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Full-Text Articles in Statistics and Probability
Using Stability To Select A Shrinkage Method, Dean Dustin
Using Stability To Select A Shrinkage Method, Dean Dustin
Department of Statistics: Dissertations, Theses, and Student Work
Shrinkage methods are estimation techniques based on optimizing expressions to find which variables to include in an analysis, typically a linear regression. The general form of these expressions is the sum of an empirical risk plus a complexity penalty based on the number of parameters. Many shrinkage methods are known to satisfy an ‘oracle’ property meaning that asymptotically they select the correct variables and estimate their coefficients efficiently. In Section 1.2, we show oracle properties in two general settings. The first uses a log likelihood in place of the empirical risk and allows a general class of penalties. The second …
An Exploration Of Link Functions Used In Ordinal Regression, Thomas J. Smith, David A. Walker, Cornelius M. Mckenna
An Exploration Of Link Functions Used In Ordinal Regression, Thomas J. Smith, David A. Walker, Cornelius M. Mckenna
Journal of Modern Applied Statistical Methods
The purpose of this study is to examine issues involved with choice of a link function in generalized linear models with ordinal outcomes, including distributional appropriateness, link specificity, and palindromic invariance are discussed and an exemplar analysis provided using the Pew Research Center 25th anniversary of the Web Omnibus Survey data. Simulated data are used to compare the relative palindromic invariance of four distinct indices of determination/discrimination, including a newly proposed index by Smith et al. (2017).