The stochastic fluctuation of the quantile regression curve

Arbeitspapier

Let (X1, Y1), . . ., (Xn, Yn) be i.i.d. rvs and let l(x) be the unknown p-quantile regression curve of Y on X. A quantile-smoother ln(x) is a localised, nonlinear estimator of l(x). The strong uniform consistency rate is established under general conditions. In many applications it is necessary to know the stochastic fluctuation of the process {ln(x) – l(x)}. Using strong approximations of the empirical process and extreme value theory allows us to consider the asymptotic maximal deviation sup06x61 |ln(x)?l(x)|. The derived result helps in the construction of a uniform confidence band for the quantile curve l(x). This confidence band can be applied as a model check, e.g. in econometrics. An application considers a labour market discrimination effect.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: SFB 649 Discussion Paper ; No. 2008,027

Classification and Topics

• Classification: Wirtschaft ; Mathematical and Quantitative Methods: General ; Semiparametric and Nonparametric Methods: General ; Labor Economics: General ; Wage Level and Structure; Wage Differentials
• Subject: Quantile Regression , Consistency Rate , Confidence Band , Check Function , Kernel Smoothing , Nonparametric Fitting ; Regression ; Statistischer Test ; Stochastischer Prozess ; Theorie ; Schätzung ; Lohn ; Lebensalter ; Arbeitsmarktdiskriminierung ; USA

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Härdle, Wolfgang Karl ; Song, Song
• Event: Veröffentlichung
• (who): Humboldt University of Berlin, Collaborative Research Center 649 - Economic Risk
• (where): Berlin
• (when): 2008

Further information

• Handle: http://hdl.handle.net/10419/25269
• Last update: 10.03.2025, 11:41 AM CET