Empirical likelihood confidence intervals for the mean of a population containing many zero values

2003 ◽  
Vol 31 (1) ◽  
pp. 53-68 ◽  
Author(s):  
Jiahua Chen ◽  
Shun-Yi Chen ◽  
J. N. K. Rao
Keyword(s):  
Confidence Intervals ◽  
Empirical Likelihood ◽  
Zero Values ◽  
The Mean

scholarly journals Confidence Intervals for the Mean Based on Exponential Type Inequalities and Empirical Likelihood

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Sandra Vucane ◽  
Janis Valeinis ◽  
George Luta
Keyword(s):  
Confidence Intervals ◽  
Empirical Likelihood ◽  
Exponential Type ◽  
Likelihood Method ◽  
Interval Length ◽  
Simple Extension ◽  
Dependent Observations ◽  
Special Cases ◽  
Coverage Accuracy ◽  
The Mean

For independent observations, recently, it has been proposed to construct the confidence intervals for the mean using exponential type inequalities. Although this method requires much weaker assumptions than those required by the classical methods, the resulting intervals are usually too large. Still in special cases, one can find some advantage of using bounded and unbounded Bernstein inequalities. In this paper, we discuss the applicability of this approach for dependent data. Moreover, we propose to use the empirical likelihood method both in the case of independent and dependent observations for inference regarding the mean. The advantage of empirical likelihood is its Bartlett correctability and a rather simple extension to the dependent case. Finally, we provide some simulation results comparing these methods with respect to their empirical coverage accuracy and average interval length. At the end, we apply the above described methods for the serial analysis of a gene expression (SAGE) data example.

scholarly journals Empirical likelihood confidence intervals for the mean of a long-range dependent process

2007 ◽  
Vol 28 (4) ◽  
pp. 576-599 ◽  
Author(s):  
Daniel J. Nordman ◽  
Philipp Sibbertsen ◽  
Soumendra N. Lahiri
Keyword(s):  
Confidence Intervals ◽  
Long Range ◽  
Empirical Likelihood ◽  
Dependent Process ◽  
The Mean

Novel empirical likelihood inference for the mean difference with right-censored data

2021 ◽  
pp. 096228022110417
Author(s):  
Kangni Alemdjrodo ◽  
Yichuan Zhao
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Censored Data ◽  
Empirical Likelihood ◽  
Likelihood Method ◽  
Right Censored Data ◽  
Empirical Likelihood Method ◽  
Chi Squared ◽  
Coverage Accuracy ◽  
The Mean

This paper focuses on comparing two means and finding a confidence interval for the difference of two means with right-censored data using the empirical likelihood method combined with the independent and identically distributed random functions representation. In the literature, some early researchers proposed empirical link-based confidence intervals for the mean difference based on right-censored data using the synthetic data approach. However, their empirical log-likelihood ratio statistic has a scaled chi-squared distribution. To avoid the estimation of the scale parameter in constructing confidence intervals, we propose an empirical likelihood method based on the independent and identically distributed representation of Kaplan–Meier weights involved in the empirical likelihood ratio. We obtain the standard chi-squared distribution. We also apply the adjusted empirical likelihood to improve coverage accuracy for small samples. In addition, we investigate a new empirical likelihood method, the mean empirical likelihood, within the framework of our study. The performances of all the empirical likelihood methods are compared via extensive simulations. The proposed empirical likelihood-based confidence interval has better coverage accuracy than those from existing methods. Finally, our findings are illustrated with a real data set.

Construction of Confidence Intervals for the Mean of a Population Containing Many Zero Values

1998 ◽  
Vol 16 (3) ◽  
pp. 362 ◽  
Author(s):  
Alan H. Kvanli ◽  
Yaung Kaung Shen ◽  
Lih Yuan Deng
Keyword(s):  
Confidence Intervals ◽  
Zero Values ◽  
The Mean

scholarly journals Mean Empirical Likelihood Inference for Response Mean with Data Missing at Random

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Hanji He ◽  
Guangming Deng
Keyword(s):  
Empirical Likelihood ◽  
Missing At Random ◽  
Confidence Regions ◽  
Likelihood Inference ◽  
High Dimensional ◽  
Finite Sample ◽  
The Mean ◽  
Data Missing ◽  
Consistency And Asymptotic Normality ◽  
The Impact

We extend the mean empirical likelihood inference for response mean with data missing at random. The empirical likelihood ratio confidence regions are poor when the response is missing at random, especially when the covariate is high-dimensional and the sample size is small. Hence, we develop three bias-corrected mean empirical likelihood approaches to obtain efficient inference for response mean. As to three bias-corrected estimating equations, we get a new set by producing a pairwise-mean dataset. The method can increase the size of the sample for estimation and reduce the impact of the dimensional curse. Consistency and asymptotic normality of the maximum mean empirical likelihood estimators are established. The finite sample performance of the proposed estimators is presented through simulation, and an application to the Boston Housing dataset is shown.

scholarly journals A Bimodal Extension of the Exponential Distribution with Applications in Risk Theory

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 679
Author(s):  
Jimmy Reyes ◽  
Emilio Gómez-Déniz ◽  
Héctor W. Gómez ◽  
Enrique Calderín-Ojeda
Keyword(s):  
Exponential Distribution ◽  
Hazard Rate ◽  
Rate Function ◽  
Estimation Methods ◽  
Inverse Gaussian ◽  
New Family ◽  
Tail Distribution ◽  
Zero Values ◽  
The Mean ◽  
Positive Support

There are some generalizations of the classical exponential distribution in the statistical literature that have proven to be helpful in numerous scenarios. Some of these distributions are the families of distributions that were proposed by Marshall and Olkin and Gupta. The disadvantage of these models is the impossibility of fitting data of a bimodal nature of incorporating covariates in the model in a simple way. Some empirical datasets with positive support, such as losses in insurance portfolios, show an excess of zero values and bimodality. For these cases, classical distributions, such as exponential, gamma, Weibull, or inverse Gaussian, to name a few, are unable to explain data of this nature. This paper attempts to fill this gap in the literature by introducing a family of distributions that can be unimodal or bimodal and nests the exponential distribution. Some of its more relevant properties, including moments, kurtosis, Fisher’s asymmetric coefficient, and several estimation methods, are illustrated. Different results that are related to finance and insurance, such as hazard rate function, limited expected value, and the integrated tail distribution, among other measures, are derived. Because of the simplicity of the mean of this distribution, a regression model is also derived. Finally, examples that are based on actuarial data are used to compare this new family with the exponential distribution.

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