Markov regime-switching tests: asymptotic critical values. (2013) Journal of Econometric Methods 2(1): pp.25-34 (with Doug Steigerwald)
Asymptotic sufficient statistics in nonparametric regression experiments with correlated noise. (2009) Journal of Probability and Statistics. vol. 2009, Article ID 275308
Asymptotic equivalence for nonparametric regression experiments with random design. Proceedings of the 2007 Joint Statistical Meetings. (2007)
Asymptotic approximation of nonparametric regression experiments with unknown variances. (2007) Annals of Statistics. 35 pp. 1644-1673.
A continuous Gaussian process approximation to a nonparametric regression in two dimensions. (2006). Bernoulli. 12(1) pp. 143-156.
Tusnády's inequality revisited.(2004) Annals of Statistics. 32 pp. 2731-2741 (with David Pollard).
Tusnády's inequality is the key ingredient in the KMT/Hungarian coupling of the empirical distribution function with a Brownian Bridge. We present an elementary proof of a result that sharpens the Tusnády's inequality, modulo constants. Our method uses the beta integral representation of Binomial tails, simple Taylor expansion, and some novel bounds for the ratios of normal tail probabilities.
Equivalence theory for density estimation, Poisson processes, and Gaussian white noise with drift. (2004) Annals of Statistics. 32 pp. 2074-2097 (with Lawrence Brown, Mark Low, and Cun-Hui Zhang).
This paper establishes the global asymptotic equivalence between a Poisson process with variable intensity and white noise with drift under sharp smoothness conditions on the unknown function. This equivalence is also extended to density estimation models. The asymptotic equivalence is established by constructing explicit equivalence mappings. The impact of such asymptotic equivalence results is that an investigation in one of these nonparametric models automatically yields asymptotically analogous results in the other model.
Deficiency distance between multinomial and multivariate normal experiments.(2002) Annals of Statistics. 30 pp. 708-730.
The deficiency distance between a multinomial and a multivariate normal experiment is bounded under a condition that the parameters are bounded away from zero.
This result can be used as a key step in establishing asymptotic normal approximations to nonparametric density estimation experiments.
The bound relies on the recursive construction of explicit Markov kernels that can be used to reproduce one experiment from the other. The distance is then bounded using classic local-limit bounds between binomial and normal distributions. Some extensions to other appropriate normal experiments are also presented.