@article{liu_tang_zhang_2009, title={A new chi-square approximation to the distribution of non-negative definite quadratic forms in non-central normal variables}, volume={53}, ISSN={["1872-7352"]}, DOI={10.1016/j.csda.2008.11.025}, abstractNote={This note proposes a new chi-square approximation to the distribution of non-negative definite quadratic forms in non-central normal variables. The unknown parameters are determined by the first four cumulants of the quadratic forms. The proposed method is compared with Pearson’s three-moment central χ2 approximation approach, by means of numerical examples. Our method yields a better approximation to the distribution of the non-central quadratic forms than Pearson’s method, particularly in the upper tail of the quadratic form, the tail most often needed in practical work.}, number={4}, journal={COMPUTATIONAL STATISTICS & DATA ANALYSIS}, author={Liu, Huan and Tang, Yongqiang and Zhang, Hao Helen}, year={2009}, month={Feb}, pages={853–856} }
 @article{tang_ghosal_2007, title={Posterior consistency of Dirichlet mixtures for estimating a transition density}, volume={137}, ISSN={0378-3758}, url={http://dx.doi.org/10.1016/j.jspi.2006.03.007}, DOI={10.1016/j.jspi.2006.03.007}, abstractNote={The Dirichlet process mixture of normal densities has been successfully used as a prior for Bayesian density estimation for independent and identically distributed (i.i.d.) observations. A Markov model, which generalizes the i.i.d. set up, may be thought of as a suitable framework for observations arising over time. The predictive density of the future observation is then given by the posterior expectation of the transition density given the observations. We consider a Dirichlet process mixture prior for the transition density and study posterior consistency. Like the i.i.d. case, posterior consistency is obtained if the Kullback–Leibler neighborhoods of the true transition density receive positive prior probabilities and uniformly exponentially consistent tests exist for testing the true density against the complement of its neighborhoods. We show that under reasonable conditions, the Kullback–Leibler property holds for the Dirichlet mixture prior. For certain topologies on the space of transition densities, we show consistency holds under appropriate conditions by constructing the required tests. This approach, however, may not always lead to the best possible results. By modifying a recent approach of Walker [2004. New approaches to Bayesian consistency. Ann. Statist. 32, 2028–2043] for the i.i.d. case, we also show that better conditions for consistency can be given for certain weaker topologies.}, number={6}, journal={Journal of Statistical Planning and Inference}, publisher={Elsevier BV}, author={Tang, Yongqiang and Ghosal, Subhashis}, year={2007}, month={Jun}, pages={1711–1726} }
 @article{brownie_glasgow_burkholder_reed_tang_2003, title={Re-evaluation of the relationship between Pfiesteria and estuarine fish kills}, volume={6}, ISSN={["1435-0629"]}, DOI={10.1007/s10021-002-0194-5}, number={1}, journal={ECOSYSTEMS}, author={Brownie, C and Glasgow, HB and Burkholder, JM and Reed, R and Tang, YQ}, year={2003}, month={Jan}, pages={1–10} }