Nonparametric Methods I (Thomas Bengtsson, chair)

Chunming Zhang (University of Wisconsin, Madison)
Yuefeng Lu (University of Wisconsin, Madison)
Nonparametric Modeling and Inference for Event-related Functional MRI Data

Friday 10:30-10:50, San Marino

Abstract:

Event-related functional magnetic resonance imaging (efMRI) emerges as a powerful technique for detecting brains' responses to brief stimuli. A crucial goal in efMRI data analysis is to estimate Haemodynamic Response Functions (HRF) and to locate activated regions in human brains when specific tasks are performed. This paper largely relaxes the assumptions of existing methods and proposes a nonparametric deconvolution method to obtain statistically more efficient estimates of the underlying HRF associated with efMRI experiments. The nonparametric hypothesis testing of HRF is conducted to identify activated brain regions with a specific function and to compare HRF across different tissue types. A new False Discovery Rate (FDR) approach which incorporates spatial information is proposed to detect the activated regions. Simulation evaluations endorse the effectiveness of our proposed method. When applied to an efMRI data set from an emotional control study, our method reveals more meaningful findings than the popular methods.

Hongjuan Liu (Department of Statistics, UC Riverside)
Inference in a Simple Random Effects Model with Low Replication and Non-normal Distributions

Friday 10:50-11:10, San Marino

Abstract:

We studied the nonparametric inference on the group effect in a random effect components of variance model when the number of groups diverges without bound, but the replications remain fixed as small as 2. It is well known that with normality assumption, the exact F-test can infer the existence of group effect. When normality assumption is not valid, it has been shown that the F-statistic is robust only in a balanced design and the asymptotic distribution of the F-statistic requires the existence of the fourth order moment. In this work, we pushed the frontier to a very general setting. Our new proposed method only requires the existence of the second order moment and can be applied to balanced or unbalanced data under skewed or heavy-tailed distribution. Our simulations have shown that the proposed method is very powerful and computationally efficient. We also show its application in microarray-based heritability analysis.

Hyunsook Lee (Department of Statistics, The Pennsylvania State University)
Detecting Outliers in Multivariate Massive Data by Convex Hull Peeling with Applications

Friday 11:10-11:30, San Marino

Abstract:

Detecting outliers is an important problem in data mining. However, outliers are not well defined in multivariate massive data. Particularly, without imposing multivariate normal distribution, outlier detection methods rarely exist. We found that convex hull peeling asymptotically describes multivariate data distribution and can be applied to outlier detection in a nonparametric sense.

In this presentation, we propose some algorithms to detect outliers in massive data sets. No assumptions are posed except the convexity of data distribution and no covariance matrix is considered. Additionally, we will show a modified algorithm for multivariate streaming data. These algorithms are exemplified with Monte Carlo simulations and Sloan Digital Sky Survey database.

Daniel Fink (Cornell Laboratory of Ornithology, Cornell Department of Statistical Science)
Hierarchical Predictive Models

Friday 11:30-11:50, San Marino

Abstract:

Semiparametric regression models incorporate flexible nonparametric components within a parametric hierarchical modeling framework. The practical appeal of this approach is that it allows one to include as much parametric structure as is justified by subject-area knowledge. At the same time, the semiparametric regression model employs nonparametric techniques to account for additional predictors and processes that are less well understood. Most semiparametric regression techniques cannot model more than a handful of predictors nonparametrically. Methodology for including a general class of nonparametric predictive models within the hierarchical framework is presented for the regression and binary classification problems. Utilizing data-mining techniques for the predictive model we show that many more predictors can be handled nonparametrically. We also show that this method can be viewed as a general approach for extending data-mining techniques to deal with dependent data. Simulation studies are used to evaluate the hierarchical predictive models. The method is also used to predict patterns of variation in North American bird populations from a large spatial data set. The information from these models provides useful information for conservation and land management.