TY  - JOUR
A1  - Bachoc, Francois
A1  - Blanchard, Gilles
A1  - Neuvial, Pierre
T1  - On the post selection inference constant under restricted isometry properties
JF  - Electronic journal of statistics
N2  - Uniformly valid confidence intervals post model selection in regression can be constructed based on Post-Selection Inference (PoSI) constants. PoSI constants are minimal for orthogonal design matrices, and can be upper bounded in function of the sparsity of the set of models under consideration, for generic design matrices. In order to improve on these generic sparse upper bounds, we consider design matrices satisfying a Restricted Isometry Property (RIP) condition. We provide a new upper bound on the PoSI constant in this setting. This upper bound is an explicit function of the RIP constant of the design matrix, thereby giving an interpolation between the orthogonal setting and the generic sparse setting. We show that this upper bound is asymptotically optimal in many settings by constructing a matching lower bound.
KW  - Inference post model-selection
KW  - confidence intervals
KW  - PoSI constants
KW  - linear regression
KW  - high-dimensional inference
KW  - sparsity
KW  - restricted isometry property
Y1  - 2018
U6  - https://doi.org/10.1214/18-EJS1490
SN  - 1935-7524
VL  - 12
IS  - 2
SP  - 3736
EP  - 3757
PB  - Institute of Mathematical Statistics
CY  - Cleveland
ER  - 
TY  - GEN
A1  - Mühlenbruch, Kristin
A1  - Kuxhaus, Olga
A1  - Pencina, Michael J.
A1  - Boeing, Heiner
A1  - Liero, Hannelore
A1  - Schulze, Matthias Bernd
T1  - A confidence ellipse for the Net Reclassification Improvement
T2  - Postprints der Universität Potsdam : Mathematisch Naturwissenschaftliche Reihe
N2  - The Net Reclassification Improvement (NRI) has become a popular metric for evaluating improvement in disease prediction models through the past years. The concept is relatively straightforward but usage and interpretation has been different across studies. While no thresholds exist for evaluating the degree of improvement, many studies have relied solely on the significance of the NRI estimate. However, recent studies recommend that statistical testing with the NRI should be avoided. We propose using confidence ellipses around the estimated values of event and non-event NRIs which might provide the best measure of variability around the point estimates. Our developments are illustrated using practical examples from EPIC-Potsdam study.
KW  - risk assessment
KW  - risk model
KW  - model comparison
KW  - reclassification
KW  - confidence intervals
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-427371
SN  - 1866-8372
IS  - 825
SP  - 299
EP  - 304
ER  -