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 Testing for Longitudinal Varying Coefficient Models

2014 ◽  
Vol 518 ◽  
pp. 356-360
Author(s):  
Chang Qing Liu
Keyword(s):  
Data Analysis ◽  
Empirical Likelihood ◽  
Real Data ◽  
Likelihood Method ◽  
Varying Coefficient Models ◽  
Empirical Likelihood Method ◽  
Real Data Analysis ◽  
Varying Coefficient ◽  
Testing Method

By using the empirical likelihood method, a testing method is proposed for longitudinal varying coefficient models. Some simulations and a real data analysis are undertaken to investigate the power of the empirical likelihood based testing method.

scholarly journals Empirical Likelihood Inference for First-Order Random Coefficient Integer-Valued Autoregressive Processes

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Zhiwen Zhao ◽  
Wei Yu
Keyword(s):  
Likelihood Ratio ◽  
Empirical Likelihood ◽  
Simulation Study ◽  
Asymptotic Theory ◽  
Likelihood Ratio Statistic ◽  
Random Coefficient ◽  
Likelihood Inference ◽  
Likelihood Method ◽  
Autoregressive Processes ◽  
First Order

We apply the empirical likelihood method to estimate the variance of random coefficient in the first-order random coefficient integer-valued autoregressive (RCINAR(1)) processes. The empirical likelihood ratio statistic is derived and some asymptotic theory for it is presented. Furthermore, a simulation study is presented to demonstrate the performance of the proposed method.

scholarly journals A New First-Order Integer-Valued Autoregressive Model with Bell Innovations

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 713
Author(s):  
Jie Huang ◽  
Fukang Zhu
Keyword(s):  
Poisson Distribution ◽  
Autoregressive Model ◽  
Real Data ◽  
Good Alternative ◽  
Distribution Functions ◽  
Infinitely Divisible ◽  
First Order ◽  
The Mean ◽  
Conditional Maximum ◽  
Mean Variance

A Poisson distribution is commonly used as the innovation distribution for integer-valued autoregressive models, but its mean is equal to its variance, which limits flexibility, so a flexible, one-parameter, infinitely divisible Bell distribution may be a good alternative. In addition, for a parameter with a small value, the Bell distribution approaches the Poisson distribution. In this paper, we introduce a new first-order, non-negative, integer-valued autoregressive model with Bell innovations based on the binomial thinning operator. Compared with other models, the new model is not only simple but also particularly suitable for time series of counts exhibiting overdispersion. Some properties of the model are established here, such as the mean, variance, joint distribution functions, and multi-step-ahead conditional measures. Conditional least squares, Yule–Walker, and conditional maximum likelihood are used for estimating the parameters. Some simulation results are presented to access these estimates’ performances. Real data examples are provided.

Empirical Likelihood Based Testing for Polynomial Regression Models

2014 ◽  
Vol 599-601 ◽  
pp. 927-930
Author(s):  
Pei Xin Zhao
Keyword(s):  
Data Analysis ◽  
Empirical Likelihood ◽  
Regression Models ◽  
Polynomial Regression ◽  
Real Data ◽  
Testing Procedure ◽  
Likelihood Method ◽  
Empirical Likelihood Method ◽  
Testing Method ◽  
Polynomial Regression Models

Based on the empirical likelihood method, a testing procedure is proposed for polynomial regression models. Some simulations and a real data analysis are undertaken to investigate the power of the empirical likelihood based testing method.

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 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 Estimation of Population Mean in Chain Ratio-Type Estimator under Systematic Sampling

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
Mursala Khan ◽  
Rajesh Singh
Keyword(s):  
Finite Population ◽  
Real Data ◽  
Survey Sampling ◽  
Systematic Sampling ◽  
Auxiliary Variables ◽  
Data Set ◽  
Population Mean ◽  
First Order ◽  
The Mean ◽  
A Chain

A chain ratio-type estimator is proposed for the estimation of finite population mean under systematic sampling scheme using two auxiliary variables. The mean square error of the proposed estimator is derived up to the first order of approximation and is compared with other relevant existing estimators. To illustrate the performances of the different estimators in comparison with the usual simple estimator, we have taken a real data set from the literature of survey sampling.

scholarly journals Empirical Likelihood Inference for Partial Functional Linear Regression Models Based on B-spline

2018 ◽  
Vol 8 (1) ◽  
pp. 135
Author(s):  
Mingao Yuan ◽  
Yue Zhang
Keyword(s):  
Linear Regression ◽  
Empirical Likelihood ◽  
Regression Models ◽  
Confidence Regions ◽  
Likelihood Method ◽  
Linear Regression Models ◽  
B Spline ◽  
Empirical Likelihood Method ◽  
Regression Parameters ◽  
Functional Linear Regression

In this paper, we apply empirical likelihood method to infer for the regression parameters in the partial functional linear regression models based on B-spline. We prove that the empirical log-likelihood ratio for the regression parameters converges in law to a weighted sum of independent chi-square distributions. Our simulation shows that the proposed empirical likelihood method produces more accurate confidence regions in terms of coverage probability than the asymptotic normality method.

Sign in / Sign up

Export Citation Format

Share Document