BIOSTATISTICS SEMINAR
Optimal Inference After Model Selection
William Fithian, Biostatistics Faculty Candidate
Stanford University
ABSTRACT
To perform inference after model selection, we propose controlling the
selective type I error; i.e., the error rate of a test given that it was performed.
By doing so, we recover long-run frequency properties among selected
hypotheses analogous to those that apply in the classical (non-adaptive)
context. Our proposal is closely related to data splitting and has a similar
intuitive justification, but is more powerful. Exploiting the classical theory of
Lehmann and Scheffe (1955), we derive most powerful unbiased selective
tests and confidence intervals for inference in exponential family models after
arbitrary selection procedures. For linear regression, we derive new selective
z-tests that generalize recent proposals for inference after model selection
and improve on their power, and new selective t-tests that do not require
knowledge of the error variance.
Based on joint work with Dennis Sun and Jonathan Taylor.
The Johns Hopkins Bloomberg School of Public Health, Department of
Biostatistics, Monday, January 5, 2015, 12:15-1:15, Room W3030
School of Public Health (Refreshments: 12:00-12:15)
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