2 edition of Improving point and interval estimates of monotone functions by rearrangement found in the catalog.
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 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 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. 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 probability level, then the rearranged confidence interval, defined by the rearranged lower and upper end-point functions, is shorter in length in common norms than the original interval and covers the target function with probability greater or equal to the pre-specified level. We illustrate the results with a computational example and an empirical example dealing with age-height growth charts. Keywords: Monotone function, improved estimation, improved inference, multivariate rearrangement, univariate rearrangement, Lorentz inequalities, growth chart, quantile regression, mean regression, series, locally linear, kernel methods. JEL Classifications: 62G08, 46F10, 62F35, 62P10
|Statement||[by] Victor Chernozhukov, Ivǹ Fernǹdez-Val [and] Alfred Galichon|
|Series||Working paper series / Massachusetts Institute of Technology, Dept. of Economics -- working paper 08-13, Working paper (Massachusetts Institute of Technology. Dept. of Economics) -- no. 08-13.|
|Contributions||Fernǹdez-Val, Ivǹ, Galichon, Alfred, Massachusetts Institute of Technology. Dept. of Economics|
|The Physical Object|
|Pagination||30 p. :|
|Number of Pages||30|
Chris Evans has proposed a new polymath project, namely to attack the “Hot Spots conjecture” for acute-angled triangles.. The details and motivation of this project can be found at the above link, but this blog post can serve as a place to discuss the problem (and, if the discussion takes off, to start organising a more formal polymath project around it). Properties of classical mathematical functions are an important part of our story. e classic Handbook of Mathematical Functions by Abramowitz and Stegun  was an indispensable reference for mathematicians for decades and was certainly a resource for the development of this book.
Dyck Paths and Positroids from Unit Interval Orders. Monday, April 3, , pm Ungar Room Abstract: It is well known that the number of non-isomorphic unit interval orders on [n] equals the n-th Catalan number. Combining work of Skandera and Reed and work of Postnikov, we will assign a rank n positroid on [2n] to each unit interval. The International Dictionary of Artificial Intelligence William J. Raynor, Jr. Glenlake Publishing Company, Ltd. (monotone increasing) functions such as a logistic or Gaussian function, although At any point, the algorithm can choose a new point x, observe the output and File Size: KB.
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Improving Point and Interval Estimates of Monotone Functions by Rearrangement Article in Biometrika 96(3) July with 44 Reads How we measure 'reads'. Victor Chernozhukov & Ivan Fernandez-Val & Alfred Galichon, "Improving point and interval estimates of monotone functions by rearrangement," CeMMAP working papers CWP17/08, Centre for Microdata Methods and Practice, Institute for Fiscal : RePEc:ifs:cemmap/ 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: Download Citation | Correcting an estimator of a multivariate monotone function with isotonic regression | In many problems, a sensible estimator of a.
Chernozhukov V, Fernandez-Val I, Galichon A () Improving point and interval estimates of monotone functions by rearrangement.
Biometrika – CrossRef Google Scholar Conroy RM, Harris RS, Benet BA () The effects of stock splits on bid-ask : Nikolaus Hautsch.
Full text of "Functional Inequalities: New Perspectives and New Applications" See other formats Functional Inequalities: New Perspectives and New Applications Nassif Ghoussoub 1 Amir Moradifam 2 Janu department of Mathematics, University of British Columbia, Vancouver, B.C.
Canada V6T 1Z2. This lively book lays out a methodology of confidence distributions and puts them through their paces. Among other merits they lead to optimal combinations of con dence from different sources of information, and they can make complex models amenable to objective and indeed prior-free analysis for less subjectively inclined statisticians.
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Necessary and sufficient conditions are derived for a cubic to be monotone on an interval. These conditions are used to develop an algorithm which constructs a visually pleasing monotone piecewise cubic interpolant to monotone data.
Several examples are given which compare this algorithm with other interpolation by: The Rearrangement algorithm of Puccetti and Rüschendorf: proving the convergence Forecasting risk with Markov-switching GARCH models: A large-scale performance study Quantitative Risk Management for Cryptocurrencies.
An even simpler rearrangement is the two-point rearrangement or polarization of a function. In general two- point rearrangements give weaker results than symmetrization. For the Cahn–Hilliard problem, however, we show that two-point rearrangements can be used to deduce that a minimizer is equal to its reflection with respect to some.
The super level measure studied in Section 5 is a possible “by-size-generalization” of the standard level measure concept. We again make a small modification of the original concept of Do and Thiele when considering a monotone measure μ on all Borel sets in X instead of an outer measure μ generated by a pre-measure σ on a collection small modification enables us Cited by: 4.
Many of the functions used in calculus and in this book are functions which map real numbers into real numbers. We are often, however, concerned with functions that map sets into real numbers.
Such functions are naturally called functions of a set or, more simply, set functions. This book provides an introduction to functional analysis and treats in detail its application to boundary-value problems and finite elements.
The book is intended for use by senior undergraduate and graduate students in mathematics, the physical sciences and engineering, who may not have been exposed to the conventional prerequisites for a.
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Full text of "CRC Encyclopedia Of Mathematics" See other formats. Niho bent functions are in one-to-one correspondence with line ovals in an a ne plane.
Points of the line oval completely de ne the dual bent function. Furthermore, Niho bent functions are in one-to-one correspondence with ovals in a projective plane PG (2 ;q) with nucleus at a designated point .
Any oval. For non-monotone submodular functions, a approximation under cardinality and matroid constraints (Gharan et al., ), and a approximation under knapsack constraint has been shown (Lee et al., ). Another result is unconstrained maximization of non-monotone submodular set functions, for which Buch-Author: Yatao An Bian.
In more direct preparation for definition of the integral, we define 'block' functions as real-valued functions of a real variable which are constant inside some finite interval of the real axis, and zero outside this interval. The integral of such a function is simply the area under its graph, which is an elementary rectangular block.
If you need to learn about resampling, this book would be a good place to start.'' вЂ”Technometrics (Review of the Second Edition) This thoroughly revised and expanded third edition is a practical guide to data analysis using the.
• In recursion theory, 0 can be used to denote the Turing degree of the partial computable functions. Related mathematical terms • A zero of a function f is a point x in the domain of the function such that f(x) = 0.
When there are ﬁnitely many zeros these are .Book Editing We’ll help you with plot, characters, language, formatting and cover design. Literature Search We’ll help you find the most relevant papers to build or support an argument.
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