Huanbin Liu College of Mathematics and Information Sciences,Shanghai Normal University,Shanghai 200234 College of Mathematics and Information sciences,Huanggang Normal University,Hubei 438000

＜正＞This paper proposes the new concept of fuzzy maximum likelihood estimator based on credibility distribution of fuzzy variables.The invariance properties of fuzzy maximum likelihood estimator are investigated.The... 详细信息

关键词： credibility measure fuzzy variable maximum principle maximum likelihood estimator

来源： cnki会议评论

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Statistical Theory and Related Fields 2023年第1期7卷 85-96页

作者： Huijuan Ma Jing Qin Fang Chen Yong Zhou KLATASDS-MOE School of Statistics and Academy of Statistics and Interdisciplinary SciencesEast China Normal UniversityShanghaiPeople’s Republic of China National Institute of Allergy and Infectious Diseases National Institutes of HealthBethesdaMDUSA School of Statistics and Management Shanghai University of Finance and EconomicsShanghaiPeople’s Republic of China

The outbreak of COVID-19 on the Diamond Princess cruise ship has attracted much attention.Motivated by the PCR testing data on the Diamond Princess,we propose a novel cure mixture nonparametric model to investigate the detection pattern.It combines a logistic regression for the probability of susceptible subjects with a nonparametric distribution for the detection of infected individuals.maximum likelihood estimators are proposed.The resulting estimators are shown to be consistent and asymptotically normal.Simulation studies demonstrate that the proposed approach is appropriate for practical use.Finally,we apply the proposed method to PCR testing data on the Diamond Princess to show its practical utility.

关键词： Cure model logistic regression maximum likelihood estimator mixture

ASYMPTOTIC DISTRIBUTION IN DIRECTED FINITE WEIGHTED RANDOM GRAPHS WITH AN INCREASING BI-DEGREE SEQUENCE

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Acta Mathematica Scientia 2020年第2期40卷 355-368页

作者：罗敬覃红汪政红 Department of Statistics South-Central University for NationalitiesWuhan 430074China Department of Statistics Zhongnan University of Economics and LawWuhan 430073China

The asymptotic normality of the fixed number of the maximum likelihood estimators(MLEs)in the directed finite weighted network models with an increasing bi-degree sequence has been established recently.In this article,we further derive the central limit theorem for linear combinations of all the MLEs with an increasing dimension when the edges take finite discrete weight.Simulation studies are provided to illustrate the asymptotic results.

关键词： Central limit theorem finite discrete network increasing number of parameters maximum likelihood estimator

Statistical Inference of Exponentiated Moment Exponential Distribution Based on Lower Record Values

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Communications in Mathematics and Statistics 2017年第3期5卷 231-260页

作者： Devendra Kumar Tanujit Dey Sanku Dey Department of Statistics Central University of HaryanaJant-PaliMahendergarh 123031HaryanaIndia Department of Quantitative Health Sciences Cleveland ClinicClevelandOH 44121USA Department of Statistics St.Anthony’s CollegeShillongMeghalayaIndia

Based on lower record values,we first derive the exact explicit expressions as well as recurrence relations for the single and product moments of record values and then use these results to compute the means,variances and coefficient of skewness and kurtosis of exponentiated moment exponential distribution(EMED),a new extension of moment exponential distribution,recently introduced by Hasnain(Exponentiated moment exponential distribution.Ph.D.Thesis,2013).Next we obtain the maximum likelihood estimators of the unknown parameters and the approximate confidence intervals of the EMED.Finally,we consider Bayes estimation under the symmetric and asymmetric loss functions using gamma priors for both shape and scale parameters.We have also derived the Bayes interval of this distribution and discussed both frequentist and the Bayesian prediction intervals of the future record values based on the observed record values.Monte Carlo simulations are performed to compare the performances of the proposed methods,and a data set has been analyzed for illustrative purposes.

关键词： Lower record values Single and product moments Recurrence relations Bayes estimator General entropy loss function maximum likelihood estimator

A LAW OF ITERATED LOGARITHM FOR THE MLE IN A RANDOM CENSORING MODEL WITH INCOMPLETE INFORMATION

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Acta Mathematica Scientia 2008年第3期28卷 501-512页

作者：宋凤丽刘禄勤 School of Mathematics and Statistics Wuhan University

In this article, a law of iterated logarithm for the maximum likelihood estimator in a random censoring model with incomplete information under certain regular conditions is obtained.

关键词： Random censoring model maximum likelihood estimator law of iterated logarithm

Robust estimators for Poisson Regression

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Open Journal of Statistics 2023年第1期13卷 112-118页

作者： Idriss Abdelmajid Idriss Weihu Cheng College of Applied Science Department of Statistics Beijing University of Technology Beijing China

The present paper proposes a new robust estimator for Poisson regression models. We used the weighted maximum likelihood estimators which are regarded as Mallows-type estimators. We perform a Monte Carlo simulation study to assess the performance of a suggested estimator compared to the maximum likelihood estimator and some robust methods. The result shows that, in general, all robust methods in this paper perform better than the classical maximum likelihood estimators when the model contains outliers. The proposed estimators showed the best performance compared to other robust estimators.

关键词： Poisson Regression Model maximum likelihood estimator Robust Estimation Contaminated Model Weighted maximum likelihood estimator

A Comparison of Four Methods of Estimating the Scale Parameter for the Exponential Distribution

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Journal of Applied Mathematics and Physics 2023年第10期11卷 2838-2847页

作者： Huda M. Alomari Department of Mathematics Al-Baha University Al Baha KSA

In this paper, the estimators of the scale parameter of the exponential distribution obtained by applying four methods, using complete data, are critically examined and compared. These methods are the maximum likelihood estimator (MLE), the Square-Error Loss Function (BSE), the Entropy Loss Function (BEN) and the Composite LINEX Loss Function (BCL). The performance of these four methods was compared based on three criteria: the Mean Square Error (MSE), the Akaike Information Criterion (AIC), and the Bayesian Information Criterion (BIC). Using Monte Carlo simulation based on relevant samples, the comparisons in this study suggest that the Bayesian method is better than the maximum likelihood estimator with respect to the estimation of the parameter that offers the smallest values of MSE, AIC, and BIC. Confidence intervals were then assessed to test the performance of the methods by comparing the 95% CI and average lengths (AL) for all estimation methods, showing that the Bayesian methods still offer the best performance in terms of generating the smallest ALs.

关键词： Bayes estimator maximum likelihood estimator Mean Squared Error (MSE) Akaike Information Criterion (AIC) Bayesian Information Criterion (BIC)