共查询到20条相似文献,搜索用时 156 毫秒
1.
We propose an algorithm for the computation ofL
1 (LAD) smoothing splines in the spacesW
M
(D), with
. We assume one is given data of the formy
i
=(f(t
i
) +
i
, i=1,...,N with {itti}
i=1
N D
, the
i
are errors withE(
i
)=0, andf is assumed to be inW
M
. The LAD smoothing spline, for fixed smoothing parameter0, is defined as the solution,s
, of the optimization problem
(1/N)
i=1
N
¦y
i
–g(t
i
¦+J
M
(g), whereJ
M
(g) is the seminorm consisting of the sum of the squaredL
2 norms of theMth partial derivatives ofg. Such an LAD smoothing spline,s
, would be expected to give robust smoothed estimates off in situations where the
i
are from a distribution with heavy tails. The solution to such a problem is a thin plate spline of known form. An algorithm for computings
is given which is based on considering a sequence of quadratic programming problems whose structure is guided by the optimality conditions for the above convex minimization problem, and which are solved readily, if a good initial point is available. The data driven selection of the smoothing parameter is achieved by minimizing aCV() score of the form
.The combined LAD-CV smoothing spline algorithm is a continuation scheme in 0 taken on the above SQPs parametrized in, with the optimal smoothing parameter taken to be that value of at which theCV() score first begins to increase. The feasibility of constructing the LAD-CV smoothing spline is illustrated by an application to a problem in environment data interpretation. 相似文献
2.
Let (,G, U) be a continuous representation of a Lie groupG by bounded operatorsg U (g) on the Banach space and let (,
,dU) denote the representation of the Lie algebra
obtained by differentiation. Ifa
1, ...,a
d
is a Lie algebra basis of
,A
i
=dU (a
i
) and
whenever =(i
1, ...,i
k
) we reconsider the operators
相似文献
3.
4.
Sufficient conditions are established for the oscillation of proper solutions of the system
5.
Shiquan WU 《应用数学学报(英文版)》1996,12(4):377-383
Letn, s
1,s
2, ... ands
n
be positive integers. Assume
is an integer for eachi}. For
,
, and
, denotes
p
(a)={j|1jn,a
j
p},
, and
.
is called anI
t
p
-intersecting family if, for any a,b
,a
i
b
i
=min(a
i
,b
i
)p for at leastt i's.
is called a greedyI
t
P
-intersecting family if
is anI
t
p
-intersecting family andW
p
(A)W
p
(B+A
c
) for anyAS
p
(
) and any
with |B|=t–1.In this paper, we obtain a sharp upper bound of |
| for greedyI
t
p
-intersecting families in
for the case 2ps
i
(1in) ands
1>s
2>...>s
n
.This project is partially supported by the National Natural Science Foundation of China (No.19401008) and by Postdoctoral Science Foundation of China. 相似文献
6.
Let {S
n}
n0 be a random walk on the line. We give criteria for the existence of a nonrandom sequence n
i for which
respectively
We thereby obtain conditions for to be a strong limit point of {S
n} or {S
n
/n}. The first of these properties is shown to be equivalent to
for some sequence a
i , where T(a) is the exit time from the interval [–a,a]. We also obtain a general equivalence between
and
for an increasing function fand suitable sequences n
i and a
i. These sorts of properties are of interest in sequential analysis. Known conditions for
and
(divergence through the whole sequence n) are also simplified. 相似文献
7.
We prove several unique prime factorization results for tensor products of type II1 factors coming from groups that can be realized either as subgroups of hyperbolic groups or as discrete subgroups of connected Lie groups of real rank 1. In particular, we show that if
is isomorphic to a subfactor in
, for some 2ri,sj, then mn. Mathematics Subject Classification (2000) Primary 46L10; Secondary 20F67 相似文献
8.
Asymptotic properties of partitions of the unit interval are studied through the entropy for random partition
9.
LetK
p(u1, ..., up) be the completep-partite graph whoseith vertex class hasu
i vertices (lip). We show that the theorem of Erds and Stone can be extended as follows. There is an absolute constant >0 such that, for allr1, 0<1 and=">1>1/r, every graphG=G
n of sufficiently large order |G|=n with at least
|