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SMOOTHED QUANTILE REGRESSION PROCESSES FOR BINARY RESPONSE MODELS

Published online by Cambridge University Press:  20 May 2019

Stanislav Volgushev
Stanislav Volgushev*
Affiliation:
University of Toronto
*
*Address correspondence to Stanislav Volgushev, Department of Statistical Sciences, University of Toronto, Toronto, ON M5S, Canada; e-mail: stanislav.volgushev@utoronto.ca.
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Abstract

In this article, we consider binary response models with linear quantile restrictions. Considerably generalizing previous research on this topic, our analysis focuses on an infinite collection of quantile estimators. We derive a uniform linearization for the properly standardized empirical quantile process and discover some surprising differences with the setting of continuously observed responses. Moreover, we show that considering quantile processes provides an effective way of estimating binary choice probabilities without restrictive assumptions on the form of the link function, heteroskedasticity, or the need for high dimensional nonparametric smoothing necessary for approaches available so far. A uniform linear representation and results on asymptotic normality are provided, and the connection to rearrangements is discussed.

Type
ARTICLES
Information
Econometric Theory , Volume 36 , Issue 2 , April 2020 , pp. 292 - 330
Copyright
Copyright © Cambridge University Press 2019 

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Footnotes

The idea of considering binary response quantile processes originated from discussions with Prof. Roger Koenker. I am thankful to him for the encouragement and many insightful discussions on this topic. My thanks also go to Prof. Jiaying Gu for many helpful discussions. Any remaining mistakes are my sole responsibility. I also thank the Editor Prof. Peter C.B. Phillips, the co-Editor Prof. Yoon-Jae Whang and three anonymous Referees for constructive and insightful comments on previous versions of this manuscript that helped to considerably improve the presentation and content of this article. Part of this research was conducted while I was a visiting scholar at UIUC. I am very grateful to the Statistics and Economics departments for their hospitality. Financial support from the DFG (grant VO1799/1-1) and from a discovery grant from NSERC of Canada is gratefully acknowledged.

References

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