A Blockwise Consistency Method for Parameter Estimation of Complex Models
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The drastic improvement in data collection and acquisition technologies has enabled scientists to collect a great amount of data. With the growing dataset size, typically comes a growing complexity of data structures and of complex models to account for the data structures. How to estimate the parameters of complex models has put a great challenge on current statistical methods. This paper proposes a blockwise consistency approach as a potential solution to the problem, which works by iteratively finding consistent estimates for each block of parameters conditional on the current estimates of the parameters in other blocks. The blockwise consistency approach decomposes the high-dimensional parameter estimation problem into a series of lower-dimensional parameter estimation problems, which often have much simpler structures than the original problem and thus can be easily solved. Moreover, under the framework provided by the blockwise consistency approach, a variety of methods, such as Bayesian and frequentist methods, can be jointly used to achieve a consistent estimator for the original high-dimensional complex model. The blockwise consistency approach is illustrated using high-dimensional linear regression with both univariate and multivariate responses. The results of both problems show that the blockwise consistency approach can provide drastic improvements over the existing methods. Extension of the blockwise consistency approach to many other complex models is straightforward.
Keywords and phrases.Coordinate descent Gaussian graphical model Multivariate regression Precision matrix Variable selection
AMS (2000) subject classification.Primary 62F10 Secondary 62P10
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Liang’s research was support in part by the grants DMS-1612924, DMS/NIGMS R01-GM117597, and NIGMS R01-GM126089. The authors thank the editor, associate editor, and two referees for their helpful comments which have led to significant improvement of this paper.
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