共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper, we consider a multidimensional diffusion process with jumps whose jump term is driven by a compound Poisson
process. Let a(x,θ) be a drift coefficient, b(x,σ) be a diffusion coefficient respectively, and the jump term is driven by a Poisson random measure p. We assume that its intensity measure qθ has a finite total mass. The aim of this paper is estimating the parameter α = (θ,σ) from some discrete data. We can observe
n + 1 data at tin = ihn,
. We suppose hn → 0, nhn → ∞, nhn2 → 0.
Final version 20 December 2004 相似文献
2.
S. Reshetov 《Journal of Mathematical Sciences》2010,167(4):537-542
We consider the problem of estimating a vector θ = (θ1, θ2,…) ∈ Θ ⊂ l
2 from observations y
i
= θ
i
+ σ
i
x
i
, i = 1, 2,…, where the random values x
i
are N(0, 1), independent, and identically distributed, the parametric set Θ is compact, orthosymmetric, convex, and quadratically
convex. We show that in that case, the minimax risk is not very different from sup?L( P) \sup {\Re_L}\left( \Pi \right) , where ?L( P) {\Re_L}\left( \Pi \right) is the minimax linear risk in the same problem with parametric set Π, and sup is taken over all the hyperrectangles Π ⊂ Θ.
Donoho, Liu, and McGibbon (1990) have obtained this result for the case of equal σ
i
, i = 1, 2,…. Bibliography: 4 titles. 相似文献
3.
Frank Aurzada 《Journal of Theoretical Probability》2007,20(4):843-858
We investigate the behaviour of the logarithmic small deviation probability of a sequence (σ
n
θ
n
) in l
p
, 0<p≤∞, where (θ
n
) are i.i.d. random variables and (σ
n
) is a decreasing sequence of positive numbers. In particular, the example σ
n
∼n
−μ
(1+log n)−ν
is studied thoroughly. Contrary to the existing results in the literature, the rate function and the small deviation constant
are expressed expli- citly in the present treatment. The restrictions on the distribution of θ
1 are kept to an absolute minimum. In particular, the usual variance assumption is removed. As an example, the results are
applied to stable and Gamma-distributed random variables. 相似文献
4.
V. V. Kapustin 《Journal of Mathematical Sciences》2007,141(5):1538-1542
Let θ be an inner function, let K
θ
= H
2 ⊖ θH
2, and let Sθ : Kθ → Sθ be defined by the formula Sθf = Pθzf, where f ∈ Kθ is the orthogonal projection of H2 onto Kθ. Consider the set A of all trace class operators L : Kθ → Kθ, L = ∑(·,un)vn, ∑∥un∥∥vn∥ < ∞ (un, vn ∈ Kθ), such that ∑ūn vn ∈ H
0
1
. It is shown that trace class commutators of the form XSθ − SθX (where X is a bounded linear operator on Kθ) are dense in A in the trace class norm. Bibliography: 2 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 333, 2006, pp. 54–61. 相似文献
5.
Wei-Min Huang 《Annals of the Institute of Statistical Mathematics》1986,38(1):137-144
Summary Let the random variablesX
1,X
2, ...,X
n
be generated by the first-order autoregressive modelX
i
=θX
i−1
+e
i
wheree
i
,i=1, 2, ...,n, are i.i.d. random variables with mean zero, variance σ2, and with unspecified density functiong(·). In the present paper we obtain a characterization of limiting distributions of nonparametric and parametric estimators
of θ as well as a local asymptotic minimax bound of the risks of estimators. 相似文献
6.
Mikhail A. Chebotar Wen-Fong Ke Pjek-Hwee Lee Ruibin Zhang 《Monatshefte für Mathematik》2006,162(1):91-101
Let R be a ring, A = M
n
(R) and θ: A → A a surjective additive map preserving zero Jordan products, i.e. if x,y ∈ A are such that xy + yx = 0, then θ(x)θ(y) + θ(y)θ(x) = 0. In this paper, we show that if R contains
\frac12\frac{1}{2}
and n ≥ 4, then θ = λϕ, where λ = θ(1) is a central element of A and ϕ: A → A is a Jordan homomorphism. 相似文献
7.
I. E. Simonova 《Journal of Mathematical Sciences》1995,75(2):1536-1539
A wide class of reliability theory models or lifetime data can be described as follows. Assume that the lifetime distribution
function is F(t, θ)=F0(λ(θ)t), where θ is the parameter characterizing some inner properties of a product and λ(θ) is an unknown increasing function.
The paper deals with methods of estimation of λ(θ) from the sample (t
i
,θ
i
),i = 1, ...,n, for the case of exponentialF
0.
Translated fromStatisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 46–51, Perm, 1991. 相似文献
8.
Mikhail A. Chebotar Wen-Fong Ke Pjek-Hwee Lee Ruibin Zhang 《Monatshefte für Mathematik》2006,149(2):91-101
Let R be a ring, A = M
n
(R) and θ: A → A a surjective additive map preserving zero Jordan products, i.e. if x,y ∈ A are such that xy + yx = 0, then θ(x)θ(y) + θ(y)θ(x) = 0. In this paper, we show that if R contains
and n ≥ 4, then θ = λϕ, where λ = θ(1) is a central element of A and ϕ: A → A is a Jordan homomorphism.
The third author is Corresponding author. 相似文献
9.
In this paper we extend and improve some results of the large deviation for random sums of random variables. Let {Xn;n 〉 1} be a sequence of non-negative, independent and identically distributed random variables with common heavy-tailed distribution function F and finite mean μ ∈R^+, {N(n); n ≥0} be a sequence of negative binomial distributed random variables with a parameter p C (0, 1), n ≥ 0, let {M(n); n ≥ 0} be a Poisson process with intensity λ 〉 0. Suppose {N(n); n ≥ 0}, {Xn; n≥1} and {M(n); n ≥ 0} are mutually independent. Write S(n) =N(n)∑i=1 Xi-cM(n).Under the assumption F ∈ C, we prove some large deviation results. These results can be applied to certain problems in insurance and finance. 相似文献
10.
For two collections of nonnegative and suitably normalized weights W = (Wj) and V = (Vn,k), a probability distribution on the set of partitions of the set {1, …, n} is defined by assigning to a generic partition
{Aj, j ≤ k} the probability Vn,k
, where |Aj| is the number of elements of Aj. We impose constraints on the weights by assuming that the resulting random partitions Π n of [n] are consistent as n varies, meaning that they define an exchangeable partition of the set of all natural numbers.
This implies that the weights W must be of a very special form depending on a single parameter α ∈ [− ∞, 1]. The case α =
1 is trivial, and for each value of α ≠ = 1 the set of possible V-weights is an infinite-dimensional simplex. We identify
the extreme points of the simplex by solving the boundary problem for a generalized Stirling triangle. In particular, we show
that the boundary is discrete for − ∞ ≤ α < 0 and continuous for 0 ≤ α < 1. For α ≤ 0 the extremes correspond to the members
of the Ewens-Pitman family of random partitions indexed by (α,θ), while for 0 < α < 1 the extremes are obtained by conditioning
an (α,θ)-partition on the asymptotics of the number of blocks of Πn as n tends to infinity. Bibliography: 29 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 325, 2005, pp. 83–102. 相似文献
11.
A rate of convergence for the set compound estimation in a family of certain retracted distributions
Yoshiko Nogami 《Annals of the Institute of Statistical Mathematics》1982,34(1):241-257
Summary This paper is concerned with the set compound squared-error loss estimation problem. Here, the author obtains Lévy consistent
estimate
of the empiric distributionG
n of the parameters θ1,...,θn for a more general family of retracted distributions on the interval [θ, θ+1) than the uniform on [θ, θ+1) as in R. Fox (1970,Ann. Math. Statist.,41, 1845–1852; 1978,Ann. Statist.,6, 846–853) and exhibits a decision procedure based on
with a convergence rateO((n
−1 logn)1/4) for the mofified regret uniformly in (θ1, θ2, ..., θn ∈ Ωn with bounded Ω. The author also gives a counterexample to the convergence of the modified regret for Ω=(−∞, ∞).
This is part of the author's Ph. D. Thesis at Michigan State University. 相似文献
12.
Longcheen Huwang Y. H. Steve Huang Yi-Hua Tina Wang 《Annals of the Institute of Statistical Mathematics》2009,61(4):789-810
Consider an ordinary errors-in-variables model. The true level α
n
(θ*) of a test at nominal level α and sample size n is said to be pointwise robust if α
n
(θ*) → α as n → ∞ for each parameter θ*. Let Ω* be a set of values of θ*. Define α
n
= sup
θ*
∈Ω*α
n
(θ*). The test is said to be uniformly robust over Ω* if α
n
→ α as n → ∞. Corresponding definitions apply to the coverage probabilities of confidence sets. It is known that all existing large-sample
tests for the parameters of the errors-in-variables model are pointwise robust. However, they might not be uniformly robust
over certain null parameter spaces. In this paper, we construct uniformly robust tests for testing the vector coefficient
parameter and vector slope parameter in the functional errors-in-variables model. These tests are established through constructing
the confidence sets for the same parameters in the model with similar desirable property. Power comparisons based on simulation
studies between the proposed tests and some existing tests in finite samples are also presented. 相似文献
13.
N. V. Lazakovich S. P. Stashulenok O. L. Yablonskii 《Lithuanian Mathematical Journal》1999,39(2):196-202
In this paper, we consider problems of approximation of stochastic θ-integrals (θ)∫
0
t
f(B(s))dB(s) with respect to a Brownian motion by sums of the form ∑
k=1
p
fn(B
n
θ
(tk-1))[B
n
θ
(tk)-B
n
θ
(tk-1], where the sequences {fn,n∈∕#x007D; and {[B
n
θ
,n∈∕} are convolution-type approximations of the functionf and Brownian motionB.
Belorussian State University, F. Skoryna ave. 4, 220050 Minsk, Belorus. Translated from Lietuvos Matematikos Rinkinys, Vol.
39, No. 2, pp. 248–256, April–June, 1999.
Translated by V. Mackevičius 相似文献
14.
Consider the standard non-linear regression model y
i
= g(x
i
, θ
0)+ε
i
, i = 1, ... ,n where g(x, θ) is a continuous function on a bounded closed region X × Θ, θ
0 is the unknown parameter vector in Θ ⊂ R
p
, {x
1, x
2, ... , x
n
} is a deterministic design of experiment and {ε1, ε2, ... , ε
n
} is a
sequence of independent random variables. This paper establishes the existences of M-estimates and the asymptotic uniform linearity of M-scores in a family of non-linear regression models when the errors are independent and identically distributed. This result
is then used to obtain the asymptotic distribution of a class of M-estimators for a large class of non-linear regression models. At the same time, we point out that Theorem 2 of Wang (1995)
(J. of Multivariate Analysis, vol. 54, pp. 227–238, Corrigenda. vol. 55, p. 350) is not correct.
This research was supported by the Natural Science Foundation of China (Grant No. 19831010 and grant No. 39930160) and the
Doctoral Foundation of China 相似文献
15.
Let F
p,t
(n) denote the number of the coefficients of (x
1+1x
2+...+x
t
)
j
, 0 ≤j≤n− 1, which are not divisible by the prime p. Define G
p,t
(n) = F
p,t
/n
θ and β(p,t) = lim infF
p,t
)(n)/n
θ, where θ = (log)/(log p). In this paper, we mainly prove that G
p,t
can be extended to a continuous function on ℝ+, and the function G
p,t
is nowhere monotonic. Both the set of differential points of the function G
p,t
and the set of non-differential points of the function G
p,t
are dense in ℝ+.
Received February 18, 2000, Accepted December 7, 2000 相似文献
16.
Steven W. Klein 《Annals of the Institute of Statistical Mathematics》1982,34(1):559-577
Summary LetX
1,...,X
m andY
t,...,Y be independent, random samples from populations which are N(θ,σ
x
2
) and N(θ,σ
y
2
), respectively, with all parameters unknown. In testingH
0:θ=0 againstH
1:θ≠0, thet-test based upon either sample is known to be admissible in the two-sample setting. If, however, one testsH
0 againstH
1:|θ|≧ε>0, with ε arbitrary, our main results show: (i) the construction of a test which is better than the particulart-test chosen, (ii) eacht-test is admissible under the invariance principle with respect to the group of scale changes, and (iii) there does not exist
a test which simultaneously is better than botht-tests. 相似文献
17.
Suppose that (F
n
)
n=1
∞
is a sequence of regular families of finite subsets of ℝ and (θ
n
)
n=1
∞
is a nonincreasing null sequence in (0,1). The mixed Tsirelson spaceT[(θ
n
,F
n
)
n=1
∞
] is the completion ofc
00 with respect to the implicitly defined norm
, where the last supremum is taken over all sequences (E
i
)
i=1
k
in [ℕ]<∞ such that maxE
i<minE
i
+1 and
. Necessary and sufficient conditions are obtained for the existence of higher order ℓ1-spreading models in every subspace generated by a subsequence of the unit vector basis ofT[(θ
n
,F
n
)
n=1
∞
]. 相似文献
18.
YU JIARONG 《高校应用数学学报(英文版)》1995,10(4):361-366
WEIGHTEDAPPROXIMATIONOFRANDOMFUNCTIONSYUJIARONGAbstract:Let(Ω,A,P)beaprobabilityspace,X(t,ω)arandomfunctioncontinuousinprobab... 相似文献
19.
Yasutaka Shimizu 《Statistical Inference for Stochastic Processes》2006,9(2):179-225
We study parametric inference for multidimensional stochastic differential equations with jumps from some discrete observations.
We consider a case where the structure of jumps is mainly controlled by a random measure which is generated by a Lévy process
with a Lévy measure fθ(z)dz, and we admit the case ∫ fθ(z)dz = ∞ in which infinitely many small jumps occur even in any finite time intervals. We propose an estimating function under
this complicated situation and show the consistency and the asymptotic normality. Although the estimators in this paper are
not completely efficient, the method can be applied to comparatively wide class of stochastic differential equations, and
it is easy to compute the estimating equations. Therefore, it may be useful in applications. We also present some simulation
results for some simple models.
Final version 25 December 2004 相似文献
20.
This paper considers empirical Bayes estimation of the mean θ of the univariate normal densityf
0 with known variance where the sample sizesm(n) may vary with the component problems but remain bounded by
<∞. Let {(θ
n
,X
n
=(X
n,1,...,X
n, m(n)
))} be a sequence of independent random vectors where theθ
n
are unobservable and iidG and, givenθ
n
=θ has densityf
θ
m(n)
. The first part of the paper exhibits estimators for the density of
and its derivative whose mean-squared errors go to zero with rates
and
respectively. LetR
m(n+1)(G) denote the Bayes risk in the squared-error loss estimation ofθ
n+1 usingX
n+1. For given 0<a<1, we exhibitt
n
(X1,...,X
n
;X
n+1) such that
.
forn>1 under the assumption that the support ofG is in [0, 1]. Under the weaker condition that E[|θ|2+γ]<∞ for some γ>0, we exhibitt
n
*
(X
1,...,X
n
;X
n+1) such that
forn>1. 相似文献