scholarly journals The Secretary Problem with a Hazard Rate Condition

2008 ◽  
pp. 708-715 ◽  
Author(s):  
Mohammad Mahdian ◽  
Randolph Preston McAfee ◽  
David Pennock
Keyword(s):  
Hazard Rate ◽  
Secretary Problem ◽  
Rate Condition

scholarly journals Optimal Provision of Multiple Excludable Public Goods

2010 ◽  
Vol 2 (4) ◽  
pp. 1-37 ◽  
Author(s):  
Hanming Fang ◽  
Peter Norman
Keyword(s):  
Public Goods ◽  
Hazard Rate ◽  
Regularity Condition ◽  
Optimal Solution ◽  
Rate Condition ◽  
Good Case ◽  
Optimal Mechanism ◽  
Excludable Public Goods

This paper studies the optimal provision mechanism for multiple excludable public goods. For a class of problems with symmetric goods and binary valuations, we show that the optimal mechanism involves bundling if a regularity condition, akin to a hazard rate condition, on the distribution of valuations is satisfied. Relative to separate provision mechanisms, the optimal bundling mechanism may increase the asymptotic provision probability of socially efficient public goods from zero to one, and decreases the extent of use exclusions. If the regularity condition is violated, the optimal solution replicates the separate provision outcome for the two-good case. (JEL D82, H41)

scholarly journals Temporal expectancy in the context of a theory of visual attention

2013 ◽  
Vol 368 (1628) ◽  
pp. 20130054 ◽  
Author(s):  
Signe Vangkilde ◽  
Anders Petersen ◽  
Claus Bundesen
Keyword(s):  
Visual Attention ◽  
Processing Speed ◽  
Hazard Rate ◽  
Stimulus Presentation ◽  
Letter Recognition ◽  
Perceptual Processing ◽  
Rate Condition ◽  
Temporal Expectancy ◽  
Temporal Expectation ◽  
Condition Stimulus

Temporal expectation is expectation with respect to the timing of an event such as the appearance of a certain stimulus. In this paper, temporal expectancy is investigated in the context of the theory of visual attention (TVA), and we begin by summarizing the foundations of this theoretical framework. Next, we present a parametric experiment exploring the effects of temporal expectation on perceptual processing speed in cued single-stimulus letter recognition with unspeeded motor responses. The length of the cue–stimulus foreperiod was exponentially distributed with one of six hazard rates varying between blocks. We hypothesized that this manipulation would result in a distinct temporal expectation in each hazard rate condition. Stimulus exposures were varied such that both the temporal threshold of conscious perception ( t 0 ms) and the perceptual processing speed ( v letters s −1 ) could be estimated using TVA. We found that the temporal threshold t 0 was unaffected by temporal expectation, but the perceptual processing speed v was a strikingly linear function of the logarithm of the hazard rate of the stimulus presentation. We argue that the effects on the v values were generated by changes in perceptual biases, suggesting that our perceptual biases are directly related to our temporal expectations.

Double-smoothing in Kernel Hazard Rate Estimation

2008 ◽  
Vol 47 (02) ◽  
pp. 167-173 ◽  
Author(s):  
A. Pfahlberg ◽  
O. Gefeller ◽  
R. Weißbach
Keyword(s):  
Hazard Rate ◽  
Nearest Neighbor ◽  
Bandwidth Selection ◽  
Study Data ◽  
Computational Effort ◽  
Finite Sample ◽  
Adaptive Smoothing ◽  
Rate Estimation ◽  
Data Adaptive ◽  
Double Smoothing

Summary Objectives: In oncological studies, the hazard rate can be used to differentiate subgroups of the study population according to their patterns of survival risk over time. Nonparametric curve estimation has been suggested as an exploratory means of revealing such patterns. The decision about the type of smoothing parameter is critical for performance in practice. In this paper, we study data-adaptive smoothing. Methods: A decade ago, the nearest-neighbor bandwidth was introduced for censored data in survival analysis. It is specified by one parameter, namely the number of nearest neighbors. Bandwidth selection in this setting has rarely been investigated, although the heuristical advantages over the frequently-studied fixed bandwidth are quite obvious. The asymptotical relationship between the fixed and the nearest-neighbor bandwidth can be used to generate novel approaches. Results: We develop a new selection algorithm termed double-smoothing for the nearest-neighbor bandwidth in hazard rate estimation. Our approach uses a finite sample approximation of the asymptotical relationship between the fixed and nearest-neighbor bandwidth. By so doing, we identify the nearest-neighbor bandwidth as an additional smoothing step and achieve further data-adaption after fixed bandwidth smoothing. We illustrate the application of the new algorithm in a clinical study and compare the outcome to the traditional fixed bandwidth result, thus demonstrating the practical performance of the technique. Conclusion: The double-smoothing approach enlarges the methodological repertoire for selecting smoothing parameters in nonparametric hazard rate estimation. The slight increase in computational effort is rewarded with a substantial amount of estimation stability, thus demonstrating the benefit of the technique for biostatistical applications.

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