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STATISTICAL INFERENCE FOR HIGH DIMENSIONAL REGRESSION WITH PROXY DATA
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DOI：10.5705/ss.202023.0088.png)
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Abstract
En 中文
Existing high-dimensional statistical methods are largely developed for analyzing individual-level data. In this work, we study estimation and inference for high-dimensional linear models when only proxy data is available. These proxies encompass marginal statistics and sample covariance matrices computed from distinct sets of individuals. We develop a rate optimal method for estimation and inference for the regression coefficient vector and its linear functionals based on the proxy data. We show the intrinsic limitations in the proxy-data based inference: the minimax optimal rate for estimation is slower than that in the conventional case where individual data are observed. These interesting findings are illustrated through simulation studies and an analysis of a dataset concerning the genetic associations of hindlimb muscle weights in a mouse population.
Keywords:
Linear functional
sparse regression
summary statistics
Journal
S
IF:
1.2
Papers:
67
Citations:
3.8K