Nonparametric least squares estimation of a multivariate convex regression function
نویسندگان
چکیده
منابع مشابه
Nonparametric regression estimation using penalized least squares
We present multivariate penalized least squares regression estimates. We use Vapnik{ Chervonenkis theory and bounds on the covering numbers to analyze convergence of the estimates. We show strong consistency of the truncated versions of the estimates without any conditions on the underlying distribution.
متن کاملVariance Function Estimation in Multivariate Nonparametric Regression
Variance function estimation in multivariate nonparametric regression is considered and the minimax rate of convergence is established. Our work uses the approach that generalizes the one used in Munk et al (2005) for the constant variance case. As is the case when the number of dimensions d = 1, and very much contrary to the common practice, it is often not desirable to base the estimator of t...
متن کاملRepresentation Theorem for Convex Nonparametric Least Squares
We examine a nonparametric least squares regression model where the regression function is endogenously selected from the family of continuous, monotonic increasing and globally concave functions that can be nondifferentiable. We show that this family of functions is perfectly represented by a subset of continuous, piece-wise linear functions whose intercept and slope coefficients are constrain...
متن کاملNonparametric Estimation of Multivariate Convex-transformed Densities.
We study estimation of multivariate densities p of the form p(x) = h(g(x)) for x ∈ ℝ(d) and for a fixed monotone function h and an unknown convex function g. The canonical example is h(y) = e(-y) for y ∈ ℝ; in this case, the resulting class of densities [Formula: see text]is well known as the class of log-concave densities. Other functions h allow for classes of densities with heavier tails tha...
متن کاملNonparametric Least Squares Estimation in Derivative Families
Cost function estimation often involves data on a function and a family of its derivatives. It is known that by using such data the convergence rates of nonparametric estimators can be substantially improved. In this paper we propose series-type estimators which incorporate various derivative data into a single, weighted, nonparametric, least-squares procedure. Convergence rates are obtained, w...
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: The Annals of Statistics
سال: 2011
ISSN: 0090-5364
DOI: 10.1214/10-aos852