共查询到20条相似文献,搜索用时 28 毫秒
1.
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
2.
Let α(n1, n2) be the probability of classifying an observation from population Π1 into population Π2 using Fisher's linear discriminant function based on samples of size n1 and n2. A standard estimator of α, denoted by T1, is the proportion of observations in the first sample misclassified by the discriminant function. A modification of T1, denoted by T2, is obtained by eliminating the observation being classified from the calculation of the discriminant function. The UMVU estimators, and , of ET1 = τ1(n1, n2) and ET2 = τ2(n1, n2) = α(n1 ? 1, n2) are derived for the case when the populations have multivariate normal distributions with common dispersion matrix. It is shown that and are nonincreasing functions of D2, the Mahalanobis sample distance. This result is used to derive the sampling distributions and moments of and . It is also shown that α is a decreasing function of Δ2 = (μ1 ? μ2)′Σ?1(μ1 ? μ2). Hence, by truncating and (or any estimator) at the value of α for Σ = 0, new estimators are obtained which, for all samples, are as close or closer to α. 相似文献
3.
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
4.
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
5.
James O. Berger 《Journal of multivariate analysis》1978,8(2):173-180
Let X be an observation from a p-variate (p ≥ 3) normal random vector with unknown mean vector θ and known covariance matrix . The problem of improving upon the usual estimator of θ, δ0(X) = X, is considered. An approach is developed which can lead to improved estimators, δ, for loss functions which are polynomials in the coordinates of (δ ? θ). As an example of this approach, the loss L(δ, θ) = |δ ? θ|4 is considered, and estimators are developed which are significantly better than δ0. When is the identity matrix, these estimators are of the form . 相似文献
6.
L.R. Haff 《Journal of multivariate analysis》1977,7(3):374-385
Let Sp×p ~ Wishart (Σ, k), Σ unknown, k > p + 1. Minimax estimators of Σ?1 are given for L1, an Empirical Bayes loss function; and L2, a standard loss function (Ri ≡ E(Li ∣ Σ), i = 1, 2). The estimators are , a, b ≥ 0, r(·) a functional on . Stein, Efron, and Morris studied the special cases and , for certain, a, b. From their work , a = k ? p ? 1, b = p2 + p ? 2; whereas, we prove . The reversal is surprising because a.e. (for a particular L2). Assume (compact) ? , the set of p × p p.s.d. matrices. A “divergence theorem” on functions Fp×p : → implies identities for Ri, i = 1, 2. Then, conditions are given for , i = 1, 2. Most of our results concern estimators with r(S) = t(U)/tr(S), U = p ∣S∣1/p/tr(S). 相似文献
7.
Winfried Stute 《Journal of multivariate analysis》1984,14(1):83-93
For a given score function ψ = ψ(x, θ), let θn be Huber's M-estimator for an unknown population parameter θ. Under some mild smoothness assumptions it is known that is asymptotically normal. In this paper the stopping times associated with the sequence of confidence intervals for θ are investigated. A useful representation of M-estimators is derived, which is also appropriate for proving laws of the iterated logarithm and Donskertype invariance principles for (πn)n. 相似文献
8.
William Alexandre 《Comptes Rendus Mathematique》2004,338(5):365-368
Let q=1,…,n?1 and D be a bounded convex domain in of finite type m. We construct two integral operators Tq and such that for all are continuous, and for all (0,q)-forms h continuous on bD with continuous on bD too, with the additional hypothesis when q=n?1 that ∫bDh∧φ=0 for all φ∈C∞n,0(bD) -fermée, we show . For this construction, we use the Diederich–Fornæss support function of Alexandre (Publ. IRMA Lille 54 (III) (2001)). To prove the continuity of Tq, we integrate by parts and take care of the tangential derivatives. The normal component in z of the kernel of will have a bad behaviour, so, in order to find a good representative of its equivalence class, we isolate the tangential component of the kernel and then integrate by parts again. To cite this article: W. Alexandre, C. R. Acad. Sci. Paris, Ser. I 338 (2004). 相似文献
9.
Morris L Eaton 《Journal of multivariate analysis》1976,6(3):422-425
Let Σ be an n × n positive definite matrix with eigenvalues λ1 ≥ λ2 ≥ … ≥ λn > 0 and let M = {x, y | x?Rn, y?Rn, x ≠ 0, y ≠ 0, x′y = 0}. Then for x, y in M, we have that and the inequality is sharp. If is a partitioning of Σ, let θ1 be the largest canonical correlation coefficient. The above result yields . 相似文献
10.
Stephen D. Fisher 《Journal of Functional Analysis》1973,12(3):236-245
Let T be the unit circle in the complex plane and let A be a vector space of bounded Lebesgue measurable functions on T. A is said to be invariant under the restricted backward shift if, whenever ? is in A and the 0-th Fourier coefficient of ? vanishes, then is also in A. The theorems of this paper provide a characterization of the uniformly closed subalgebras of C(T) which contain the constants and which are invariant under the restricted backward shift and, a similar characterization of the weak-1 closed subalgebras of L∞(T, dθ) which contain the constants and which are invariant under the restricted backward shift. 相似文献
11.
Arthur Lubin 《Journal of Functional Analysis》1974,17(4):388-394
Let m and vt, 0 ? t ? 2π be measures on T = [0, 2π] with m smooth. Consider the direct integral = ⊕L2(vt) dm(t) and the operator on , where e(s, t) = exp ∫st ∫Tdvλ(θ) dm(λ). Let μt be the measure defined by for all continuous ?, and let ?t(z) = exp[?∫ (eiθ + z)(eiθ ? z)?1dμt(gq)]. Call {vt} regular iff for all for 1 a.e. 相似文献
12.
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
13.
William Alexandre 《Comptes Rendus Mathematique》2003,336(7):555-558
Ck estimates for convex domains of finite type in are known from Alexandre (C. R. Acad. Paris, Ser. I 335 (2002) 23–26). We now want to show the same result for annuli. Precisely, we show that for all convex domains D and D′ relatively compact of , of finite type m and m′ such that , for all q=1,…,n?2, there exists a linear operator from to such that for all and all (0,q)-form f, -closed of regularity Ck up to the boundary, is of regularity Ck+1/max(m,m′) up to the boundary and . We fit the method of Diederich, Fisher and Fornaess to the annuli by switching z and ζ. However, the integration kernel will not have the same behavior on the frontier as in the Diederich–Fischer–Fornaess case and we have to alter the Diederich–Fornaess support function which will not be holomorphic anymore. Also, we take care of the so generated residual term in the homotopy formula and show that it is extremely regular so that solve the problem for it will not be difficult. To cite this article: W. Alexandre, C. R. Acad. Sci. Paris, Ser. I 336 (2003). 相似文献
14.
Let be the number of conjugacy classes of elements in SL(2, ) with trace t, and let be the number of equivalence classes of binary quadratic forms with discriminant n. Then for t≠±2, . For all real θ > 0 there is a T(θ) such that whenever |t|>T(θ), . There is a c>0 such that for those t such that t2?4 is squarefree, . 相似文献
15.
Let Fn(x) be the empirical distribution function based on n independent random variables X1,…,Xn from a common distribution function F(x), and let be the sample mean. We derive the rate of convergence of to normality (for the regular as well as nonregular cases), a law of iterated logarithm, and an invariance principle for . 相似文献
16.
Robert L McFarland 《Journal of Combinatorial Theory, Series A》1973,15(1):1-10
A construction is given for difference sets in certain non-cyclic groups with the parameters , , , n = q2s for every prime power q and every positive integer s. If qs is odd, the construction yields at least inequivalent difference sets in the same group. For q = 5, s = 2 a difference set is obtained with the parameters (v, k, λ, n) = (4000, 775, 150, 625), which has minus one as a multiplier. 相似文献
17.
Harry Dym 《Journal of Functional Analysis》1978,28(1):33-57
Let PT denote the orthogonal projection of L2(R1, dΔ) onto the space of entire functions of exponential type ? T which are square summable on the line with respect to the measure , and let G denote the operator of multiplication by a suitably restricted complex valued function g. It is shown that if is summable, if is locally summable, and if belongs to the span in L∞ of e?iyTH∞:T ? 0, in which h is chosen to be an outer function and h#(γ) agrees with the complex conjugate of h(γ) on the line, then exists and is independent of h for every positive integer n. This extends the range of validity of a formula due to Mark Kac who evaluated this limit in the special case h = 1 using a different formalism. It also extends earlier results of the author which were established under more stringent conditions on h. The conclusions are based in part upon a preliminary study of a more general class of projections. 相似文献
18.
Real constant coefficient nth order elliptic operators, Q, which generate strongly continuous semigroups on L2(k) are analyzed in terms of the elementary generator, , for n even. Integral operators are defined using the fundamental solutions pn(x, t) to ut = Au and using real polynomials ql,…, qk on m by the formula, for q = (ql,…, qk), m. It is determined when, strongly on L2(k), . If n = 2 or k = 1, this can always be done. Otherwise the symbol of Q must have a special form. 相似文献
19.
Kamal C Chanda 《Statistics & probability letters》1985,3(5):261-268
Let {Xt; t = 1, 2,…} be a linear process with a location parameter θ defined by Xt ? θ = Σ0∞grZt?r where {Zt; t = 0, ±1,…} is a sequence of independent and identically distributed random variables, with E∥Z1∥δ < ∞ for some δ > 0. If δ ? 1 we assume further than E(Z1) = 0. Let η = δ if 0 < δ < 2, and η = 2 if δ ? 2. Then assume that Σ0∞∥ gr ∥η < ∞. Consider the class of estimators given by is of the form cnt = Σp = 0sβnptp for some s ? 0. An attempt has been made to investigate the distributional properties of in large samples for various choices of βnp (0 ? p ? s), s, and the distribution of Z1 under the constraints Σ0∞rkgr = 0, 0 ? k ? q where q in an arbitrary integer, 0 ? q ? s. 相似文献
20.
Georg Lindgren 《Journal of multivariate analysis》1980,10(2):181-206
Let ζ(t), η(t) be continuously differentiable Gaussian processes with mean zero, unit variance, and common covariance function r(t), and such that ζ(t) and η(t) are independent for all t, and consider the movements of a particle with time-varying coordinates (ζ(t), η(t)). The time and location of the exists of the particle across a circle with radius u defines a point process in R3 with its points located on the cylinder {(t, u cos θ, u sin θ); t ≥ 0, 0 ≤ θ < 2π}. It is shown that if r(t) log t → 0 as t → ∞, the time and space-normalized point process of exits converges in distribution to a Poisson process on the unit cylinder. As a consequence one obtains the asymptotic distribution of the maximum of a χ2-process, χ2(t) = ζ2(t) + η2(t), P{sup0≤t≤Tχ2(t) ≤ u2} → e?τ if as T, u → ∞. Furthermore, it is shown that the points in R3 generated by the local ?-maxima of χ2(t) converges to a Poisson process in R3 with intensity measure (in cylindrical polar coordinates) (2πr2)?1dtdθdr. As a consequence one obtains the asymptotic extremal distribution for any function g(ζ(t), η(t)) which is “almost quadratic” in the sense that has a limit as r → ∞. Then if as T, u → ∞. 相似文献