Optimal rates of convergence for nonparametric estimators

CJ Stone - The annals of Statistics, 1980 - JSTOR
Let d denote a positive integer, |x| = (x 2 1 + ⋯ + x 2 d ) 1/2 the Euclidean norm of x = (x 1 , ⋯,
x d ) ∈ R d , ka nonnegative integer, C k the collection of k times continuously differentiable …

Optimal global rates of convergence for nonparametric regression

CJ Stone - The annals of statistics, 1982 - JSTOR
Consider a p-times differentiable unknown regression function θ of a d-dimensional measurement
variable. Let T(θ) denote a derivative of θ of order m and set r = (p - m)/(2p + d). Let T̂ …

Consistent nonparametric regression

CJ Stone - The annals of statistics, 1977 - JSTOR
Let (X, Y) be a pair of random variables such that X is R d -valued and Y is R d' -valued. Given
a random sample (X 1 , Y 1 ), ⋯, (X n , Y n ) from the distribution of (X, Y), the conditional …

Additive regression and other nonparametric models

CJ Stone - The annals of Statistics, 1985 - projecteuclid.org
Let $(X, Y)$ be a pair of random variables such that $X = (X_1, \cdots, X_J)$ and let $f$ by a
function that depends on the joint distribution of $(X, Y).$ A variety of parametric and …

[BOOK][B] Introduction to stochastic processes

PG Hoel, SC Port, CJ Stone - 1986 - books.google.com
An excellent introduction for computer scientists and electrical and electronics engineers
who would like to have a good, basic understanding of stochastic processes! This clearly …

The use of polynomial splines and their tensor products in multivariate function estimation

CJ Stone - The annals of statistics, 1994 - projecteuclid.org
… In the additive (d = 1) regression context, the results in this paper were obtained by Stone
(… paper, Stone (1990b), which involved only the regression context. The results in Stone (1985) …

Polynomial splines and their tensor products in extended linear modeling: 1994 Wald memorial lecture

CJ Stone, MH Hansen, C Kooperberg… - The Annals of …, 1997 - projecteuclid.org
Analysis of variance type models are considered for a regression function or for the logarithm
of a probability function, conditional probability function, density function, conditional …

An asymptotically optimal window selection rule for kernel density estimates

CJ Stone - The Annals of Statistics, 1984 - JSTOR
Kernel estimates of an unknown multivariate density are investigated, with mild restrictions
being placed on the kernel. A window selection rule is considered, which can be interpreted …

The dimensionality reduction principle for generalized additive models

CJ Stone - The Annals of Statistics, 1986 - JSTOR
Let (X, Y) be a pair of random variables such that X = (X 1 ,⋯, X J ) ranges over C = [ 0, 1] J .
The conditional distribution of Y given X = x is assumed to belong to a suitable exponential …

A comparison of techniques for coupling porous flow and geomechanics

RH Dean, X Gai, CM Stone, SE Minkoff - Spe Journal, 2006 - onepetro.org
This paper compares three techniques for coupling multiphase porous flow and geomechanics.
Sample simulations are presented to highlight the similarities and differences in the …