Up or Out—or Stay Put? Product Positioning in an Evolving Technology Environment

When the development cycle for a product is longer than the development cycle for a core technology that is embedded in it, designers may need to modify the product̂s design to avail of upgrades in this core technology. We model optimal product positioning with regard to technology choice in this setting, using a stochastic dynamic programming framework. Under fairly general assumptions, we find that there are three possible optimal actions: to abandon the project, to maintain the current technology, or to reposition so as to use the best technology currently available. We characterize the optimal positioning sequence in different design environments, discussing throughout the practical implications of our model. Previous research and conventional wisdom suggest early finalization of product specifications if design flexibility is decreasing over time. In contrast, we find that in some design environments, repositioning late in the development cycle can be optimal.     

Large-scale simultaneous inference under dependence

Simultaneous inference allows for the exploration of data while deciding on criteria for proclaiming discoveries. It was recently proved that all admissible post hoc inference methods for the true discoveries must employ closed testing. In this paper, we investigate efficient closed testing with local tests of a special form: thresholding a function of sums of test scores for the individual hypotheses. Under this special design, we propose a new statistic that quantifies the cost of multiplicity adjustments, and we develop fast (mostly linear-time) algorithms for post hoc inference. Paired with recent advances in global null tests based on generalized means, our work instantiates a series of simultaneous inference methods that can handle many dependence structures and signal compositions. We provide guidance on the method choices via theoretical investigation of the conservativeness and sensitivity for different local tests, as well as simulations that find analogous behavior for local tests and full closed testing.