Estimating a monotone trend
@article{Zhao2008EstimatingAM, title={Estimating a monotone trend}, author={Ou Zhao and Michael Woodroofe}, journal={arXiv: Statistics Theory}, year={2008} }
Motivated by global warming issues, we consider a time se- ries that consists of a nondecreasing trend observed with station- ary fluctuations, nonparametric estimation of the trend under monotonicity assumption is considered. The rescaled isotonic es- timators at an interior point are shown to converge to Chernoff's distribution under minimal conditions on the stationary errors. Since the isotonic estimators suffer from the spiking problem at the end point, two modifications are proposed. The…
15 Citations
ST ] 1 3 Ja n 20 14 INFERENCE FOR MONOTONE TRENDS UNDER DEPENDENCE By
- Mathematics
- 2014
We focus on the problem estimating a monotone trend function under additive and dependent noise. New point-wise confidence interval estimators under both shortand long-range dependent errors are…
Inference for Monotone Functions Under Short- and Long-Range Dependence: Confidence Intervals and New Universal Limits
- Mathematics
- 2016
ABSTRACT We introduce new point-wise confidence interval estimates for monotone functions observed with additive, dependent noise. Our methodology applies to both short- and long-range dependence…
Detecting gradual changes in locally stationary processes
- Mathematics
- 2015
In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the properties are (approximately)…
Invariance principles for linear processes with application to isotonic regression
- Mathematics
- 2011
In this paper, we prove maximal inequalities and study the functional central limit theorem for the partial sums of linear processes generated by dependent innovations. Due to the general weights,…
Estimating red noise spectra of climatological time series
- Environmental Science
- 2013
Spectral densities of climatological time series can be generally well approximated by red noise spectra. A common way of the spectral analysis is therefore based on a comparison of the periodogram…
Estimating spectra of unevenly spaced climatological time series
- Mathematics
- 2015
Spectral analysis is often based on a comparison of the periodogram and the spectral density of a so-called background noise. This spectral density is estimated by fitting a first order…
Testing Un-Separated Hypotheses by Estimating a Distance
- MathematicsBayesian Analysis
- 2018
In this paper we propose a Bayesian answer to testing problems when the hypotheses are not well separated. The idea of the method is to study the posterior distribution of a discrepancy measure…
Topics on Threshold Estimation, Multistage Methods and Random Fields.
- Mathematics, Computer Science
- 2013
This dissertation addresses problems ranging from threshold estimation in Euclidean spaces to multistage procedures in M-estimation and central limit theorems for random fields with a novel approach that relies on the dichotomous behavior of p-value type statistics around this threshold.
Adaptive Bayes Test for Monotonicity
- Mathematics
- 2014
We study the asymptotic behavior of a Bayesian nonparametric test of qualitative hypotheses. More precisely, we focus on the problem of testing monotonicity of a regression function. Even if some…
Threshold estimation based on a p-value framework in dose-response and regression settings.
- MathematicsBiometrika
- 2011
We use p-values to identify the threshold level at which a regression function leaves its baseline value, a problem motivated by applications in toxicological and pharmacological dose-response…
References
SHOWING 1-10 OF 20 REFERENCES
Stationary Random Walks and Isotonic Regression.
- Mathematics
- 2008
This thesis makes some contributions to the study of stationary processes, with a view towards applications to time series analysis. Ever since the work of Gordin [15], martingale approximations have…
A general asymptotic scheme for inference under order restrictions
- Mathematics
- 2006
Limit distributions for the greatest convex minorant and its derivative are considered for a general class of stochastic processes including partial sum processes and empirical processes, for…
The behavior of the NPMLE of a decreasing density near the boundaries of the support
- Mathematics
- 2004
We investigate the behavior of the nonparametric maximum likelihood estimator f n for a decreasing density f near the boundaries of the support of f. We establish the limiting distribution of f n (n…
Central limit theorems for additive functionals of Markov chains
- Mathematics
- 2000
Central limit theorems and invariance principles are obtained for additive functionals of a stationary ergodic Markov chain, say S n = g(X 1 ) + … + g(X n ), where E[g(X 1 )] = 0 and E[g(X 1 ) 2 ] <…
A Kiefer–Wolfowitz comparison theorem for Wicksell’s problem
- Mathematics
- 2007
We extend the isotonic analysis for Wicksell’s problem to estimate a regression function, which is motivated by the problem of estimating dark matter distribution in astronomy. The main result is a…
Computing Chernoff's Distribution
- Mathematics
- 2001
A distribution that arises in problems of estimation of monotone functions is that of the location of the maximum of two-sided Brownian motion minus a parabola. Using results from the first author's…
A new maximal inequality and invariance principle for stationary sequences
- Mathematics
- 2005
We derive a new maximal inequality for stationary sequences under a martingale-type condition introduced by Maxwell and Woodroofe [Ann. Probab. 28 (2000) 713-724]. Then, we apply it to establish the…
Real Analysis and Probability
- Mathematics
- 1989
1. Foundations: set theory 2. General topology 3. Measures 4. Integration 5. Lp spaces: introduction to functional analysis 6. Convex sets and duality of normed spaces 7. Measure, topology, and…