Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/162298
Authors: 
Boot, Tom
Nibbering, Didier
Year of Publication: 
2017
Series/Report no.: 
Tinbergen Institute Discussion Paper 17-032/III
Abstract: 
In modern data sets, the number of available variables can greatly exceed the number of observations. In this paper we show how valid confidence intervals can be constructed by approximating the inverse covariance matrix by a scaled Moore-Penrose pseudoinverse, and using the lasso to perform a bias correction. In addition, we propose random least squares, a new regularization technique which yields narrower confidence intervals with the same theoretical validity. Random least squares estimates the inverse covariance matrix using multiple low-dimensional random projections of the data. This is shown to be equivalent to a generalized form of ridge regularization. The methods are illustrated in Monte Carlo experiments and an empirical example using quarterly data from the FRED-QD database, where gross domestic product is explained by a large number of macroeconomic and financial indicators.
Subjects: 
high-dimensional regression
confidence intervals
random projection
Moore-Penrose pseudoinverse
JEL: 
C12
C13
O40
Document Type: 
Working Paper

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