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Register a new userInterpretable High-Dimensional Inference Via Score Projection with an Application in Neuroimaging
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Added by
Simon Vandekar
Publication date
2017
fields
Mathematical Statistics
and research's language is
English
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In the fields of neuroimaging and genetics, a key goal is testing the association of a single outcome with a very high-dimensional imaging or genetic variable. Often, summary measures of the high-dimensional variable are created to sequentially test and localize the association with the outcome. In some cases, the results for summary measures are significant, but subsequent tests used to localize differences are underpowered and do not identify regions associated with the outcome. Here, we propose a generalization of Raos score test based on projecting the score statistic onto a linear subspace of a high-dimensional parameter space. In addition, we provide methods to localize signal in the high-dimensional space by projecting the scores to the subspace where the score test was performed. This allows for inference in the high-dimensional space to be performed on the same degrees of freedom as the score test, effectively reducing the number of comparisons. Simulation results demonstrate the test has competitive power relative to others commonly used. We illustrate the method by analyzing a subset of the Alzheimers Disease Neuroimaging Initiative dataset. Results suggest cortical thinning of the frontal and temporal lobes may be a useful biological marker of Alzheimers risk.
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In this paper we develop an online statistical inference approach for high-dimensional generalized linear models with streaming data for real-time estimation and inference. We propose an online debiased lasso (ODL) method to accommodate the special structure of streaming data. ODL differs from offline debiased lasso in two important aspects. First, in computing the estimate at the current stage, it only uses summary statistics of the historical data. Second, in addition to debiasing an online lasso estimator, ODL corrects an approximation error term arising from nonlinear online updating with streaming data. We show that the proposed online debiased estimators for the GLMs are consistent and asymptotically normal. This result provides a theoretical basis for carrying out real-time interim statistical inference with streaming data. Extensive numerical experiments are conducted to evaluate the performance of the proposed ODL method. These experiments demonstrate the effectiveness of our algorithm and support the theoretical results. A streaming dataset from the National Automotive Sampling System-Crashworthiness Data System is analyzed to illustrate the application of the proposed method.
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