Adaptive risk bounds in unimodal regression
نویسندگان
چکیده
منابع مشابه
Adaptive Risk Bounds in Unimodal Regression
We study the statistical properties of the least squares estimator in unimodal sequence estimation. Although closely related to isotonic regression, unimodal regression has not been as extensively studied. We show that the unimodal least squares estimator is adaptive in the sense that the risk scales as a function of the number of values in the true underlying sequence. Such adaptivity properti...
متن کاملRisk 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...
متن کاملUnimodal regression via prefix isotonic regression
This paper gives optimal algorithms for determining realvalued univariate unimodal regressions, that is, for determining the optimal regression which is increasing and then decreasing. Such regressions arise in a wide variety of applications. They are shape-constrained nonparametric regressions, closely related to isotonic regression. For unimodal regression on weighted points our algorithm for...
متن کاملOptimal Algorithms for Unimodal Regression
This paper gives optimal algorithms for determining realvalued univariate unimodal regressions, that is, for determining the optimal regression which is increasing and then decreasing. Such regressions arise in a wide variety of applications. They are a form of shape-constrained nonparametric regression, closely related to isotonic regression. For the L2 metric our algorithm requires only (n) t...
متن کاملImproved Risk Bounds in Isotonic Regression
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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bernoulli
سال: 2019
ISSN: 1350-7265
DOI: 10.3150/16-bej922