Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/64669
Authors: 
Chernozhukov, Victor
Fernández-Val, Iván
Galichon, Alfred
Year of Publication: 
2008
Series/Report no.: 
cemmap working paper CWP17/08
Abstract: 
Suppose that a target function f0 : Rd -> R is monotonic, namely weakly increasing, and an original estimate f of this target function is available, which is not weakly increasing. Many common estimation methods used in statistics produce such estimates f. We show that these estimates can always be improved with no harm by using rearrangement techniques: The rearrangement methods, univariate and multivariate, transform the original estimate to a monotonic estimate f*, and the resulting estimate is closer to the true curve f0 in common metrics than the original estimate f. The improvement property of the rearrangement also extends to the construction of confidence bands for monotone functions. Let l and u be the lower and upper endpoint functions of a simultaneous confidence interval [l,u] that covers the true function f0 with probability (1-a), then the rearranged confidence interval [l*,u*], defined by the rearranged lower and upper end-point functions l* and u*, is shorter in length in common norms than the original interval and covers the true function f0 with probability greater or equal to (1-a). We illustrate the results with a computational example and an empirical example dealing with age-height growth charts.
Subjects: 
monotone function
improved estimation
improved inference
multivariate rearrangement
univariate rearrangement
Lorentz inequalities
growth chart
quantile regression
mean regression
series
locally linear
kernel methods
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

Files in This Item:
File
Size





Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.