共查询到20条相似文献,搜索用时 15 毫秒
1.
Shichi Yamamoto 《Indagationes Mathematicae》1999,10(4):615
In this paper, we study numerical properties of Chern classes of certain covering manifolds. One of the main results is the following: Let ψ : X → Pn be a finite covering of the n-dimensional complex projective space branched along a hypersurface with only simple normal crossings and suppose X is nonsingular. Let ci(X) be the i-th Chern class of X. Then (i) if the canonical divisor KX is numerically effective, then (−1)kck(X) (k ≥ 2) is numerically positive, and (ii) if X is of general type, then (−1)ncil (X) cir, (X) > 0, where il + … + ir = n. Furthermore we show that the same properties hold for certain Kummer coverings. 相似文献
2.
Bimal Kumar Sinha 《Journal of multivariate analysis》1976,6(4):617-625
Treated in this paper is the problem of estimating with squared error loss the generalized variance | Σ | from a Wishart random matrix S: p × p Wp(n, Σ) and an independent normal random matrix X: p × k N(ξ, Σ Ik) with ξ(p × k) unknown. Denote the columns of X by X(1) ,…, X(k) and set ψ(0)(S, X) = {(n − p + 2)!/(n + 2)!} | S |, ψ(i)(X, X) = min[ψ(i−1)(S, X), {(n − p + i + 2)!/(n + i + 2)!} | S + X(1) X′(1) + + X(i) X′(i) |] and Ψ(i)(S, X) = min[ψ(0)(S, X), {(n − p + i + 2)!/(n + i + 2)!}| S + X(1) X′(1) + + X(i) X′(i) |], i = 1,…,k. Our result is that the minimax, best affine equivariant estimator ψ(0)(S, X) is dominated by each of Ψ(i)(S, X), i = 1,…,k and for every i, ψ(i)(S, X) is better than ψ(i−1)(S, X). In particular, ψ(k)(S, X) = min[{(n − p + 2)!/(n + 2)!} | S |, {(n − p + 2)!/(n + 2)!} | S + X(1)X′(1)|,…,| {(n − p + k + 2)!/(n + k + 2)!} | S + X(1)X′(1) + + X(k)X′(k)|] dominates all other ψ's. It is obtained by considering a multivariate extension of Stein's result (Ann. Inst. Statist. Math. 16, 155–160 (1964)) on the estimation of the normal variance. 相似文献
3.
Let X1,…, Xn be i.i.d. random variables symmetric about zero. Let Ri(t) be the rank of |Xi − tn−1/2| among |X1 − tn−1/2|,…, |Xn − tn−1/2| and Tn(t) = Σi = 1nφ((n + 1)−1Ri(t))sign(Xi − tn−1/2). We show that there exists a sequence of random variables Vn such that sup0 ≤ t ≤ 1 |Tn(t) − Tn(0) − tVn| → 0 in probability, as n → ∞. Vn is asymptotically normal. 相似文献
4.
The odd girth of a graph G gives the length of a shortest odd cycle in G. Let ƒ(k, g) denote the smallest n such that there exists a k-regular graph of order n and odd girth g. It is known that ƒ(k, g) ≥ kg/2 and that ƒ(k, g) = kg/2 if k is even. The exact values of ƒ(k, g) are also known if k = 3 or g = 5. Let xe denote the smallest even integer no less than x, δ(g) = (−1)g − 1/2, and s(k) = min {p + q | k = pq, where p and q are both positive integers}. It is proved that if k ≥ 5 and g ≥ 7 are both odd, then [formula] with the exception that ƒ(5, 7) = 20. 相似文献
5.
Let (X, Y) be an
d ×
-valued random vector and let (X1, Y1),…,(XN, YN) be a random sample drawn from its distribution. Divide the data sequence into disjoint blocks of length l1, …, ln, find the nearest neighbor to X in each block and call the corresponding couple (Xi*, Yi*). It is shown that the estimate mn(X) = Σi = 1n wniYi*/Σi = 1n wni of m(X) = E{Y|X} satisfies E{|mn(X) − m(X)|p}
0 (p ≥ 1) whenever E{|Y|p} < ∞, ln
∞, and the triangular array of positive weights {wni} satisfies supi ≤ nwni/Σi = 1n wni
0. No other restrictions are put on the distribution of (X, Y). Also, some distribution-free results for the strong convergence of E{|mn(X) − m(X)|p|X1, Y1,…, XN, YN} to zero are included. Finally, an application to the discrimination problem is considered, and a discrimination rule is exhibited and shown to be strongly Bayes risk consistent for all distributions. 相似文献
6.
We consider asymptotic expansions for sums Sn on the form Sn = ƒ0(X0) + ƒ(X1, X0) + … + ƒ(Xn, Xn−1), where Xi is a Markov chain. Under different ergodicity conditions on the Markov chain and certain conditional moment conditions on ƒ(Xi, Xi−1), a simple representation of the characteristic function of Sn is obtained. The representation is in term of the maximal eigenvalue of the linear operator sending a function g(x) into the function x → E(g(Xi)exp[itƒ(Xi, x)]|Xi−1 = x). 相似文献
7.
Let F be a Banach space with a sufficiently smooth norm. Let (Xi)i≤n be a sequence in LF2, and T be a Gaussian random variable T which has the same covariance as X = Σi≤nXi. Assume that there exists a constant G such that for s, δ≥0, we have P(sTs+δ)Gδ. (*) We then give explicit bounds of Δ(X) = supi|P(|X|≤t)−P(|T|≤t)| in terms of truncated moments of the variables Xi. These bounds hold under rather mild weak dependence conditions of the variables. We also construct a Gaussian random variable that violates (*). 相似文献
8.
B. Feigin M. Jimbo M. Kashiwara T. Miwa E. Mukhin Y. Takeyama 《European Journal of Combinatorics》2004,25(8):1197
Let V(Λi) (resp., V(−Λj)) be a fundamental integrable highest (resp., lowest) weight module of
. The tensor product V(Λi)V(−Λj) is filtered by submodules
, n≥0, n≡i−j mod 2, where viV(Λi) is the highest vector and
is an extremal vector. We show that Fn/Fn+2 is isomorphic to the level 0 extremal weight module V(n(Λ1−Λ0)). Using this we give a functional realization of the completion of V(Λi)V(−Λj) by the filtration (Fn)n≥0. The subspace of V(Λi)V(−Λj) of
-weight m is mapped to a certain space of sequences (Pn,l)n≥0,n≡i−jmod2,n−2l=m, whose members Pn,l=Pn,l(X1,…,Xlz1,…,zn) are symmetric polynomials in Xa and symmetric Laurent polynomials in zk, with additional constraints. When the parameter q is specialized to
, this construction settles a conjecture which arose in the study of form factors in integrable field theory. 相似文献
9.
J. E. Yukich 《Journal of multivariate analysis》1985,17(3):245-260
Let (X,
, P) be a probability space and
n, n ≥ 1, a sequence of classes of measurable complex-valued functions on (X,
, P). Under a weak metric entropy condition on
n and sup {g∞: g
n}, Glivenko-Cantelli theorems are established for the classes
n with respect to the probability measure P; i.e., limn → ∞ supg
n ∫ g(dPn − dP) = 0 a.s. The result is applied to kernel density estimation and a law of the logarithm is derived for the maximal deviation between a kernel density estimator and its expected value, improving upon and generalizing the recent results of W. Stute (Ann. Probab. 10 (1982), 414–422). This result is also used to derive improved rates of uniform convergence for the empirical characteristic function. 相似文献
10.
Let F(s, t) = P(X > s, Y > t) be the bivariate survival function which is subject to random censoring. Let
be the bivariate product limit estimator (PL-estimator) by Campbell and Földes (1982, Proceedings International Colloquium on Non-parametric Statistical Inference, Budapest 1980, North-Holland, Amsterdam). In this paper, it was shown that
, where {ζi(s, t)} is i.i.d. mean zero process and Rn(s, t) is of the order O((n−1log n)3/4) a.s. uniformly on compact sets. Weak convergence of the process {n−1 Σi = 1n ζi(s, t)} to a two-dimensional-time Gaussian process is shown. The covariance structure of the limiting Gaussian process is also given. Corresponding results are also derived for the bootstrap estimators. The result can be extended to the multivariate cases and are extensions of the univariate case of Lo and Singh (1986, Probab. Theory Relat. Fields, 71, 455–465). The estimator
is also modified so that the modified estimator is closer to the true survival function than
in supnorm. 相似文献
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11.
Let X be a real Banach space and let (f(n)) be a positive nondecreasing sequence. We consider systems of unit vectors (xi)∞i=1 in X which satisfy ∑iA±xi|A|−f(|A|), for all finite A
and for all choices of signs. We identify the spaces which contain such systems for bounded (f(n)) and for all unbounded (f(n)). For arbitrary unbounded (f(n)), we give examples of systems for which [xi] is H.I., and we exhibit systems in all isomorphs of ℓ1 which are not equivalent to the unit vector basis of ℓ1. We also prove that certain lacunary Haar systems in L1 are quasi-greedy basic sequences. 相似文献
12.
Let X1, X2, …, Xn be random vectors that take values in a compact set in Rd, d ≥ 1. Let Y1, Y2, …, Yn be random variables (“the responses”) which conditionally on X1 = x1, …, Xn = xn are independent with densities f(y | xi, θ(xi)), i = 1, …, n. Assuming that θ lives in a sup-norm compact space Θq,d of real valued functions, an optimal L1-consistent estimator
of θ is constructed via empirical measures. The rate of convergence of the estimator to the true parameter θ depends on Kolmogorov's entropy of Θq,d. 相似文献
13.
Let Xn, n
, be i.i.d. with mean 0, variance 1, and E(¦Xn¦r) < ∞ for some r 3. Assume that Cramér's condition is fulfilled. We prove that the conditional probabilities P(1/√n Σi = 1n Xi t¦B) can be approximated by a modified Edgeworth expansion up to order o(1/n(r − 2)/2)), if the distances of the set B from the σ-fields σ(X1, …, Xn) are of order O(1/n(r − 2)/2)(lg n)β), where β < −(r − 2)/2 for r
and β < −r/2 for r
. An example shows that if we replace β < −(r − 2)/2 by β = −(r − 2)/2 for r
(β < −r/2 by β = −r/2 for r
) we can only obtain the approximation order O(1/n(r − 2)/2)) for r
(O(lg lgn/n(r − 2)/2)) for r
). 相似文献
14.
Rasul A. Khan 《Journal of multivariate analysis》1978,8(4):550-558
Let X1, X2,… be idd random vectors with a multivariate normal distribution N(μ, Σ). A sequence of subsets {Rn(a1, a2,…, an), n ≥ m} of the space of μ is said to be a (1 − α)-level sequence of confidence sets for μ if P(μ Rn(X1, X2,…, Xn) for every n ≥ m) ≥ 1 − α. In this note we use the ideas of Robbins Ann. Math. Statist. 41 (1970) to construct confidence sequences for the mean vector μ when Σ is either known or unknown. The constructed sequence Rn(X1, X2, …, Xn) depends on Mahalanobis'
or Hotelling's
according as Σ is known or unknown. Confidence sequences for the vector-valued parameter in the general linear model are also given. 相似文献
15.
John R. Collins 《Journal of multivariate analysis》1982,12(4):480-492
Let X1,…,Xn be i.i.d. random vectors in Rm, let θεRm be an unknown location parameter, and assume that the restriction of the distribution of X1−θ to a sphere of radius d belongs to a specified neighborhood
of distributions spherically symmetric about 0. Under regularity conditions on
and d, the parameter θ in this model is identifiable, and consistent M-estimators of θ (i.e., solutions of Σi=1nψ(|Xi−
|)(Xi−
)=0) are obtained by using “re-descenders,” i.e., ψ's wh satisfy ψ(x)=0 for x≥c. An iterative method for solving for
is shown to produce consistent and asymptotically normal estimates of θ under all distributions in
. The following asymptotic robustness problem is considered: finding the ψ which is best among the re-descenders according to Huber's minimax variance criterion. 相似文献
16.
Dale Umbach 《Journal of multivariate analysis》1978,8(4):518-531
The behavior of the posterior for a large observation is considered. Two basic situations are discussed; location vectors and natural parameters.Let X = (X1, X2, …, Xn) be an observation from a multivariate exponential distribution with that natural parameter Θ = (Θ1, Θ2, …, Θn). Let θx* be the posterior mode. Sufficient conditions are presented for the distribution of Θ − θx* given X = x to converge to a multivariate normal with mean vector 0 as |x| tends to infinity. These same conditions imply that E(Θ | X = x) − θx* converges to the zero vector as |x| tends to infinity.The posterior for an observation X = (X1, X2, …, Xn is considered for a location vector Θ = (Θ1, Θ2, …, Θn) as x gets large along a path, γ, in Rn. Sufficient conditions are given for the distribution of γ(t) − Θ given X = γ(t) to converge in law as t → ∞. Slightly stronger conditions ensure that γ(t) − E(Θ | X = γ(t)) converges to the mean of the limiting distribution.These basic results about the posterior mean are extended to cover other estimators. Loss functions which are convex functions of absolute error are considered. Let δ be a Bayes estimator for a loss function of this type. Generally, if the distribution of Θ − E(Θ | X = γ(t)) given X = γ(t) converges in law to a symmetric distribution as t → ∞, it is shown that δ(γ(t)) − E(Θ | X = γ(t)) → 0 as t → ∞. 相似文献
17.
Rong-Qing Jia 《Journal of Approximation Theory》1983,37(4):293-310
For an integer k 1 and a geometric mesh (qi)−∞∞ with q ε (0, ∞), let Mi,k(x): = k[qi + k](· − x)+k − 1, Ni,k(x): = (qi + k − qiMi,k(x)/k, and let Ak(q) be the Gram matrix (∝Mi,kNj,k)i,jεz. It is known that Ak(q)−1∞ is bounded independently of q. In this paper it is shown that Ak(q)−1∞ is strictly decreasing for q in [1, ∞). In particular, the sharp upper bound and lower bound for Ak (q)−1 are obtained: for all q ε (0, ∞). 相似文献
18.
M. A. Botto 《Journal of Approximation Theory》1976,16(4):347-365
We investigate two sequences of polynomial operators, H2n − 2(A1,f; x) and H2n − 3(A2,f; x), of degrees 2n − 2 and 2n − 3, respectively, defined by interpolatory conditions similar to those of the classical Hermite-Féjer interpolators H2n − 1(f, x). If H2n − 2(A1,f; x) and H2n − 3(A2,f; x) are based on the zeros of the jacobi polynomials Pn(α,β)(x), their convergence behaviour is similar to that of H2n − 1(f;, x). If they are based on the zeros of (1 − x2)Tn − 2(x), their convergence behaviour is better, in some sense, than that of H2n − 1(f, x). 相似文献
19.
Guy Wolfovitz 《Random Structures and Algorithms》2011,39(4):539-543
Consider the triangle‐free process, which is defined as follows. Start with G(0), an empty graph on n vertices. Given G(i ‐ 1), let G(i) = G(i ‐ 1) ∪{g(i)}, where g(i) is an edge that is chosen uniformly at random from the set of edges that are not in G(i ? 1) and can be added to G(i ‐ 1) without creating a triangle. The process ends once a maximal triangle‐free graph has been created. Let H be a fixed triangle‐free graph and let XH(i) count the number of copies of H in G(i). We give an asymptotically sharp estimate for ??(XH(i)), for every \begin{align*}1 \ll i \le 2^{-5} n^{3/2} \sqrt{\ln n}\end{align*}, at the limit as n →∞. Moreover, we provide conditions that guarantee that a.a.s. XH(i) = 0, and that XH(i) is concentrated around its mean.© 2011 Wiley Periodicals, Inc. Random Struct. Alg., 2011 相似文献
20.
In a symmetrizable Kac–Moody algebra g(A), let α=∑i=1nkiαi be an imaginary root satisfying ki>0 and α,αi<0 for i=1,2,…,n. In this paper, it is proved that for any xαgα{0}, satisfying [xα,fn]≠0 and [xα,fi]=0 for i=1,2,…,n−1, there exists a vector y such that the subalgebra generated by xα and y contains g′(A), the derived subalgebra of g(A). 相似文献