Past, Present, and Future of Statistical Science was commissioned in 2013 by the Committee of Presidents of Statistical Societies (COPSS) to celebrate its 50th anniversary and the International Year of Statistics. COPSS consists of five charter member statistical societies in North America and is best known for sponsoring prestigious awards in stat

We develop a specification test for the transition density of a discretely-sampled continuous-time diffusion process, based on a comparison of a nonparametric estimate of the transition density or distribution function to their corresponding parametric counterparts assumed by the null hypothesis. We provide a direct comparison of the two densities for an arbitrary specification of the null parametric model using three different discrepancy measures between the null and alternative transition density and distribution functions. We establish the asymptotic null distributions of proposed test statistics and compute their power functions. The finite sample properties are critically investigated via simulation studies and are compared with other tests. Our approaches are illustrated by applications to implied volatility data and Treasury bill data.

An aggregated method of nonparametric estimators based on time-domain and state-domain estimators is proposed and studied. To attenuate the <i>curse of dimensionality</i>, we propose a factor modeling strategy. We first investigate the asymptotic behavior of nonparametric estimators of the volatility matrix in the time domain and in the state domain. Asymptotic normality is separately established for nonparametric estimators in the time domain and state domain. These two estimators are asymptotically independent. Hence, they can be combined, through a dynamic weighting scheme, to improve the efficiency of volatility matrix estimation. The optimal dynamic weights are derived, and it is shown that the aggregated estimator uniformly dominates volatility matrix estimators using time-domain or state-domain smoothing alone. A simulation study, based on an essentially affine model for the term structure, is

This paper is concerned with the problem of top- K ranking from pairwise comparisons. Given a collection of K items and a few pairwise comparisons across them, one wishes to identify the set of K items that receive the highest ranks. To tackle this problem, we adopt the logistic parametric model---the Bradley-Terry-Luce model, where each item is assigned a latent preference score, and where the outcome of each pairwise comparison depends solely on the relative scores of the two items involved. Recent works have made significant progress towards characterizing the performance (eg the mean square error for estimating the scores) of several classical methods, including the spectral method and the maximum likelihood estimator (MLE). However, where they stand regarding top- K ranking remains unsettled.

This paper studies hypothesis testing and parameter estimation in the context of the divide-and-conquer algorithm. In a unified likelihood based framework, we propose new test statistics and point estimators obtained by aggregating various statistics from k subsamples of size n/k, where n is the sample size. In both low dimensional and sparse high dimensional settings, we address the important question of how large k can be, as n grows large, such that the loss of efficiency due to the divide-and-conquer algorithm is negligible. In other words, the resulting estimators have the same inferential efficiencies and estimation rates as an oracle with access to the full sample. Thorough numerical results are provided to back up the theory.