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A theoretical approach to inference based on maximum observations

Qing Li, 2004
Faculty Advisor: Maria Vassalou
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Abstract

This paper presents a simple theoretical framework where a decision maker either only receives or can only process the most favorable signal. This notion sets this research apart from other word by emphasizing limited attention and concentrated focus on most extreme observations, and has numerous applications in the real world. A decision maker can either accept the status quo, or move to an alternative. He or she receives a noisy signal about the value of each alternative. Due to limited ability, the decision maker processes only the most favorable signal.

Under very general assumptions, this papers shows that the decision maker should either accept status quo or choose the alternative that corresponds to the most favorable signal. Moreover, the optimal rule is a cutoff strategy. That is, the decision maker has a cutoff level, and he or she accepts the alternative if and only if the signal is high enough. This paper also presents the how the optimal cutoff level is related to the number of alternatives, the variance of signals, and the variance of noises.

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