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Cun-Hui Zhang, Rutgers University

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Inference of Low-Dimensional Parameters with High-Dimensional Dat
19 November 2015 from 4:00 PM to 5:00 PM
201 Thomas Building
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We consider sample size requirements for statistical inference in a semi-low-dimensional approach to the analysis of high-dimensional data. The relationship between this semi-low- dimensional approach and regularized estimation of high-dimensional objects is parallel to the more familiar one between semiparametric analysis and nonparametric estimation. We discuss three equivalent forms of a low-dimensional projection estimator and two choices in approximating the direction of the least favorable submodel for the estimation of the low-dimensional parameter. We discuss regular efficiency cases where the sample size requirement is n » (s log p)2 for the approach to work, where p is the nominal dimension and s is a measure of the complexity of the model. Examples of regular efficiency include the estimation of a quadratic function of a high-dimensional vector and graphical model estimation. We also discuss super-efficiency cases where the sample size requirement can be as low as n » s log p. Examples of super-efficiency include the estimation of a treatment effect in a randomized experiment and the estimation of regression coefficients with certain knowledge of the population Gram matrix. Ancillarity and benefits of unlabeled data will be discussed if time permits.


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