Empirical likelihood for quantiles under negatively associated samples

Joint empirical likelihood confidence regions for a finite number of quantiles under negatively associated samples

“…Proof (10) follows from Lemma 4.3 and from (4.10) and (4.13) in [3] we can easily verify (9) and (12). It remains to prove (11).…”

“…Following the proof of (4.17) in [3], we can show that Var(T n1j ) = o(1) for j = 1, 2, 3. Therefore, to prove (14), it suffices to show that ET n1 = a T V r a + o p (1).…”

Empirical Likelihood Confidence Intervals for Distribution Functions under Negatively Associated Samples

“…By using Lemma 4.3, this result can be proved by using the same method as in the proof of Theorem 1 in Lei and Qin (2011). We thus omit its proof.…”

“…used the EL method to construct confidence regions for the regression parameters in a linear model under negatively associated errors. Lei and Qin (2011) and , respectively, constructed EL confidence intervals for the quantiles and the probability density function of a population under NA samples. We note that mixing, NA and PA samples have different dependent structures and no one covers another.…”

A Progressive Block Empirical Likelihood Method for Time Series

“…Such data-blocking has also played an important role in extending bootstrap and subsampling methods to time series, such as the moving block bootstrap of Künsch (1989) and Liu and Singh (1992), and time subsampling methods of Carlstein (1986), Politis and Romano (1993), and Politis, Romano, and Wolf (1999); see Lahiri (2003) for an overview of block resampling methods for time series. BEL has been shown to apply for time series inference in a wide range of problems (see Lin and Zhang 2001;Bravo 2002Bravo , 2005Bravo , 2009Zhang 2006;Nordman 2009;Chen and Zhang 2010;Lei and Qin 2011;Wu and Cao 2011). The standard implementation of BEL typically involves data blocks of constant length for an observed time series, and therefore requires a corresponding block length selection.…”