Empirical Likelihood for Single-Index Regression Models under Negatively Associated Errors

In this article, we use bockwise empirical likelihood technique to construct confidence regions for the parameter of the single-index models under negatively associated errors. It is shown that the blockwise empirical likelihood ratio statistic for the parameter of interest is asymptotically χ²-type distributed. The result can be used to obtain confidence regions for the parameter of interest.     

Confidence intervals for probability density functions under associated samples

In this paper, we study the construction of confidence intervals for a probability density function under a (positively) associated sample by using the blockwise technique. It is shown that the blockwise empirical likelihood (EL) ratio statistic is asymptotically χ²-type${\chi }^2\mathrm{-}\mathrm{type}$ distributed. The result is used to obtain EL-based confidence interval for the probability density function.     

Empirical likelihood for probability density functions under negatively associated samples

In this paper, we study the construction of confidence intervals for a probability density function under a negatively associated sample by using the blockwise technique. It is shown that the blockwise empirical likelihood (EL) ratio statistic is asymptotically χ²‐type distributed. The result is used to obtain EL based confidence interval on the probability density function.     

Empirical Likelihood for Partial Linear Models under Negatively Associated Errors

In this paper, we use blockwise empirical likelihood (EL) technique to construct confidence regions for the parameter of the partial linear models under negatively associated errors. It is shown that the blockwise EL ratio statistic for the parameter of interest is asymptotically χ²-type distributed by employing the large-block and small-block arguments. The result can be used to obtain confidence regions for the parameter of interest.     

Maximal inequalities and strong law of large numbers for sequences of m-asymptotically almost negatively associated random variables

In this paper, we establish some inequalities for maximum of partial sums of m-asymptotically almost negatively associated random variables. With the help of these inequalities we prove some strong law of large numbers.     

Empirical Likelihood Confidence Intervals for Distribution Functions under Negatively Associated Samples

In this article, we discuss the construction of the confidence intervals for distribution functions under negatively associated samples. It is shown that the blockwise empirical likelihood (EL) ratio statistic for a distribution function is asymptotically χ²-type distributed. The result is used to obtain an EL-based confidence interval for the distribution function.