False Discovery Rate Control of Step‐Up‐Down Tests with Special Emphasis on the Asymptotically Optimal Rejection Curve

Abstract. This paper is concerned with exact control of the false discovery rate (FDR) for step‐up‐down (SUD) tests related to the asymptotically optimal rejection curve (AORC). Since the system of equations and/or constraints for critical values and FDRs is numerically extremely sensitive, existence and computation of valid solutions is a challenging problem. We derive explicit formulas for upper bounds of the FDR and show that under a well‐known monotonicity condition, control of the FDR by a step‐up procedure results in control of the FDR by a corresponding SUD procedure. Various methods for adjusting the AORC to achieve finite FDR control are investigated. Moreover, we introduce alternative FDR bounding curves and study their connection to rejection curves as well as the existence of critical values for exact FDR control with respect to the underlying FDR bounding curve. Finally, we propose an iterative method for the computation of critical values.     

EXPERIMENTAL ANALYSIS OF RISK AND UNCERTAINTY IN PROVISIONING PRIVATE AND PUBLIC GOODS

This paper uses laboratory evidence from public goods games to examine how in payoff-equivalent situations, decision makers contribute toward private or public goods when they are exposed to different kinds of risks and uncertainties in the provision of these goods. We find that location matters with subjects moving away from the environmental uncertainty in favor of strategic uncertainty when that uncertainty is located on the private good. When the uncertainty relates to the public good, subjects face both kinds of uncertainties on the same good, leading to a significant drop in contributions. An opportunity to reduce uncertainty increases cooperation. ( JEL C90, D81, H41)