Multiple Change-point Detection: a Selective Overview

Very long and noisy sequence data arise from biological sciences to social science including high throughput data in genomics and stock prices in econometrics. Often such data are collected in order to identify and understand shifts in trend, e.g., from a bull market to a bear market in finance or from a normal number of chromosome copies to an excessive number of chromosome copies in genetics. Thus, identifying multiple change points in a long, possibly very long, sequence is an important problem. In this article, we review both classical and new multiple change-point detection strategies. Considering the long history and the extensive literature on the change-point detection, we provide an in-depth discussion on a normal mean change-point model from aspects of regression analysis, hypothesis testing, consistency and inference. In particular, we present a strategy to gather and aggregate local information for change-point detection that has become the cornerstone of several emerging methods because of its attractiveness in both computational and theoretical properties.Comment: 26 pages, 2 figure

Nonparametric estimation of genewise variance for microarray data

Estimation of genewise variance arises from two important applications in microarray data analysis: selecting significantly differentially expressed genes and validation tests for normalization of microarray data. We approach the problem by introducing a two-way nonparametric model, which is an extension of the famous Neyman--Scott model and is applicable beyond microarray data. The problem itself poses interesting challenges because the number of nuisance parameters is proportional to the sample size and it is not obvious how the variance function can be estimated when measurements are correlated. In such a high-dimensional nonparametric problem, we proposed two novel nonparametric estimators for genewise variance function and semiparametric estimators for measurement correlation, via solving a system of nonlinear equations. Their asymptotic normality is established. The finite sample property is demonstrated by simulation studies. The estimators also improve the power of the tests for detecting statistically differentially expressed genes. The methodology is illustrated by the data from microarray quality control (MAQC) project.Comment: Published in at http://dx.doi.org/10.1214/10-AOS802 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Complementarity of LHC and EDMs for Exploring Higgs CP Violation

We analyze the constraints on a CP-violating, flavor conserving, two Higgs doublet model from the measurements of Higgs properties and from the search for heavy Higgs bosons at LHC, and show that the stronger limits typically come from the heavy Higgs search channels. The limits on CP violation arising from the Higgs sector measurements are complementary to those from EDM measurements. Combining all current constraints from low energy to colliders, we set generic upper bounds on the CP violating angle which parametrizes the CP odd component in the 126 GeV Higgs boson.Comment: 34 pages, 17 figures, 2 tables; references added, constraints from Higgs decay into tau updated, version accepted for publication in JHE

Trade Facilitation and Expanding the Benefits of Trade: Evidence from Firm Leval Data

Existing empirical studies on trade costs and trade facilitation largely focus on aggregate impacts of reform due to data availability. We take a step toward filling in this gap in literature. Using the World Bank Enterprises Surveys, the study extends the scope of empirical literature to firm dimension with a focus on SMEs.Trade Facilitation, Expanding the Benefits of Trade