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Chinese Science Bulletin 1993年第8期38卷 617-620页

作者：梁华成平 Institute of Systems Science Academia Sinica

ON THE BEST UNIFORM CONVERGENCE RATE OF EB estimators

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Systems Science and Mathematical Sciences 1995年第1期8卷 52-56页

作者： LIANG Hua (Institute of Systems Science, Academia Sinica, Beijing 100080, China)YUAN Yahua (Department of Arizona State University, Az 85287-1804, U.S.A.) 中科院系统科学所北京 Arizona State University 美国

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关键词： Empirical Bayes estimators best uniform convergence rate.

estimators of Linear Regression Model and Prediction under Some Assumptions Violation

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Open Journal of Statistics 2012年第5期2卷 534-546页

作者： Kayode Ayinde Emmanuel O. Apata Oluwayemisi O. Alaba Department of Statistics Ladoke Akintola University of Technology Ogbomoso Nigeria Department of Statistics University of Ibadan Ibadan Nigeria

The development of many estimators of parameters of linear regression model is traceable to non-validity of the assumptions under which the model is formulated, especially when applied to real life situation. This notwithstanding, regression analysis may aim at prediction. Consequently, this paper examines the performances of the Ordinary Least Square (OLS) estimator, Cochrane-Orcutt (COR) estimator, Maximum Likelihood (ML) estimator and the estimators based on Principal Component (PC) analysis in prediction of linear regression model under the joint violations of the assumption of non-stochastic regressors, independent regressors and error terms. With correlated stochastic normal variables as regressors and autocorrelated error terms, Monte-Carlo experiments were conducted and the study further identifies the best estimator that can be used for prediction purpose by adopting the goodness of fit statistics of the estimators. From the results, it is observed that the performances of COR at each level of correlation (multicollinearity) and that of ML, especially when the sample size is large, over the levels of autocorrelation have a convex-like pattern while that of OLS and PC are concave-like. Also, as the levels of multicollinearity increase, the estimators, except the PC estimators when multicollinearity is negative, rapidly perform better over the levels autocorrelation. The COR and ML estimators are generally best for prediction in the presence of multicollinearity and autocorrelated error terms. However, at low levels of autocorrelation, the OLS estimator is either best or competes consistently with the best estimator, while the PC estimator is either best or competes with the best when multicollinearity level is high(λ>0.8 or λ-0.49).

关键词： Prediction estimators Linear Regression Model Autocorrelated Error Terms Correlated Stochastic Normal Regressors

Variable Selection via Biased estimators in the Linear Regression Model

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Open Journal of Statistics 2020年第1期10卷 113-126页

作者： Manickavasagar Kayanan Pushpakanthie Wijekoon Postgraduate Institute of Science University of Peradeniya Peradeniya Sri Lanka Department of Physical Science Vavuniya Campus of the University of Jaffna Vavuniya Sri Lanka Department of Statistics and Computer Science University of Peradeniya Peradeniya Sri Lanka

Least Absolute Shrinkage and Selection Operator (LASSO) is used for variable selection as well as for handling the multicollinearity problem simultaneously in the linear regression model. LASSO produces estimates having high variance if the number of predictors is higher than the number of observations and if high multicollinearity exists among the predictor variables. To handle this problem, Elastic Net (ENet) estimator was introduced by combining LASSO and Ridge estimator (RE). The solutions of LASSO and ENet have been obtained using Least Angle Regression (LARS) and LARS-EN algorithms, respectively. In this article, we proposed an alternative algorithm to overcome the issues in LASSO that can be combined LASSO with other exiting biased estimators namely Almost Unbiased Ridge Estimator (AURE), Liu Estimator (LE), Almost Unbiased Liu Estimator (AULE), Principal Component Regression Estimator (PCRE), r-k class estimator and r-d class estimator. Further, we examine the performance of the proposed algorithm using a Monte-Carlo simulation study and real-world examples. The results showed that the LARS-rk and LARS-rd algorithms,?which are combined LASSO with r-k class estimator and r-d class estimator,?outperformed other algorithms under the moderated and severe multicollinearity.

关键词： Variable Selection Least Absolute Shrinkage and Selection Operator (LASSO) Least Angle Regression (LARS) Elastic Net (ENet) Biased estimators

Nelson-Aalen and Kaplan-Meier estimators in Competing Risks

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Applied Mathematics 2014年第4期5卷 765-776页

作者： Didier Alain Njamen-Njomen Joseph Ngatchou-Wandji Department of Mathematics and Computer Sciences Faculty of Sciences University of Maroua Maroua Cameroon Department of Mathematics Faculty of Sciences University of Yaounde 1 Yaounde Cameroon University of Lorraine Lorraine France

In this paper, stochastic processes developed by Aalen [1]?[2] are adapted to the Nelson-Aalen and Kaplan-Meier?[3] estimators in a context of competing risks. We focus only on the probability distributions of complete downtime individuals whose causes are known and which bring us to consider a partition of individuals into sub-groups for each cause. We then study the asymptotic properties of nonparametric estimators obtained.

关键词： Censored Data Counting Process Competitive Risk Non-Parametric estimators The Cumulative Incidence Function Risk Function Specific Cause Conditional Distribution Function

A Class of estimators for Population Ratio in Simple Random Sampling Using Variable Transformation

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Open Journal of Statistics 2014年第4期4卷 284-291页

作者： A. C. Onyeka V. U. Nlebedim C. H. Izunobi Department of Statistics Federal University of Technology Owerri Nigeria

This paper is an extension and generalization of the study carried out by [1] on the estimation of the population ratio (R) of the population means of two variables (y and x) under Simple Random Sampling (SRS) scheme, using a variable transformation of the auxiliary variable, x. All the six estimators proposed by [1] are easily identified as special cases of the proposed class of estimators. Asymptotic properties of the proposed class of estimators are derived theoretically and subsequently verified using empirical illustrations. Some of the proposed estimators are found to have relatively large gains in efficiency over the customary ratio estimator, ?for the given data set.

关键词： Variable Transformation Ratio Product and Regression-Type estimators Mean Squared Error

Asymptotic Comparison of Method of Moments estimators and Maximum Likelihood estimators of Parameters in Zero-Inflated Poisson Model

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Applied Mathematics 2012年第6期3卷 610-616页

作者： G. Nanjundan T. Raveendra Naika Department of Statistics Bangalore University Bangalore India Maharani’s Science College for Women Bangalore India

This paper discusses the estimation of parameters in the zero-inflated Poisson (ZIP) model by the method of moments. The method of moments estimators (MMEs) are analytically compared with the maximum likelihood estima... 详细信息

关键词： Zero-Inflated Poisson Model Maximum Likelihood and Moment estimators EM Algorithm Asymptotic Relative Efficiency

Using Residual estimators to Detect Outliers and Potential Controlling Observations in Structural Equation Modelling: QQ Plot Approach

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Open Journal of Statistics 2020年第5期10卷 905-914页

作者： A. R. Abdul-Aziz Albert Luguterah Bashiru I. I. Saeed Department of Mathematics & Statistics Kumasi Technical University (KsTU) Kumasi Ghana Department of Statistics Faculty of Mathematical Sciences C.K. Tedam University of Technology and Applied Sciences (CKT-UTAS) Navrongo Ghana Department of Statistical Sciences Tamale Technical University (TaTU) Tamale Ghana

The structural equation model (SEM) concept is generally influenced by the presence of outliers and controlling variables. To a very large extent, this could have consequential effects on the parameters and the model fitness. Though previous researches have studied outliers and controlling observations from various perspectives including the use of box plots, normal probability plots, among others, the use of uniform horizontal QQ plot is yet to be explored. This study is, therefore, aimed at applying uniform QQ plots to identifying outliers and possible controlling observations in SEM. The results showed that all the three methods of estimators manifest the ability to identify outliers and possible controlling observations in SEM. It was noted that the Anderson-Rubin estimator of QQ plot showed a more efficient or visual display of spotting outliers and possible controlling observations as compared to the other methods of estimators. Therefore, this paper provides an efficient way identifying outliers as it fragments the data set.

关键词： Outliers Controlling Observations estimators QQ Plots Structural Equation Modelling

Asymptotic Normality of the Nelson-Aalen and the Kaplan-Meier estimators in Competing Risks

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Applied Mathematics 2019年第7期10卷 545-560页

作者： Didier Alain Njamen Njomen Department of Mathematics and Computer Science Faculty of Science University of Maroua Maroua Cameroon

This paper studies the asymptotic normality of the Nelson-Aalen and the Kaplan-Meier estimators in a competing risks context in presence of independent right-censorship. To prove our results, we use Robelledo’s theorem which makes it possible to apply the central limit theorem to certain types of particular martingales. From the results obtained, confidence bounds for the hazard and the survival functions are provided.

关键词： Censored Data Right-Censoring Counting Process Competing Risks Nelson-Aalen and Kaplan-Meier estimators Asymptotic Properties of estimators Confidence Bands

Separate-Type estimators for Estimating Population Ratio in Post-Stratified Sampling Using Variable Transformation

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Open Journal of Statistics 2015年第1期5卷 27-34页

作者： Aloy Chijioke Onyeka Chinyeaka Hostensia Izunobi Iheanyi Sylvester Iwueze Department of Statistics Federal University of Technology Owerri Nigeria

The study proposes, along the line of [1], six separate-type estimators for estimating the population ratio of two variables in post-stratified sampling, using variable transformation. Properties of the proposed estimators were obtained up to first order approximations, both for achieved sample configurations (conditional argument) and over repeated samples of fixed size n (unconditional argument). Efficiency conditions, under which the proposed separate-type estimators would perform better than the associated customary separate-type estimators in terms of having smaller mean squared errors, were obtained. Furthermore, conditions under which some of the proposed separate-type estimators would perform better than other proposed separate-type estimators were also obtained. The optimum estimators among the proposed separate-type estimators were obtained and an empirical illustration confirmed the theoretical results.

关键词： Variable Transformation Separate-Type Estimator Optimum estimators Ratio Product and Regression-Type estimators Mean Squared Error