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.

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.

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

scholarly journals Interval Estimation of Random Coefficient Integer-Valued Autoregressive Model Based on Mean Empirical Likelihood Method

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Xianghong Xu ◽  
Dehui Wang ◽  
Zhiwen Zhao
Keyword(s):  
Data Analysis ◽  
Empirical Likelihood ◽  
Autoregressive Model ◽  
Interval Estimation ◽  
Real Data ◽  
Confidence Regions ◽  
Random Coefficient ◽  
Likelihood Method ◽  
First Order ◽  
The Mean

In this paper, we study the use of the mean empirical likelihood (MEL) method in a first-order random coefficient integer-valued autoregressive model. The MEL ratio statistic is established, its limiting properties are discussed, and the confidence regions for the parameter of interest are derived. Furthermore, a simulation study is presented to demonstrate the performance of the proposed method. Finally, a real data analysis of dengue fever is performed.

EMPIRICAL-LIKELIHOOD-BASED CONFIDENCE INTERVALS FOR CONDITIONAL VARIANCE IN HETEROSKEDASTIC REGRESSION MODELS

2010 ◽  
Vol 27 (1) ◽  
pp. 154-177 ◽  
Author(s):  
Ngai Hang Chan ◽  
Liang Peng ◽  
Dabao Zhang
Keyword(s):  
Confidence Intervals ◽  
Empirical Likelihood ◽  
Regression Models ◽  
Variance Reduction ◽  
Normal Approximation ◽  
Conditional Variance ◽  
Likelihood Method ◽  
Simulation Studies ◽  
Likelihood Methods ◽  
Reduction Techniques

Fan and Yao (1998) proposed an efficient method to estimate the conditional variance of heteroskedastic regression models. Chen, Cheng, and Peng (2009) applied variance reduction techniques to the estimator of Fan and Yao (1998) and proposed a new estimator for conditional variance to account for the skewness of financial data. In this paper, we apply empirical likelihood methods to construct confidence intervals for the conditional variance based on the estimator of Fan and Yao (1998) and the reduced variance modification of Chen et al. (2009). Simulation studies and data analysis demonstrate the advantage of the empirical likelihood method over the normal approximation method.

Bayesian and influence function-based empirical likelihoods for inference of sensitivity in diagnostic tests

2020 ◽  
Vol 29 (12) ◽  
pp. 3457-3491
Author(s):  
Yan Hai ◽  
Xiaoyi Min ◽  
Gengsheng Qin ◽  
Keyword(s):  
Empirical Likelihood ◽  
Influence Function ◽  
Poor Performance ◽  
Real Data ◽  
Likelihood Method ◽  
Interval Length ◽  
Finite Sample ◽  
Data Set ◽  
Numerical Studies ◽  
Medical Diagnostic

In medical diagnostic studies, a diagnostic test can be evaluated based on its sensitivity under a desired specificity. Existing methods for inference on sensitivity include normal approximation-based approaches and empirical likelihood (EL)-based approaches. These methods generally have poor performance when the specificity is high, and some require choosing smoothing parameters. We propose a new influence function-based empirical likelihood method and Bayesian empirical likelihood methods to overcome such problems. Numerical studies are performed to compare the finite sample performance of the proposed approaches with existing methods. The proposed methods are shown to perform better in terms of both coverage probability and interval length. A real data set from Alzheimer’s Disease Neuroimaging Initiative (ANDI) is analyzed.

scholarly journals Assessing the Accuracy of Approximate Confidence Intervals Proposed for the Mean of Poisson Distribution

2020 ◽  
Vol 18 (1) ◽  
pp. 2-13
Author(s):  
Alireza Shirvani ◽  
Malek Fathizadeh
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Poisson Distribution ◽  
Count Data ◽  
Coverage Probability ◽  
Discrete Distribution ◽  
Interval Length ◽  
Average Confidence ◽  
The Mean ◽  
Approximate Confidence Intervals

The Poisson distribution is applied as an appropriate standard model to analyze count data. Because this distribution is known as a discrete distribution, representation of accurate confidence intervals for its distribution mean is extremely difficult. Approximate confidence intervals were presented for the Poisson distribution mean. The purpose of this study is to simultaneously compare several confidence intervals presented, according to the average coverage probability and accurate confidence coefficient and the average confidence interval length criteria.

Decoration technique and surface physics

1978 ◽  
Vol 36 (1) ◽  
pp. 436-437 ◽  
Author(s):  
H. Bethge
Keyword(s):  
Diffusion Path ◽  
Special Importance ◽  
Surface Physics ◽  
Step Structure ◽  
Initial Stage ◽  
Special Cases ◽  
Atomic Surface ◽  
The Mean ◽  
Bulk Structure ◽  
Decoration Technique

Besides the atomic surface structure, diverging in special cases with respect to the bulk structure, the real structure of a surface Is determined by the step structure. Using the decoration technique /1/ it is possible to image step structures having step heights down to a single lattice plane distance electron-microscopically. For a number of problems the knowledge of the monatomic step structures is important, because numerous problems of surface physics are directly connected with processes taking place at these steps, e.g. crystal growth or evaporation, sorption and nucleatlon as initial stage of overgrowth of thin films.To demonstrate the decoration technique by means of evaporation of heavy metals Fig. 1 from our former investigations shows the monatomic step structure of an evaporated NaCI crystal. of special Importance Is the detection of the movement of steps during the growth or evaporation of a crystal. From the velocity of a step fundamental quantities for the molecular processes can be determined, e.g. the mean free diffusion path of molecules.

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.

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