Bing-Yi Jing

Jackknife Empirical Likelihood

Empirical likelihood has been found very useful in many different occasions. However, when applied directly to some more complicated statistics such as U-statistics, it runs into serious computational difficulties. In this paper, we introduce a so-called jackknife empirical likelihood (JEL) method. The new method is extremely simple to use in practice. In particular, the JEL is shown to be very effective in handling one and two-sample U-statistics. The JEL can be potentially useful for other nonlinear statistics.

Two-sample empirical likelihood method

The empirical likelihood method is applied to the two-sample problem and is shown to be Bartlett correctable.

Empirical Likelihood for Censored Linear Regression

In this paper we investigate the empirical likelihood method in a linear regression model when the observations are subject to random censoring. An empirical likelihood ratio for the slope parameter vector is defined and it is shown that its limiting distribution is a weighted sum of independent chi-square distributions. This reduces to the empirical likelihood to the linear regression model first studied by Owen (1991) if there is no censoring present. Some simulation studies are presented to compare the empirical likelihood method with the normal approximation based method proposed in Lai et al. (1995). It was found that the empirical likelihood method performs much better than the normal approximation method.

Improved Pivotal Methods for Constructing Confidence Regions with Directional Data

Abstract The importance of pivoting is well established in the context of nonparametric confidence regions. It ensures enhanced coverage accuracy. However, pivoting for directional data cannot be achieved simply by rescaling. A somewhat cumbersome pivotal method, which involves passing first into a space of higher dimension, has been developed by Fisher and Hall for samples of unit vectors. Although that method has some advantages over nonpivotal techniques, it does suffer from certain drawbacks—in particular, the operation of passing to a higher dimension. Here we suggest alternative pivotal approaches, the implementation of which does not require us to increase the intrinsic dimension of the data and which in practice seem to achieve greater coverage accuracy. These methods are of two types: new pivotal bootstrap techniques and techniques that exploit the “implicit pivotalness” of the empirical likelihood algorithm. Unlike the method proposed by Fisher and Hall, these methods are also applicable to axia...

Empirical Likelihood for a Class of Functionals of Survival Distribution with Censored Data

The empirical likelihood was introduced by Owen, although its idea originated from survival analysis in the context of estimating the survival probabilities given by Thomas and Grunkemeier. In this paper, we investigate how to apply the empirical likelihood method to a class of functionals of survival function in the presence of censoring. We define an adjusted empirical likelihood and show that it follows a chi-square distribution. Some simulation studies are presented to compare the empirical likelihood method with the Studentized-t method. These results indicate that the empirical likelihood method works better than or equally to the Studentized-t method, depending on the situations.

WaVPeak: picking NMR peaks through wavelet-based smoothing and volume-based filtering

Motivation: Nuclear magnetic resonance (NMR) has been widely used as a powerful tool to determine the 3D structures of proteins in vivo. However, the post-spectra processing stage of NMR structure determination usually involves a tremendous amount of time and expert knowledge, which includes peak picking, chemical shift assignment and structure calculation steps. Detecting accurate peaks from the NMR spectra is a prerequisite for all following steps, and thus remains a key problem in automatic NMR structure determination. Results: We introduce WaVPeak, a fully automatic peak detection method. WaVPeak first smoothes the given NMR spectrum by wavelets. The peaks are then identified as the local maxima. The false positive peaks are filtered out efficiently by considering the volume of the peaks. WaVPeak has two major advantages over the state-of-the-art peak-picking methods. First, through wavelet-based smoothing, WaVPeak does not eliminate any data point in the spectra. Therefore, WaVPeak is able to detect weak peaks that are embedded in the noise level. NMR spectroscopists need the most help isolating these weak peaks. Second, WaVPeak estimates the volume of the peaks to filter the false positives. This is more reliable than intensity-based filters that are widely used in existing methods. We evaluate the performance of WaVPeak on the benchmark set proposed by PICKY (Alipanahi et al., 2009), one of the most accurate methods in the literature. The dataset comprises 32 2D and 3D spectra from eight different proteins. Experimental results demonstrate that WaVPeak achieves an average of 96%, 91%, 88%, 76% and 85% recall on 15N-HSQC, HNCO, HNCA, HNCACB and CBCA(CO)NH, respectively. When the same number of peaks are considered, WaVPeak significantly outperforms PICKY. Availability: WaVPeak is an open source program. The source code and two test spectra of WaVPeak are available at http://faculty.kaust.edu.sa/sites/xingao/Pages/Publications.aspx. The online server is under construction. Contact: statliuzhi@xmu.edu.cn; ahmed.abbas@kaust.edu.sa; majing@ust.hk; xin.gao@kaust.edu.sa

EMPIRICAL LIKELIHOOD FOR COX REGRESSION MODEL UNDER RANDOM CENSORSHIP

In this paper we investigate the empirical likelihood method for Cox regression model when the failure times are subject to random censoring. An empirical likelihood ratio for the vector of regression coefficients is defined and it is shown that its limiting distribution is a chi-square distributions with p degrees of freedom. Some simulation studies are presented to compare the empirical likelihood method with the normal approximation method.

MODELING HIGH-FREQUENCY FINANCIAL DATA BY PURE JUMP PROCESSES

HK RGC [HKUST6011/07P, HKUST6015/08P, HKUST6019/10P]; Humanity and Social Science Youth Foundation of Chinese Ministry of Education [12YJC910003]

Saddlepoint approximation for Student’s t-statistic with no moment conditions

A saddlepoint approximation of the Students t-statistic was derived by Daniels and Young [Biometrika 78 (1991) 169-179] under the very stringent exponential moment condition that requires that the underlying density function go down at least as fast as a Normal density in the tails. This is a severe restriction on the approximations applicability. In this paper we show that this strong exponential moment restriction can be completely dispensed with, that is, saddlepoint approximation of the Students t-statistic remains valid without any moment condition. This confirms the folklore that the Students t-statistic is robust against outliers. The saddlepoint approximation neat only provides a very accurate approximation for the Students t-statistic, but it also can be applied much more widely in statistical inference. As a result, saddlepoint approximations should always be used whenever possible. Some numerical work will be given to illustrate these points.

Feature subset selection using naive Bayes for text classification

The global selection index can be determined from the local selection indexes.The local selection index can be calculated in its own dimension.The prediction function can be factorized.The NB models can be selectively pruned by thresholding the LSIs.Feature selection and weighting work hand-in-hand to improve classification. Feature subset selection is known to improve text classification performance of various classifiers. The model using the selected features is often regarded as if it had generated the data. By taking its uncertainty into account, the discrimination capabilities can be measured by a global selection index (GSI), which can be used in the prediction function. In this paper, we propose a latent selection augmented naive (LSAN) Bayes classifier. By introducing a latent feature selection indicator, the GSI can be factorized into each local selection index (LSI). Using conjugate priors, the LSI for feature evaluation can be explicitly calculated. Then the feature subset selection models can be pruned by thresholding the LSIs, and the LSAN classifier can be achieved by the product of a small percentage of single feature model averages. The numerical results on some real datasets show that the proposed method outperforms the contrast feature weighting methods, and is very competitive if compared with some other commonly used classifiers such as SVM.