Networks are a popular tool for representing elements in a system and their interconnectedness. Many observed networks can be viewed as only samples of some true underlying network. Such is frequently the case, for example, in the monitoring and study of massive, online social networks. We study the problem of how to estimate the degree distribution -- an object of fundamental interest -- of a true underlying network from its sampled network. In particular, we show that this problem can be formulated as an inverse problem.
The Statistics Department hosts weekly colloquia on a variety of statistcal subjects, bringing in speakers from around the world.
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Various estimation methods in time series are reviewed in a unified framework via martingale estimating functions. In particular, maximum likelihood and quasi-likelihood are discussed in the context of asymptotic optimality within certain estimating functions. Both ergodic and non-ergodic processes are considered. To illustrate the main results, various parameter estimates for GARCH processes, bifurcating and explosive AR processes, conditionally linear autoregressive processes, and branching Markov processes are presented.
In psychiatric and behavioral research, about six out of ten people with a substance use disorder suffer from another form of mental illness as well, making it necessary to consider multiple conditions as we study the etiologies of these conditions. The occurrence of multiple disorders in the same patient is referred to as comorbidity. Identifying the risk factors for comorbidity is an important yet difficult topic in psychiatric research. The effort of studying the genetics for comorbidity can be traced back to a century ago.
Clinical trials that evaluate treatment benefit focus primarily on estimating the average benefit. However, a treatment reported to be effective may not be beneficial to all patients. For example, the benefit of giving chemotherapy prior to hormone therapy with Tamoxifen in the adjuvant treatment of postmenopausal women with lymph node negative breast cancer depends on the ER-status. Due to the toxicity of chemotherapy, it is crucial to identify patients who will and will not benefit from chemotherapy. This gives rise to the need of accurately predicting benefit based on important markers.
For high dimensional genetic data, an important problem is to search for associations between genetic variables and a phenotype---typically, a discrete variable (diseased versus normal). A conventional solution is to characterize such relationships through regression models in which a phenotype is treated as the response variable and genetic variables are treated as the covariates. Not surprisingly, such a way incurs the challenging problem of the number of variables much larger than the number of observations.
Dynamic treatment regimes (DTRs) are sequential decision rules for individual patients that can adapt over time to an evolving illness. Discovering DTRs from a SMART trial is challenging due to high-dimensional information and complex interactions between a patient's temporal characteristics and treatments. In this work, we introduce a new statistical learning method, namely outcome weighted learning (O-learning), for estimating the optimal DTR.
We consider nonparametric estimation of the covariance function for dense functional data using computationally efficient tensor product B-splines. We develop both local and global asymptotic distributions for the proposed estimator, and show that our estimator is as efficient as an "oracle" estimator where the true mean function is known. Simultaneous confidence envelopes are developed based on asymptotic theory to quantify the variability in the covariance estimator and to make global inferences on the true covariance.
The multiple testing procedure plays an important role in detecting the presence of spatial signals for large-scale imaging data. Typically, the spatial signals are sparse but clustered.
This paper is concerned with feature screening and variable selection for varying coefficient models with ultrahigh dimensional covariates. We propose a new feature screening procedure for these models based on conditional correlation coefficient. We systematically study the theoretical properties of the proposed procedure, and establish their sure screening property and the ranking consistency. To enhance the finite sample performance of the proposed procedure, we further develop an iterative feature screening procedure.