On risk bounds in isotonic and other shape restricted regression problems
نویسندگان
چکیده
منابع مشابه
Risk Bounds in Isotonic Regression
Nonasymptotic risk bounds are provided for maximum likelihood-type isotonic estimators of an unknown nondecreasing regression function, with general average loss at design points. These bounds are optimal up to scale constants, and they imply uniform n−1/3-consistency of the p risk for unknown regression functions of uniformly bounded variation, under mild assumptions on the joint probability d...
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We consider the problem of estimating an unknown non-decreasing sequence θ from finitely many noisy observations. We give an improved global risk upper bound for the isotonic least squares estimator (LSE) in this problem. The obtained risk bound behaves differently depending on the form of the true sequence θ – one gets a whole range of rates from log n/n (when θ is constant) to n−2/3 (when θ i...
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For the problem of estimating a regression function, μ say, subject to shape constraints, like monotonicity or convexity, it is argued that the divergence of the maximum likelihood estimator provides a useful measure of the effective dimension of the model. Inequalities are derived for the expected mean squared error of the maximum likelihood estimator and the expected residual sum of squares. ...
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Regression splines are smooth, flexible, and parsimonious nonparametric function estimators. They are known to be sensitive to knot number and placement, but if assumptions such as monotonicity or convexity may be imposed on the regression function, the shaperestricted regression splines are robust to knot choices. Monotone regression splines were introduced by Ramsay [Statist. Sci. 3 (1998) 42...
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Shape restricted regressions, including isotonic regression and concave regression as special cases, are studied using priors on Bernstein polynomials and Markov chain Monte Carlo methods. These priors have large supports, select only smooth functions, can easily incorporate geometric information into the prior, and can be generated without computational difficulty. Algorithms generating priors...
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ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 2015
ISSN: 0090-5364
DOI: 10.1214/15-aos1324