A general asymptotic scheme for inference under order restrictions
By D. Anevski, Ola G. Hössjer. 2006
48 citations recorded by the source corpus.
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 independent, weakly dependent and long range dependent data. The results are applied to isotonic regression, isotonic regression after kernel smoothing, estimation of convex regression functions, and estimation of monotone and convex density functions. Various pointwise limit distributions are obtained, and the rate of convergence depends on the self similarity properties and on the rate of convergence of the processes considered.
Subfields: Artificial Intelligence, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/f0dd82b1fa23777a49d818b08e04b5a54f05a274
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In Artificial Intelligence
In Statistics and Probability
- Adityanand Guntuboyina
- Bodhisattva Sen
- Pierre C. Bellec
- Richard J. Samworth
- Yining Chen
- Fang Han
- Cécile Durot
- Sabyasachi Chatterjee
Citations in the corpus
- Nonparametric Shape-Restricted Regression (2017, background): “e relaxed substantially, e.g., we can allow for dependent, heteroscedastic errors and the x i’s can be any sequence whose empirical distribution converges to a probability measure on [0;1]; see e.g., [4], [137, Section 3.2.15]. We start with another useful characterization of the isotonic LSE ([17, ”