|
B-spline
Estimate of the
Regression
Function under
General
Censorship Model
Ilhem Laroussi (1)
(1) Laboratory
of Mathematics
and Sciences of
the Decision (LAMASD),
Freres
Mentouri
University,
25017
Constantine,
Algeria
Email address:
33laroussi@gmail.com
Doi :
https://doi.org/10.47013/17.1.11
Cited by :
Jordan J. Math &
Stat.,
17 (1) (2024),
179 - 197
PDF
Received on:
Dec. 20,
2022;
Accepted
on: Aug. 7,
2023
Abstract. In a
continuity
reasoning of the
different
estimators
proposed by de
Kebabi et al.
[21] and
recently Douas
et al. [11] and
Laroussi [26].
The construction
of the
regression
function
estimator is
based on three
axes. The first
one is the
application of
the
non-parametric
estimate,
namely, the
least-squares
technique. The
second axis
represents the
general
censorship which
combines all the
existing types
of censorship.
Hence, empirical
L2-error
estimates are
constructed over
data-dependent
spaces of B-spline
functions. The
almost sure
convergence of
the proposed
estimator is
studied.
Essentially, two
models subject
to twice or
right censorship
are assessed and
this phenomena
of censorship
identified by
the simulation
shows the
interest of this
estimator.
Keywords: Least squares
regression, B-spline
function,
censored data,
convergence,
almost sure.
|
