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1 
Jackknife Empirical Likelihood for the Variance in the Linear Regression ModelLin, HuiLing 25 July 2013 (has links)
The variance is the measure of spread from the center. Therefore, how to accurately estimate variance has always been an important topic in recent years. In this paper, we consider a linear regression model which is the most popular model in practice. We use jackknife empirical likelihood method to obtain the interval estimate of variance in the regression model. The proposed jackknife empirical likelihood ratio converges to the standard chisquared distribution. The simulation study is carried out to compare the jackknife empirical likelihood method and standard method in terms of coverage probability and interval length for the confidence interval of variance from linear regression models. The proposed jackknife empirical likelihood method has better performance. We also illustrate the proposed methods using two real data sets.

2 
Empirical Likelihood Inference for TwoSample ProblemsYan, Ying January 2010 (has links)
In this thesis, we are interested in empirical likelihood (EL) methods for twosample problems, with focus on the difference of the two population means. A
weighted empirical likelihood method (WEL) for twosample problems is developed. We also consider a scenario where sample data on auxiliary variables are fully observed for both samples but values of the response variable are subject to missingness. We develop an adjusted empirical likelihood method for inference of the difference of the two population means for this scenario where missing values are handled by a regression imputation method. Bootstrap calibration for WEL is also developed. Simulation studies are conducted to evaluate the performance of naive EL, WEL and WEL with bootstrap calibration (BWEL) with comparison to the usual twosample ttest in terms of power of the tests and coverage accuracies. Simulation for the adjusted EL for the linear regression model with missing data is also conducted.

3 
Empirical Likelihood Inference for TwoSample ProblemsYan, Ying January 2010 (has links)
In this thesis, we are interested in empirical likelihood (EL) methods for twosample problems, with focus on the difference of the two population means. A
weighted empirical likelihood method (WEL) for twosample problems is developed. We also consider a scenario where sample data on auxiliary variables are fully observed for both samples but values of the response variable are subject to missingness. We develop an adjusted empirical likelihood method for inference of the difference of the two population means for this scenario where missing values are handled by a regression imputation method. Bootstrap calibration for WEL is also developed. Simulation studies are conducted to evaluate the performance of naive EL, WEL and WEL with bootstrap calibration (BWEL) with comparison to the usual twosample ttest in terms of power of the tests and coverage accuracies. Simulation for the adjusted EL for the linear regression model with missing data is also conducted.

4 
Empirical Likelihood Confidence Intervals for the Population Mean Based on Incomplete DataValdovinos Alvarez, Jose Manuel 09 May 2015 (has links)
The use of doubly robust estimators is a key for estimating the population mean response in the presence of incomplete data. Cao et al. (2009) proposed an alternative doubly robust estimator which exhibits strong performance compared to existing estimation methods. In this thesis, we apply the jackknife empirical likelihood, the jackknife empirical likelihood with nuisance parameters, the profile empirical likelihood, and an empirical likelihood method based on the influence function to make an inference for the population mean. We use these methods to construct confidence intervals for the population mean, and compare the coverage probabilities and interval lengths using both the ``usual'' doubly robust estimator and the alternative estimator proposed by Cao et al. (2009). An extensive simulation study is carried out to compare the different methods. Finally, the proposed methods are applied to two real data sets.

5 
Jackknife Empirical Likelihood Inference For The Pietra RatioSu, Yueju 17 December 2014 (has links)
Pietra ratio (Pietra index), also known as Robin Hood index, Schutz coefficient (RicciSchutz index) or half the relative mean deviation, is a good measure of statistical heterogeneity in the context of positivevalued data sets. In this thesis, two novel methods namely "adjusted jackknife empirical likelihood" and "extended jackknife empirical likelihood" are developed from the jackknife empirical likelihood method to obtain interval estimation of the Pietra ratio of a population. The performance of the two novel methods are compared with the jackknife empirical likelihood method, the normal approximation method and two bootstrap methods (the percentile bootstrap method and the bias corrected and accelerated bootstrap method). Simulation results indicate that under both symmetric and skewed distributions, especially when the sample is small, the extended jackknife empirical likelihood method gives the best performance among the six methods in terms of the coverage probabilities and interval lengths of the confidence interval of Pietra ratio; when the sample size is over 20, the adjusted jackknife empirical likelihood method performs better than the other methods, except the extended jackknife empirical likelihood method. Furthermore, several real data sets are used to illustrate the proposed methods.

6 
Jackknife Empirical Likelihood Inference for the Absolute Mean Deviationmeng, xueping 15 July 2013 (has links)
In statistics it is of interest to find a better interval estimator of the absolute mean deviation. In this thesis, we focus on using the jackknife, the adjusted and the extended jackknife empirical likelihood methods to construct confidence intervals for the mean absolute deviation of a random variable. The empirical loglikelihood ratio statistics is derived whose asymptotic distribution is a standard chisquare distribution. The results of simulation study show the comparison of the average length and coverage probability by using jackknife empirical likelihood methods and normal approximation method. The proposed adjusted and extended jackknife empirical likelihood methods perform better than other methods for symmetric and skewed distributions. We use real data sets to illustrate the proposed jackknife empirical likelihood methods.

7 
Empirical Likelihood Based Confidence Intervals for the Difference between Two Sensitivities of Continuousscale Diagnostic Tests at a Fixed Level of SpecificityYao, Suqin 28 November 2007 (has links)
Diagnostic testing is essential to distinguish nondiseased individuals from diseased individuals. The sensitivity and specificity are two important indices for the diagnostic accuracy of continuousscale diagnostic tests. If we want to compare the effectiveness of two tests, it is of interest to construct a confidence interval for the difference of the two sensitivities at a fixed level of specificity. In this thesis, we propose two empirical likelihood based confidence intervals (HBELI and HBELII) for the difference of two sensitivities at a predetermined specificity level. Simulation studies show that when correlation between the two test results exists, HBELI and HBELII intervals perform better than the existing bootstrap based BCa, BTI and BTII intervals due to shorter interval lengths. However, when there is no correlation, BCa, BTI and BTII intervals outperform HBELI and HBELII intervals due to better coverage probability in most simulation settings.

8 
HYPOTHESIS TESTING IN FINITE SAMPLES WITH TIME DEPENDENT DATA: APPLICATIONS IN BANKINGAllen, Jason, 1974 26 September 2007 (has links)
This thesis is concerned with hypothesis testing in models where data exhibits
time dependence. The focus is on two cases where the dependence of observations
across time leads to nonstandard hypothesis testing techniques.
This thesis first considers models estimated by Generalized Method of Moments
(GMM, Hansen (1982)) and the approach to inference. The main problem with
standard tests are size distortions in the test statistics. An innovative resampling
method, which we label Empirical Likelihood Block Bootstrapping, is proposed. The
firstorder asymptotic validity of the proposed procedure is proven, and a series of
Monte Carlo experiments show it may improve test sizes over conventional block
bootstrapping. Also staying in the context of GMM this thesis shows that the testcorrection
given in Hall (2000) which improves power, can distort size with time
dependent data. In this case it is of even greater importance to use a bootstrap that
can have good size in finite samples.
The empirical likelihood is applied to a multifactor model of U.S. bank risk estimated
by GMM. The approach to inference is found to be important to the overall
conclusion about bank risk. The results suggest U.S. bank stock returns are sensitive
to movements in market and liquidity risk.
In the context of panel data, this thesis is the first to my knowledge to consider
the estimation of costfunctions as well as conduct inference taking into account the
strong dependence of data across time. This thesis shows that standard approaches
to estimating costfunctions for a set of Canadian banks lead to a downward bias in
the estimated coefficients and therefore an upward bias in the measure of economies
of scale. When nonstationary panel techniques are applied results suggest economies
of scale of around 6 per cent in Canadian banking as well as costefficiency differences
across banks that are correlated with size. / Thesis (Ph.D, Economics)  Queen's University, 20070924 17:25:22.212

9 
Jackknife Empirical Likelihood Inferences for the Skewness and KurtosisZhang, Yan 10 May 2014 (has links)
Skewness and kurtosis are measures used to describe shape characteristics of distributions. In this thesis, we examine the interval estimates about the skewness and kurtosis by using jackknife empirical likelihood (JEL), adjusted JEL, extended JEL, traditional bootstrap, percentile bootstrap, and BCa bootstrap methods. The limiting distribution of the JEL ratio is the standard chisquared distribution. The simulation study of this thesis makes a comparison of different methods in terms of the coverage probabilities and interval lengths under the standard normal distribution and exponential distribution. The proposed adjusted JEL and extended JEL perform better than the other methods. Finally we illustrate the proposed JEL methods and different bootstrap methods with three real data sets.

10 
Generalized Empirical Likelihood EstimatorsJanuary 2013 (has links)
abstract: Schennach (2007) has shown that the Empirical Likelihood (EL) estimator may not be asymptotically normal when a misspecified model is estimated. This problem occurs because the empirical probabilities of individual observations are restricted to be positive. I find that even the EL estimator computed without the restriction can fail to be asymptotically normal for misspecified models if the sample moments weighted by unrestricted empirical probabilities do not have finite population moments. As a remedy for this problem, I propose a group of alternative estimators which I refer to as modified EL (MEL) estimators. For correctly specified models, these estimators have the same higher order asymptotic properties as the EL estimator. The MEL estimators are obtained by the Generalized Method of Moments (GMM) applied to an exactly identified model. The simulation results provide promising evidence for these estimators. In the second chapter, I introduce an alternative group of estimators to the Generalized Empirical Likelihood (GEL) family. The new group is constructed by employing demeaned moment functions in the objective function while using the original moment functions in the constraints. This designation modifies the higherorder properties of estimators. I refer to these new estimators as Demeaned Generalized Empirical Likelihood (DGEL) estimators. Although Newey and Smith (2004) show that the EL estimator in the GEL family has fewer sources of bias and is higherorder efficient after biascorrection, the demeaned exponential tilting (DET) estimator in the DGEL group has those superior properties. In addition, if data are symmetrically distributed, every estimator in the DGEL family shares the same higherorder properties as the best member.   / Dissertation/Thesis / Ph.D. Economics 2013

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