Let
f(
x),
x ∈ ?
M,
M ≥ 1, be a density function on ?
M, and
X1, ….,
Xn a sample of independent random vectors with this common density. For a rectangle
B in ?
M, suppose that the
X's are censored outside
B, that is, the value
Xk is observed only if
Xk ∈
B. The restriction of
f(
x) to
x ∈
B is clearly estimable by established methods on the basis of the censored observations. The purpose of this paper is to show how to extrapolate a particular estimator, based on the censored sample, from the rectangle
B to a specified rectangle
C containing
B. The results are stated explicitly for
M = 1, 2, and are directly extendible to
M ≥ 3. For
M = 2, the extrapolation from the rectangle
B to the rectangle
C is extended to the case where
B and
C are triangles. This is done by means of an elementary mapping of the positive quarter‐plane onto the strip {(
u, v): 0 ≤
u ≤ 1,
v > 0}. This particular extrapolation is applied to the estimation of the survival distribution based on censored observations in clinical trials. It represents a generalization of a method proposed in 2001 by the author [2]. The extrapolator has the following form: For
m ≥ 1 and
n ≥ 1, let
Km, n(
x) be the classical kernel estimator of
f(
x),
x ∈
B, based on the orthonormal Legendre polynomial kernel of degree
m and a sample of
n observed vectors censored outside
B. The main result, stated in the cases
M = 1, 2, is an explicit bound for
E|
Km, n(
x) ?
f(
x)| for
x ∈
C, which represents the expected absolute error of extrapolation to
C. It is shown that the extrapolator is a consistent estimator of
f(
x),
x ∈
C, if
f is sufficiently smooth and if
m and
n both tend to ∞ in a way that
n increases sufficiently rapidly relative to
m. © 2006 Wiley Periodicals, Inc.
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