共查询到20条相似文献,搜索用时 31 毫秒
1.
M.E Bock 《Journal of multivariate analysis》1985,17(2):127-147
Let X be a p-dimensional random vector with density f(6X?θ6) where θ is an unknown location vector. For p ≥ 3, conditions on f are given for which there exist minimax estimators θ?(X) satisfying 6Xt6 · 6θ?(X) ? X6 ≤ C, where C is a known constant depending on f. (The positive part estimator is among them.) The loss function is a nondecreasing concave function of 6θ?? θ62. If θ is assumed likely to lie in a ball in p, then minimax estimators are given which shrink from the observation X outside the ball in the direction of P(X) the closest point on the surface of the ball. The amount of shrinkage depends on the distance of X from the ball. 相似文献
2.
R Michel 《Journal of multivariate analysis》1979,9(3):393-400
It is shown that—under appropriate regularity conditions—the conditional distribution of the first p components of a normalized sum of i.i.d. m-dimensional random vectors, given the complementary subvector, admits a Chebyshev-Cramér asymptotic expansion of order , uniformly over all Borelsets in p and uniformly in a region of the conditioning subvector that includes moderate deviations. 相似文献
3.
The following estimate of the pth derivative of a probability density function is examined: , where hk is the kth Hermite function and Σi = 1nhk(p)(Xi) is calculated from a sequence X1,…, Xn of independent random variables having the common unknown density. If the density has r derivatives the integrated square error converges to zero in the mean and almost completely as rapidly as O(n?α) and O(n?α log n), respectively, where . Rates for the uniform convergence both in the mean square and almost complete are also given. For any finite interval they are O(n?β) and , respectively, where . 相似文献
4.
In [6, theorem IV.8.18], relatively norm compact sets K in Lp(μ) are characterized by means of strong convergence of conditional expectations, Eπf → f in Lp(μ), uniformly for f ∈ K, where (Eπ) is the family of conditional expectations corresponding to the net of all finite measurable partitions.In this paper we extend the above result in several ways: we consider nets of not necessarily finite partitions; we consider spaces of vector valued pth power Bochner integrable functions (and spaces M(Σ, E) of vector valued measures with finite variation); we characterize relatively strong compact sets K in by means of uniform strong convergence Eπf → f, as well as relatively weak compact sets K by means of uniform weak convergence Eπf → f. Previously, in [4], uniform strong convergence (together with some other conditions) was proved to be sufficient (but not necessary) for relative weak compactness. 相似文献
5.
Donald Richards 《Statistics & probability letters》1983,1(3):141-145
Recent articles by Kushner and Meisner (1980) and Kushner, Lebow and Meisner (1981) have posed the problem of characterising the ‘EP’ functions f(S) for which Ef(S) for which E(f(S)) = λnf(Σ) for some λn ? , whenever the m × m matrix S has the Wishart distribution W(m, n, Σ). In this article we obtain integral representations for all nonnegative EP functions. It is also shown that any bounded EP function is harmonic, and that EP polynomials may be used to approximate the functions in certain Lp spaces. 相似文献
6.
Karl J Witsch 《Journal of Mathematical Analysis and Applications》1976,54(3):820-839
Denote by L a second order strongly elliptic operator in the Euclidian p-space p, and by P some real polynomial in one variable. First the wholespace-problem for the equation P(L)u = f is considered and asymptotic conditions are derived which yield an existence and uniqueness theorem. Then for the Dirichlet problem in some exterior domain G ? p a “Fredholm alternative theorem” is proved. 相似文献
7.
R Michel 《Journal of multivariate analysis》1979,9(3):401-409
Let Pη, η = (θ, γ) ∈ Θ × Γ ? × k, be a (k + 1)-dimensional exponential family. Let , n ∈ , be an optimal similar test for the hypothesis {P(θ,γ)n: γ ∈ Γ} (θ ∈ Θ fixed) against alternatives P(θ1,γ1)n, θ1 > θ, γ1 ∈ Γ. It is shown that (?n1)n∈ is third order efficient in the class of all test-sequences that are asymptotically similar of level α + o(n?1) (locally uniformly in the nuisance parameter γ). 相似文献
8.
Zahava Shmuely 《Journal of Combinatorial Theory, Series A》1976,21(3):369-383
The (isotone) map f: X → X is an increasing (decreasing) operator on the poset X if f(x) ? f2(x) (f2(x) ? f(x), resp.) holds for each x ∈ X. Properties of increasing (decreasing) operators on complete lattices are studied and shown to extend and clarify those of closure (resp. anticlosure) operators. The notion of the decreasing closure, , (the increasing anticlosure, ,) of the map f: X → X is introduced extending that of the transitive closure, , of f. , and are all shown to have the same set of fixed points. Our results enable us to solve some problems raised by H. Crapo. In particular, the order structure of H(X), the set of retraction operators on X is analyzed. For X a complete lattice H(X) is shown to be a complete lattice in the pointwise partial order. We conclude by claiming that it is the increasing-decreasing character of the identity maps which yields the peculiar properties of Galois connections. This is done by defining a u-v connection between the posets X and Y, where u: X → X (v: Y → Y) is an increasing (resp. decreasing) operator to be a pair f, g of maps f; X → Y, g: Y → X such that gf ? u, fg ? v. It is shown that the whole theory of Galois connections can be carried over to u-v connections. 相似文献
9.
Allan R Sampson 《Journal of multivariate analysis》1983,13(2):375-381
Let X1, …, Xp have p.d.f. g(x12 + … + xp2). It is shown that (a) X1, …, Xp are positively lower orthant dependent or positively upper orthant dependent if, and only if, X1,…, Xp are i.i.d. N(0, σ2); and (b) the p.d.f. of |X1|,…, |Xp| is TP2 in pairs if, and only if, In g(u) is convex. Let X1, X2 have p.d.f. . Necessary and sufficient conditions are given for f(x1, x2) to be TP2 for fixed correlation ?. It is shown that if f is TP2 for all ? >0. then (X1, X2)′ ~ N(0, Σ). Related positive dependence results and applications are also considered. 相似文献
10.
《Advances in Mathematics》1985,56(3):238-282
Let n be the Lie algebra gln(C), let S(n) be the symmetric algebra of n, and let T(n) be the tensor algebra of n. In a recent paper, R. K. Gupta studied certain sequences of representations R∞ = (Rn)∞n = 1, where Rn is a representation of n. These sequences have the property that every irreducible representation occurring in S(n) is in exactly one of these sequences. Fixing f, she considers s(R∞, f) which is the limit on n of the multiplicity of Rn in Sf(n), the fth-graded piece of S(n). She and R. P. Stanley independently showed that the limit s(R∞, f) exists and is given by an amazingly elegant formula. They call s(R∞, f) the stable multiplicity of Rn in Sf(n). In this paper, an entirely different approach is used to extend the above result in several directions. Appropriately defined sequences R∞ for all of the classical Lie algebras n are studied, and a simple formula for the stable multiplicity m(R)∞, ψ, f, ∞) of Rn in the ψ-isotypic component of Tf(n), where ψ is any irreducible character of the symmetric group tSf, is obtained. As in the work of Gupta and Stanley, the expressions for m(R)∞, ψ, f, ∞) are amazingly simple. Special cases include the stable decomposition of the tensor algebra, the symmetric algebra and the exterior algebra of n. As a byproduct of our proof, a “stable” decomposition of every isotypic component of T(n) is obtained. This combinatorial decomposition is in some sense a generalization of Kostant's decomposition of S(n) into direct sum of the harmonics and the ideal generated by the invariants of positive degree. To be precise, for f <n the combinatorial decomposition of Tf(n) projects onto Kostant's decomposition of Sf(n). 相似文献
11.
Let θ(n) denote the maximum likelihood estimator of a vector parameter, based on an i.i.d. sample of size n. The class of estimators θ(n) + n?1q(θ(n)), with q running through a class of sufficiently smooth functions, is essentially complete in the following sense: For any estimator T(n) there exists q such that the risk of θ(n) + n?1q(θ(n)) exceeds the risk of T(n) by an amount of order o(n?1) at most, simultaneously for all loss functions which are bounded, symmetric, and neg-unimodal. If is chosen such that is unbiased up to , then this estimator minimizes the risk up to an amount of order o(n?1) in the class of all estimators which are unbiased up to .The results are obtained under the assumption that T(n) admits a stochastic expansion, and that either the distributions have—roughly speaking—densities with respect to the lebesgue measure, or the loss functions are sufficiently smooth. 相似文献
12.
R.S. Singh 《Journal of multivariate analysis》1976,6(1):111-122
On the basis of a random sample of size n on an m-dimensional random vector X, this note proposes a class of estimators fn(p) of f(p), where f is a density of X w.r.t. a σ-finite measure dominated by the Lebesgue measure on Rm, p = (p1,…,pm), pj ≥ 0, fixed integers, and for x = (x1,…,xm) in Rm, f(p)(x) = ?p1+…+pm f(x)/(?p1x1 … ?pmxm). Asymptotic unbiasedness as well as both almost sure and mean square consistencies of fn(p) are examined. Further, a necessary and sufficient condition for uniform asymptotic unbisedness or for uniform mean square consistency of fn(p) is given. Finally, applications of estimators of this note to certain statistical problems are pointed out. 相似文献
13.
F. Götze 《Journal of multivariate analysis》1981,11(2):260-272
Let P(Θ, τ) 6 , θ ∈ Θ ? , τ ∈ T ? p denote a family of probability measures, where τ denotes the vector of nuisance parameters. Starting from randomized asymptotic maximum likelihood (as. m. l.) estimators for (θ, τ) we construct randomized estimators which are asymptotically median unbiased up to resp. test procedures which are as. similar of level (for testing θ = θ0, τ ∈ T against one sided alternatives). The estimation procedures are second-order efficient in the class of estimators which are median unbiased up to and the test procedures are second-order efficient in the class of tests which are as. of level . These results hold without any continuity condition on the family of probability measures. 相似文献
14.
Let (Ω, , μ) be a measure space, a separable Banach space, and 1 the space of all bounded conjugate linear functionals on . Let f be a weak1 summable positive B(1)-valued function defined on Ω. The existence of a separable Hilbert space , a weakly measurable B()-valued function Q satisfying the relation is proved. This result is used to define the Hilbert space L2,f of square integrable operator-valued functions with respect to f. It is shown that for B+(1)-valued measures, the concepts of weak1, weak, and strong countable additivity are all the same. Connections with stochastic processes are explained. 相似文献
15.
William E Strawderman 《Journal of multivariate analysis》1974,4(3):255-264
Families of minimax estimators are found for the location parameters of a p-variate distribution of the form , where G(·) is a known c.d.f. on (0, ∞), p ≥ 3 and the loss is sum of squared errors. The estimators are of the form where 0 ≤ a ≤ 2, r(X′X) is nondecreasing, and is nonincreasing. Generalized Bayes minimax estimators are found for certain G(·)'s. 相似文献
16.
S Sorin 《Journal of Mathematical Analysis and Applications》1984,98(1):296-303
For each p in the simplex P of k we introduce convex subsets of P, ΠI(p) and ΠII(p). For f a real function on P we define Cav1f to be the smallest function greater than f on P and concave on Π1(p) for each p in P (and similarly VexIIf). Given u a continuous real function on P we prove that the following problems: have the same solution which is also the only solution of f = Vex11 max{u,f} = Cav1 min{u,f}. This is an extension of a former proof by Mertens and Zamir for the case where P is a. product of convex R and S with ΠI(p) = r × S and ΠII(p) = R × s. 相似文献
17.
Sylvia Halász 《Journal of Combinatorial Theory, Series A》1984,37(1):85-90
Given a convex domain C and a positive integer k, inscribe k nonoverlapping convex domains into C, all of them similar to C. Denote by f(k) the maximal sum of their circumferences. In this paper it is shown, that for C square, parallelogram or triangle (1) the first increase of f(k) after k = l2 occurs not later than at k = l2 + 2, (2) constructions can be given, where the following lower bounds are attained for f(k) = f(l2 + j): where c denotes the circumference of C. 相似文献
18.
Hendrik S.V de Snoo 《Journal of Mathematical Analysis and Applications》1983,92(1):172-179
With an ordinary differential expression L = ∑nk=0PkDk on an open interval I? is associated a selfadjoint operator H in a Hilbert space, possibly beyond =L2(l). The set H∩ only depends on the generalized spectral family associated with H. It is shown that the (differentiated) eigenfunction expansion given by H converges uniformly on compact subintervals of l for functions in (H)∩ In case H is a semibounded selfadjoint operator in =L2T, a similar result is proved for functions in |H|, which is the set of all ∈ for which there exists a sequence fn∈(H) such that fn→f in and (H(fn ? fm), fn ? fm → 0 as n, m → ∞. 相似文献
19.
Anna Maria Mantero 《Journal of Functional Analysis》1982,47(1):7-25
Let K be a distribution on 2. We denote by λ(K) the twisted convolution operator f → K × f defined by the formula K × f(x, y) = ∝∝ dudvK(x ? u, y ? v) f(u, v) exp(ixv ? iyu). We show that there exists K such that the operator λ(K) is bounded on Lp(R)2 for every p in (1, 2¦, but is unbounded on Lq(R)2 for every q > 2. 相似文献
20.
A function f(x) defined on = 1 × 2 × … × n where each i is totally ordered satisfying f(x ∨ y) f(x ∧ y) ≥ f(x) f(y), where the lattice operations ∨ and ∧ refer to the usual ordering on , is said to be multivariate totally positive of order 2 (MTP2). A random vector Z = (Z1, Z2,…, Zn) of n-real components is MTP2 if its density is MTP2. Classes of examples include independent random variables, absolute value multinormal whose covariance matrix Σ satisfies ?DΣ?1D with nonnegative off-diagonal elements for some diagonal matrix D, characteristic roots of random Wishart matrices, multivariate logistic, gamma and F distributions, and others. Composition and marginal operations preserve the MTP2 properties. The MTP2 property facilitate the characterization of bounds for confidence sets, the calculation of coverage probabilities, securing estimates of multivariate ranking, in establishing a hierarchy of correlation inequalities, and in studying monotone Markov processes. Extensions on the theory of MTP2 kernels are presented and amplified by a wide variety of applications. 相似文献