Fixed-smoothing asymptotics for time series

In this paper, we derive higher order Edgeworth expansions for the finite sample distributions of the subsampling-based t-statistic and the Wald statistic in the Gaussian location model under the so-called fixed-smoothing paradigm. In particular, we show that the error of asymptotic approximation is at the order of the reciprocal of the sample size and obtain explicit forms for the leading error terms in the expansions. The results are used to justify the second-order correctness of a new bootstrap method, the Gaussian dependent bootstrap, in the context of Gaussian location model.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1113 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Adaptive Testing for Alphas in High-dimensional Factor Pricing Models

This paper proposes a new procedure to validate the multi-factor pricing theory by testing the presence of alpha in linear factor pricing models with a large number of assets. Because the market's inefficient pricing is likely to occur to a small fraction of exceptional assets, we develop a testing procedure that is particularly powerful against sparse signals. Based on the high-dimensional Gaussian approximation theory, we propose a simulation-based approach to approximate the limiting null distribution of the test. Our numerical studies show that the new procedure can deliver a reasonable size and achieve substantial power improvement compared to the existing tests under sparse alternatives, and especially for weak signals

Structure Adaptive Lasso

Lasso is of fundamental importance in high-dimensional statistics and has been routinely used to regress a response on a high-dimensional set of predictors. In many scientific applications, there exists external information that encodes the predictive power and sparsity structure of the predictors. In this article, we develop a new method, called the Structure Adaptive Lasso (SA-Lasso), to incorporate these potentially useful side information into a penalized regression. The basic idea is to translate the external information into different penalization strengths for the regression coefficients. We study the risk properties of the resulting estimator. In particular, we generalize the state evolution framework recently introduced for the analysis of the approximate message-passing algorithm to the SA-Lasso setting. We show that the finite sample risk of the SA-Lasso estimator is consistent with the theoretical risk predicted by the state evolution equation. Our theory suggests that the SA-Lasso with an informative group or covariate structure can significantly outperform the Lasso, Adaptive Lasso, and Sparse Group Lasso. This evidence is further confirmed in our numerical studies. We also demonstrate the usefulness and the superiority of our method in a real data application.Comment: 42 pages, 24 figure

Comparison between spatio-temporal random processes and application to climate model data

Comparing two spatio-temporal processes are often a desirable exercise. For example, assessments of the difference between various climate models may involve the comparisons of the synthetic climate random fields generated as simulations from each model. We develop rigorous methods to compare two spatio-temporal random processes both in terms of moments and in terms of temporal trend, using the functional data analysis approach. A highlight of our method is that we can compare the trend surfaces between two random processes, which are motivated by evaluating the skill of synthetic climate from climate models in terms of capturing the pronounced upward trend of real-observational data. We perform simulations to evaluate our methods and then apply the methods to compare different climate models as well as to evaluate the synthetic temperature fields from model simulations, with respect to observed temperature fields