Who's Afraid of Selection Bias? Robust Inference in the Presence of Competitive Selection

Noe, Thomas (2013) Who's Afraid of Selection Bias? Robust Inference in the Presence of Competitive Selection. University of Oxford.

Abstract

This paper considers competitive selection dominance: what conditions on the unconditional distribution of of a random prospect will ensure that the prospect stochastically dominates a rival random prospect conditioned on competitive selection, i.e., conditioned on the prospect's realized value exceeding its rivals? Because standard distributional orders, such as stochastic dominance and the monotone likelihood ratio property (MLRP), do not provide either necessary or sufficient restrictions on the unconditional distributions to ensure selection dominance, new distribution orders are required. We provide the requisite orders, which we term supermultiplicativity on average and geometric dominance. These orderings generate conditions, satisfied by many, but not all, scale shifts of standard textbook distributions, under which the selection-conditioned distribution is stochastically dominant if and only if the unconditional distribution is stochastically dominant. When these conditions are satisfied, robust qualitative inferences concerning the unconditional population distribution can be drawn from the selection-conditioned subsample distribution and vice versa.

Item Type: Other Working Paper
Keywords: distribution orders, selection bias, shochastic dominance, finance
Subject(s): Finance
Date Deposited: 22 Oct 2013 14:38
Last Modified: 02 Mar 2017 10:47
Funders: N/A
URI: http://eureka.sbs.ox.ac.uk/id/eprint/4863

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