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 increasing. 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 simultaneous confidence interval, which covers the target function with probability at least $1-\alpha$, is defined by an upper and lower end-point functions that are not weakly increasing. Then the rearranged confidence interval, defined by the rearranged upper and lower end-point functions, is shorter in length in common norms than the original interval and also covers the target function with probability at least $1-\alpha$. We demonstrate the utility of the improved point and interval estimates with an age-height growth chart example.

24 pages, 4 figures, 3 tables

References in corpus (1)

• Rearranging Edgeworth-Cornish-Fisher Expansions

Cited by in corpus (23)

• Estimation in functional linear quantile regression
• Sensitivity analysis via the proportion of unmeasured confounding
• On multivariate quantiles under partial orders
• Calibration of self-decomposable Lévy models
• Exact mean integrated squared error and bandwidth selection for kernel distribution function estimators
• Quantile autoregressive conditional heteroscedasticity
• Monotonicity-Constrained Nonparametric Estimation and Inference for First-Price Auctions
• Monotone function estimation in the presence of extreme data coarsening: Analysis of preeclampsia and birth weight in urban Uganda
• Change point analysis in non-stationary processes - a mass excess approach
• Bayesian Quantile Estimation and Regression with Martingale Posteriors
• Compensating data shortages in manufacturing with monotonicity knowledge
• The Sorted Effects Method: Discovering Heterogeneous Effects Beyond Their Averages
• Estimation of a discrete monotone distribution
• Nonparametric inference on Lévy measures of compound Poisson-driven Ornstein-Uhlenbeck processes under macroscopic discrete observations
• A projection approach for multiple monotone regression
• A Unifying Framework for Testing Shape Restrictions
• Least Squares Estimation of a Quasiconvex Regression Function
• Regression Adjustment for Noncrossing Bayesian Quantile Regression
• Noncrossing simultaneous Bayesian quantile curve fitting
• Improved Density and Distribution Function Estimation
• Forecasting dynamic return distributions based on ordered binary choice
• mBART: Multidimensional Monotone BART
• Hypotheses tests in boundary regression models