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31.
M. S. Ginovian 《Probability Theory and Related Fields》1994,100(3):395-406
Summary A central limit theorem for Toeplitz type quadratic functionals of a stationary Gaussian processX(t),t, is proved, generalizing the result of Avram [1] for discrete time processes. The result is applied to the problem of nonparametric estimation of linear functionals of an unknown spectral density function. We give some upper bounds for the minimax mean square risk of the nonparametric estimators, similar to those by Ibragimov and Has'minskii [12] for a probability density function. 相似文献
32.
Yoshinobu Kamishima 《Annals of Global Analysis and Geometry》1994,12(1):261-289
A strictly pseudoconvex pseudo-Hermitian manifoldM admits a canonical Lorentz metric as well as a canonical Riemannian metric. Using these metrics, we can define a curvaturelike function 62lq2671/xxlarge923.gif" alt="Lambda" align="BASELINE" BORDER="0"> onM. AsM supports a contact form, there exists a characteristic vector field 62lq2671/xxlarge958.gif" alt="xgr" align="MIDDLE" BORDER="0"> dual to the contact structure. If 62lq2671/xxlarge958.gif" alt="xgr" align="MIDDLE" BORDER="0"> induces a local one-parameter group ofCR transformations, then a strictly pseudoconvex pseudo-Hermitian manifoldM is said to be a standard pseudo-Hermitian manifold. We study topological and geometric properties of standard pseudo-Hermitian manifolds of positive curvature 62lq2671/xxlarge923.gif" alt="Lambda" align="BASELINE" BORDER="0"> or of nonpositive curvature 62lq2671/xxlarge923.gif" alt="Lambda" align="BASELINE" BORDER="0">. By the definition, standard pseudo-Hermitian manifolds are calledK-contact manifolds by Sasaki. In particular, standard pseudo-Hermitian manifolds of constant curvature 62lq2671/xxlarge923.gif" alt="Lambda" align="BASELINE" BORDER="0"> turn out to be Sasakian space forms. It is well known that a conformally flat manifold contains a class of Riemannian manifolds of constant curvature. A sphericalCR manifold is aCR manifold whose Chern-Moser curvature form vanishes (equivalently, Weyl pseudo-conformal curvature tensor vanishes). In contrast, it is emphasized that a sphericalCR manifold contains a class of standard pseudo-Hermitian manifolds of constant curvature 62lq2671/xxlarge923.gif" alt="Lambda" align="BASELINE" BORDER="0"> (i.e., Sasakian space forms). We shall classify those compact Sasakian space forms. When 62lq2671/xxlarge923.gif" alt="Lambda" align="BASELINE" BORDER="0">62lq2671/xxlarge8804.gif" alt="le" align="MIDDLE" BORDER="0">0, standard pseudo-Hermitian closed aspherical manifolds are shown to be Seifert fiber spaces. We consider a deformation of standard pseudo-Hermitian structure preserving a sphericalCR structure.Dedicated to Professor Sasao Seiya for his sixtieth birthday 相似文献
33.
Considered are modifications of a rank test of randomness for the one- and multi-dimensional regular design cases as well as for the one- and multi-dimensional random design cases. The null hypothesis is that all observations are independent and identically distributed. The main result is the proof of consistency of the test in each of the above cases against two general alternatives.Alternative 1: there exists a pairwise disjoint partion U
i
=1
m
D
i
=D, where D d1, is a bounded domain inside which one makes observations, such that (1) if an observation point falls insideD
i
, then the corresponding observed value is the realization of a random variable i
i = l,...,m; (2) there exists an ordering % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaamXvP5wqonvsaeHbfv3ySLgzaGqbaiab-Tha7jabe67a4Hqbdiab% +LgaPnaaBaaaleaacaWGRbaabeaakiab-1ha9naaDaaaleaacaWGRb% Gaeyypa0JaaGymaaqaaiaad2gaaaaaaa!4C2D!\[\{ \xi i_k \} _{k = 1}^m \], where % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiabe67a4nXvP5wqonvsaeHbfv3ySLgzaGqbdiab-LgaPnaaBaaa% leaacaWGRbaabeaaaaa!454D!\[\xi i_k \] is stochastically smaller than % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiabe67a4nXvP5wqonvsaeHbfv3ySLgzaGqbdiab-LgaPnaaBaaa% leaacaWGRbaabeaakmaaBaaaleaacqGHRaWkcaaIXaaabeaakiaacY% cacaWGRbGaeyypa0JaaGymaiaacYcacaGGUaGaaiOlaiaac6cacaGG% SaGaamyBaiabgkHiTiaaigdaaaa!509B!\[\xi i_k _{ + 1} ,k = 1,...,m - 1\], (3) the partition is independent of the number of observation points. Note thatm, this ordering, and the sets D
i
are not known a priori: one tests only for the existence of such a partition. Note also that in the one-dimensional case the initial sequence need not be stochastically monotone under the alternative.Alternative 2: there exists an arbitrary asymptotically continuous trend in location. Asymptotically continuous means that the trend converges to some continuous, not identically constant function as the number of data points goes to infinity. This function need not be monotone.A numerical example illustrating the use of the obtained results for image analysis (edge detection) is presented. 相似文献
34.
B. Gyires 《Periodica Mathematica Hungarica》1978,9(1-2):109-113
This paper contains applications of theorems of [1] for quadratic statistics which have constant regression on linear statistics. Two theorems are proved. The first is a sufficient condition which assumes that the characteristic function of a sample is an entire function. The second gives a new characterization of the normal distribution. 相似文献
35.
Shie-Shien Yang 《Annals of the Institute of Statistical Mathematics》1981,33(1):463-470
Summary Let (X
1,Y
1), (X
2,Y
2),…, (X
n,Y
n) be i.i.d. as (X, Y). TheY-variate paired with therth orderedX-variateX
rn is denoted byY
rn and terms the concomitant of therth order statistic. Statistics of the form
are considered. The asymptotic normality ofT
n is established. The asymptotic results are used to test univariate and bivariate normality, to test independence and linearity
ofX andY, and to estimate regression coefficient based on complete and censored samples. 相似文献
36.
Ab initio gradient calculations were performed on BF3 and BCl3 to evaluate the 62j6p2276634018/xxlarge960.gif" alt="pgr" align="BASELINE" BORDER="0">-contribution in these compounds. The influence of the basis set on the results is studied for borontrifluoride. For the chlorine compound the 62j6p2276634018/xxlarge960.gif" alt="pgr" align="BASELINE" BORDER="0">-contribution is smaller than for the fluorine compound. 相似文献
37.
This paper reviews the theory of search. The main viewpoint is statistical but considerable space is spent on connections with other fields such as logic and optimisation. Three primitive ideas dominate: consistency, entropy, and Bayes' methods. The theory of screening provides one of the central examples and there is a section on nonsequential random search deriving from the work of Renyi. The game of Bulls and Cows provides a motivating example for both sequential and nonsequential algorithms. 相似文献
38.
Harald Luschgy 《Probability Theory and Related Fields》1992,93(1):39-66
Summary Let
(Q) be the statistical experiment based on the observation of an unknown function in the presence of an additive noise process with distributionQ. The (possible) loss of information whenQ is replaced by some other noise distributionP is measured by the deficiency of
(P) relative to
(Q). This deficiency and its relation to the variational distance ofP andQ are studied mainly for Gaussian noise processes. Gaussian diffusion processes and special set-indexed processes are treated in detail.Research supported by a Heisenberg grant of the Deutsche Forschungsgemeinschaft 相似文献
39.
Enno Mammen 《Probability Theory and Related Fields》1992,93(4):439-455
Summary We show for an i.i.d. sample that bootstrap estimates consistently the distribution of a linear statistic if and only if the normal approximation with estimated variance works. An asymptotic approach is used where everything may depend onn. The result is extended to the case of independent, but not necessarily identically distributed random variables. Furthermore it is shown that wild bootstrap works under the same conditions as bootstrap.This work has been supported by the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 123 Stochastische Mathematische Modelle 相似文献
40.
Helmut Strasser 《Journal of multivariate analysis》1975,5(2):206-226
Let (X, ) be a measurable space, Θ ? an open interval and PΩ ∥ , Ω ? Θ, a family of probability measures fulfilling certain regularity conditions. Let be the maximum likelihood estimate for the sample size n. Let λ be a prior distribution on Θ and let be the posterior distribution for the sample size n given . denotes a loss function fulfilling certain regularity conditions and Tn denotes the Bayes estimate relative to λ and L for the sample size n. It is proved that for every compact K ? Θ there exists cK ≥ 0 such that This theorem improves results of Bickel and Yahav [3], and Ibragimov and Has'minskii [4], as far as the speed of convergence is concerned. 相似文献