2 edition of **Improving estimates of monotone functions by rearrangement** found in the catalog.

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Published
**2007**
by Massachusetts Institute of Technology, Dept. of Economics in Cambridge, MA
.

Written in English

Suppose that a target function is monotonic, namely, weakly increasing, and an original estimate of the target function is available, which is not weakly increasing. Many common estimation methods used in statistics produce such estimates. We show that these estimates can always be improved with no harm using rearrangement techniques: The rearrangement methods, univariate and multivariate, transform the original estimate to a monotonic estimate, and the resulting estimate is closer to the true curve in common metrics than the original estimate. We illustrate the results with a computational example and an empirical example dealing with age-height growth charts. Keywords: Monotone function, improved approximation, multivariate rearrangement, univariate rearrangement, growth chart, quantile regression, mean regression, series, locally linear, kernel methods. JEL Classifications: Primary 62G08; Secondary 46F10, 62F35, 62P10.

**Edition Notes**

Statement | Victor Chernozhukov, Ivǹ Fernǹdez-Val [and] Alfred Galichon |

Series | Working paper series / Massachusetts Institute of Technology, Dept. of Economics -- working paper 07-14, Working paper (Massachusetts Institute of Technology. Dept. of Economics) -- no. 07-14. |

Contributions | Fernǹdez-Val, Ivǹ, Galichon, Alfred, Massachusetts Institute of Technology. Dept. of Economics |

The Physical Object | |
---|---|

Pagination | 31 p. : |

Number of Pages | 31 |

ID Numbers | |

Open Library | OL24641702M |

OCLC/WorldCa | 137297288 |

how they produce better estimates of distributions and quantiles of sample statistics. In Section 4, we illustrate the procedure with several additional examples. 2. Improving Approximations of Monotone Functions by Rearrangement In what follows, let X be a compact interval. We ﬂrst consider an interval of the form X = [0;1]. Noncrossing quantile regression curve estimation Howard D. Bondell. Department of Statistics, Improving point and interval estimators of monotone functions by rearrangement, Non-crossing non-parametric estimates of quantile curves, Cited by:

The improvement property of the rearrangement also extends to the construction of confidence bands for monotone functions. Suppose we have the lower and upper endpoint functions of a simultaneous confidence interval that covers the target function with a pre-specified Pages: Rearrangement inequalities for functionals with monotone integrands Almut Burchard∗ and Hichem Hajaiej† June ; ﬁnal revision March Dedicated to Albert Baernstein, II on the occasion of his 65th birthday. Abstract The inequalities of Hardy-Littlewood and Riesz say that certain integrals involving.

The authors propose a new monotone nonparametric estimate for a regression function of two or more variables. Their method consists in applying successively one-dimensional isotonization. Keywords--Monotone rearrangement, Relative rearrangement. 1. INTRODUCTION It was shown by Rakotoson and Temam [1,2] that for a bounded open connected set whose boundary is Lipchitz then for u E WI'p(~), its monotone decreasing rearrangement u, is in Wllo'~(0, meas(~t)), 1 Cited by: 1.

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Estimatesproduces(monotonic)estimatesthatimprovetheapproximationpropertiesof theoriginalestimates by bringing them closer tothetargetcurve. Furthermore, the re. Many common estimation methods used in statistics produce such estimates.

We show that these estimates can always be improved with no harm using rearrangement techniques: The rearrangement methods, univariate and multivariate, transform the original estimate to a monotonic estimate, and the resulting estimate is closer to the true curve in common metrics than the original by: Improving estimates of monotone functions by rearrangement book is monotonic, namely, weakly increasing, and an original estimate ^ f of the target function is available, which is not weakly increasing.

Many common estimation methods used. We show that these estimates can always be improved with no harm using rearrangement techniques: The rearrangement methods, univariate and multivariate, transform the original estimate to a monotonic estimate, and the resulting estimate is closer to the true curve in common metrics than the original estimate.

We show that these estimates can always be improved with no harm using rearrangement techniques: The rearrangement methods, univariate and multivariate, transform the original estimate to a monotonic estimate ˆ f ∗, and the resulting estimate is closer to the true curve f0 in common metrics than the original estimate ˆ f.

We show that these estimates can always be improved with no harm 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.

Improving Point Estimates of Monotone Functions by Rearrangement Common Estimates of Monotonic Functions. A basic problem in many areas of statistics is the estimation of an unknown function f0: Rd.

Rusing the available information. Suppose we know that the target function f0 is monotonic, namely weakly increasing. Suppose. Title:Improving Point and Interval Estimates of Monotone Functions by Rearrangement.

Abstract: Suppose that a target function is monotonic, namely, weakly increasing, and an available original estimate of this target function is not weakly by: one-step procedure of Ramsay (), which projects on a class of monotone spline functions called I-splines.

Later in the paper we will compare and combine these procedures with the rearrangement. Improving Point Estimates of Monotone Functions by Rearrangement Formulation of the problem. A basic problem in many areas of statistics is.

Improving Point and Interval Estimates of Monotone Functions by Rearrangement Article in Biometrika 96(3) July with 44 Reads How we measure 'reads'.

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, and the resulting estimate is closer to the true curve in common metrics than the original estimate.

We show that these estimates can always be improved with no harm using rearrangement techniques: The rearrangement methods, univariate and multivariate, transform the original estimate to a monotonic estimate, and the resulting estimate is closer to the true curve in common metrics than the original by: Victor Chernozhukov & Ivan Fernandez-Val & Alfred Galichon, "Improving Point and Interval Estimates of Monotone Functions by Rearrangement," Papers, revised Nov Handle: RePEc:arx:papersCited by: Rearrangements, univariate and multivariate, transform the original estimate to a monotonic estimate that always lies closer in common metrics to the target function.

Furthermore, suppose an original confidence interval, which covers the target function with probability at least 1-α, is defined by an upper and lower endpoint functions that are Cited by: Improving estimates of monotone functions by rearrangement.

By Victor Chernozhukov, Ivan Fernandez-Val and Alfred Galichon. Get PDF (4 MB) Abstract. Suppose that a target function is monotonic, namely, weakly increasing, and an original estimate of the target function is available, which is not weakly increasing.

The rearrangement methods. IMPROVING ESTIMATES OF MONOTONE FUNCTIONS BY REARRANGEMENT. We show that these estimates can always be improved with no harm using rearrangement techniques: The rearrangement methods, univariate and multivariate, transform the original estimate to a monotonic estimate /*, and the resulting estimate is closer to the true curve /o in common.

Improving estimates of monotone functions by rearrangement. By Victor Chernozhukov, We show that these estimates can always be improved with no harm using rearrangement techniques: The rearrangement methods, univariate and multivariate, transform the original estimate to a monotonic estimate ˆ f ∗, and the resulting estimate is closer.

Suppose that a target function is monotonic, namely weakly increasing, and an original estimate of this target function is available, which is not weakly increasing. Many common estimation methods used in statistics produce such estimates.

We show that these estimates can always be improved with no harm by using rearrangement techniques: The rearrangement Cited by: Improving estimates of monotone functions by rearrangement.

By Victor Chernozhukov, Iv\ue1n Fern\ue1ndez-Val and Alfred Galichon. Download PDF (4 MB) Cite. BibTex; Full citation The rearrangement methods, univariate and multivariate, transform the original estimate to a monotonic estimate, and the resulting estimate is closer to the true.

CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Abstract. Suppose that a target function is monotonic, namely, weakly increasing, and an available original estimate of this target function is not weakly increasing. Rearrangements, univariate and multivariate, transform the original estimate to a monotonic estimate that always lies closer.

Improving point and interval estimates of monotone functions by rearrangement. By Victor Chernozhukov, Ivan Fernandez-Val and Alfred Galichon. The rearrangement methods, univariate and multivariate, transform the original estimate to a monotonic estimate, and the resulting estimate is closer to the true curve in common metrics than the.Monotonize a step function by rearrangement.

Usage rearrange(f,xmin,xmax) xmax: maximum of the support of the rearranged f. Details. Given a stepfunction Q(u), not necessarily monotone, let F(y V., I. Fernandez-Val, and A.

Galichon, () Improving Estimates of Monotone Functions by Rearrangement, Biometrika, 96, –Monotone Rearrangement, a method of improving density estimates of monotone prob-ability densities. Being such a recently developed method in this application, it sparked my interest and we decided it would be a suitable subject for a bachelor thesis.

A common challenge in statistics is the estimation of an unknown density function.