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1.
Summary Estimation-preceded-by-testing is studied in the context of estimating the mean vector of a multivariate normal distribution
under squared error loss together with a complexity cost. It is shown that although the preliminary test estimator is admissible
for the univariate problem (cf Meeden and Arnold (1979),J. Amer. Statist. Assoc.,74, 872–874), for dimensionp≧3, the estimator is inadmissible. A new preliminary test estimator is obtained, which depends on the cost for each component
and dominates the usual preliminary test estimator.
Research partially supported by the NSF Grant Number DMS-82-18091 and partially by the DSR Research Development Award, University
of Florida. 相似文献
2.
Kei Takeuchi Akimichi Takemura 《Annals of the Institute of Statistical Mathematics》1987,39(1):307-324
Summary Distribution of sum of vectors of 0–1 random variables is discussed generalizing the univariate results obtained in our previous
article Takeuchi and Takemura (1987,Ann. Inst. Statist. Math.,39, 85–102). As in our previous article no assumption is made on the independence of the 0–1 random variables. 相似文献
3.
We give a general result to characterize a multivariate distribution from a relationship between the left truncated mean function
and the hazard gradient function. This result allows us to obtain new characterizations of multivariate distributions. In
particular, we show that, for the multivariate normal distribution, the simple relationship, obtained in standardized form
by McGill (1992,Communications in Statistics. Theory Methods,21(11), 3053–3060), actually characterizes the multivariate normal distribution.
Supported by Ministerio de Ciencia y Tecnologia under grant BFM2000-0362. 相似文献
4.
We consider the problem of estimating a continuous bounded multivariate probability density function (pdf) when the random
field X
i
, i ∈ Z
d
from the density is contaminated by measurement errors. In particular, the observations Y
i
, i ∈ Z
d
are such that Y
i
= X
i
+ ε
i
, where the errors ε
i
are a sample from a known distribution. We improve the existing results in at least two directions. First, we consider random
vectors in contrast to most existing results which are only concerned with univariate random variables. Secondly, and most
importantly, while all the existing results focus on the temporal cases (d = 1), we develop the results for random vectors with a certain spatial interaction. Precise asymptotic expressions and bounds
on the mean-squared error are established, along with rates of both weak and strong consistencies, for random fields satisfying
a variety of mixing conditions. The dependence of the convergence rates on the density of the noise field is also studied.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
5.
Mindaugas Bloznelis 《Acta Appl Math》2007,96(1-3):71-86
We show that the without replacement bootstrap of Booth, Butler and Hall (J. Am. Stat. Assoc.
89, 1282–1289, 1994) provides second order correct approximation to the distribution function of a Studentized U-statistic based on simple random
sample drawn without replacement. In order to achieve similar approximation accuracy for the bootstrap procedure due to Bickel
and Freedman (Ann. Stat.
12, 470–482, 1984) and Chao and Lo (Sankhya Ser. A
47, 399–405, 1985) we introduce randomized adjustments to the resampling fraction.
相似文献
6.
Pierre Duchesne 《Annals of the Institute of Statistical Mathematics》2005,57(3):575-595
Portmanteau test statistics are useful for checking the adequacy of many time series models. Here we generalized the omnibus
procedure proposed by Duchesne and Roy (2004,Journal of Multivariate Analysis,89, 148–180) for multivariate stationary autoregressive models with exogenous variables (VARX) to the case of cointegrated (or
partially nonstationary) VARX models. We show that for cointegrated VARX time series, the test statistic obtained by comparing
the spectral density of the errors under the null hypothesis of non-correlation with a kernel-based spectral density estimator,
is asymptotically standard normal. The parameters of the model can be estimated by conditional maximum likelihood or by asymptotically
equivalent estimation procedures. The procedure relies on a truncation point or a smoothing parameter. We state conditions
under which the asymptotic distribution of the test statistic is unaffected by a data-dependent method. The finite sample
properties of the test statistics are studied via a small simulation study. 相似文献
7.
Ibrahim A. Ahmad 《Annals of the Institute of Statistical Mathematics》1982,34(1):351-358
Summary For a sequence of independent and identically distributed random vectors, with finite moment of order less than or equal to
the second, the rate at which the deviation between the distribution functions of the vectors of partial sums and maximums
of partial sums is obtained both when the sample size is fixed and when it is random, satisfying certain regularity conditions.
When the second moments exist the rate is of ordern
−1/4 (in the fixed sample size case). Two applications are given, first, we compliment some recent work of Ahmad (1979,J. Multivariate Anal.,9, 214–222) on rates of convergence for the vector of maximum sums and second, we obtain rates of convergence of the concentration
functions of maximum sums for both the fixed and random sample size cases. 相似文献
8.
Summary An urn contains balls ofs different colors. The problem of the reinforcement of a specified color and random depletion of balls has been considered
by Bernard (1977,Bull. Math. Biol.,39, 463–470) and Shenton (1981,Bull. Math. Biol.,43, 327–340), (1983,Bull. Math. Biol.,45, 1–9). Here we consider a special relation between a reinforcement and depletion, leading to a hypergeometric distribution.
Research sponsored in part by the Applied Mathematical Sciences Research Program, Office of Energy Research, U.S. Department
of Energy under contract DE-AC05-840R21400 with the Martin Marietta Energy Systems, Inc. 相似文献
9.
Precise Large Deviations for Sums of Negatively Associated Random Variables with Common Dominatedly Varying Tails 总被引:1,自引:0,他引:1
Yue Bao WANG Kai Yong WANG Dong Ya CHENG 《数学学报(英文版)》2006,22(6):1725-1734
In this paper, we obtain results on precise large deviations for non-random and random sums of negatively associated nonnegative random variables with common dominatedly varying tail distribution function. We discover that, under certain conditions, three precise large-deviation prob- abilities with different centering numbers are equivalent to each other. Furthermore, we investigate precise large deviations for sums of negatively associated nonnegative random variables with certain negatively dependent occurrences. The obtained results extend and improve the corresponding results of Ng, Tang, Yan and Yang (J. Appl. Prob., 41, 93-107, 2004). 相似文献
10.
F. Carbonell K. J. Worsley L. Galan 《Annals of the Institute of Statistical Mathematics》2011,63(1):1-27
The statistical problem addressed in this paper is to approximate the P value of the maximum of a smooth random field of Wilks’s Λ statistics. So far results are only available for the usual univariate
statistics (Z, t, χ2, F) and a few multivariate statistics (Hotelling’s T
2, maximum canonical correlation, Roy’s maximum root). We derive results for any differentiable scalar function of two independent
Wishart random fields, such as Wilks’s Λ random field. We apply our results to a problem in brain shape analysis. 相似文献
11.
Amir Dembo Nina Gantert Yuval Peres Ofer Zeitouni 《Probability Theory and Related Fields》2002,122(2):241-288
In the study of large deviations for random walks in random environment, a key distinction has emerged between quenched asymptotics, conditional on the environment, and annealed asymptotics, obtained from averaging over environments. In this paper we consider a simple random walk {X
n
} on a Galton–Watson tree T, i.e., on the family tree arising from a supercritical branching process. Denote by |X
n
| the distance between the node X
n
and the root of T. Our main result is the almost sure equality of the large deviation rate function for |X
n
|/n under the “quenched measure” (conditional upon T), and the rate function for the same ratio under the “annealed measure” (averaging on T according to the Galton–Watson distribution). This equality hinges on a concentration of measure phenomenon for the momentum of the walk. (The momentum at level n, for a specific tree T, is the average, over random walk paths, of the forward drift at the hitting point of that level). This concentration, or
certainty, is a consequence of the uncertainty in the location of the hitting point. We also obtain similar results when {X
n
} is a λ-biased walk on a Galton–Watson tree, even though in that case there is no known formula for the asymptotic speed.
Our arguments rely at several points on a “ubiquity” lemma for Galton–Watson trees, due to Grimmett and Kesten (1984).
Received: 15 November 2000 / Revised version: 27 February 2001 / Published online: 19 December 2001 相似文献
12.
We give a shorter proof of Kanter’s (J. Multivariate Anal. 6, 222–236, 1976) sharp Bessel function bound for concentrations of sums of independent symmetric random vectors. We provide
sharp upper bounds for the sum of modified Bessel functions I0(x) + I1(x), which might be of independent interest. Corollaries improve concentration or smoothness bounds for sums of independent
random variables due to Čekanavičius & Roos (Lith. Math. J. 46, 54–91, 2006); Roos (Bernoulli, 11, 533–557, 2005), Barbour & Xia (ESAIM Probab. Stat. 3, 131–150, 1999), and Le Cam (Asymptotic Methods in Statistical Decision Theory. Springer, Berlin Heidelberg New York, 1986).
相似文献
13.
N. Balakrishnan S. Kocherlakota K. Kocherlakota 《Annals of the Institute of Statistical Mathematics》1986,38(1):529-538
Summary The distribution of the errors of misclassification in procedures based on dichotomous and normal variables is derived. The
expressions forE(e
12) andE(e
21) are also obtained. The results in the paper extend those of Chang and Afifi (1974,J. Amer. Statist. Ass.,69, 336–339), using the earlier papers due to John (1961,Ann. Math. Statist.,32, 1125–1144), Subrahmaniam and Chinganda (1978,J. Statist. Plann. Inf.,2, 79–91). 相似文献
14.
Margus Pihlak 《Mathematica Slovaca》2008,58(5):635-652
In the paper the unknown distribution function is approximated with a known distribution function by means of Taylor expansion.
For this approximation a new matrix operation — matrix integral — is introduced and studied in [PIHLAK, M.: Matrix integral, Linear Algebra Appl. 388 (2004), 315–325]. The approximation is applied in the bivariate case when the unknown distribution function is approximated
with normal distribution function. An example on simulated data is also given.
相似文献
15.
On the admissibility of an estimator of a normal mean vector under a linex loss function 总被引:7,自引:0,他引:7
Ahmad Parsian 《Annals of the Institute of Statistical Mathematics》1990,42(4):657-669
For ap-variate normal mean with known variances, the model proposed by Zellner (1986,J. Amer. Statist. Assoc.,81, 446–451) is discussed in a slightly different framework. A generalized Bayes estimate is derived from a three-stage Bayes
point of view under the asymmetric loss function, and the admissibility of such estimators is proved. 相似文献
16.
Jin Ho KWAK Ju Mok OH 《数学学报(英文版)》2006,22(5):1305-1320
A graph G is one-regular if its automorphism group Aut(G) acts transitively and semiregularly on the arc set. A Cayley graph Cay(Г, S) is normal if Г is a normal subgroup of the full automorphism group of Cay(Г, S). Xu, M. Y., Xu, J. (Southeast Asian Bulletin of Math., 25, 355-363 (2001)) classified one-regular Cayley graphs of valency at most 4 on finite abelian groups. Marusic, D., Pisanski, T. (Croat. Chemica Acta, 73, 969-981 (2000)) classified cubic one-regular Cayley graphs on a dihedral group, and all of such graphs turn out to be normal. In this paper, we classify the 4-valent one-regular normal Cayley graphs G on a dihedral group whose vertex stabilizers in Aut(G) are cyclic. A classification of the same kind of graphs of valency 6 is also discussed. 相似文献
17.
Suppose we have a renewal process observed over a fixed length of time starting from a random time point and only the times
of renewals that occur within the observation window are recorded. Assuming a parametric model for the renewal time distribution
with parameter θ, we obtain the likelihood of the observed data and describe the exact and asymptotic behavior of the Fisher information (FI)
on θ contained in this window censored renewal process. We illustrate our results with exponential, gamma, and Weibull models
for the renewal distribution. We use the FI matrix to determine optimal window length for designing experiments with recurring
events when the total time of observation is fixed. Our results are useful in estimating the standard errors of the maximum
likelihood estimators and in determining the sample size and duration of clinical trials that involve recurring events associated
with diseases such as lupus. 相似文献
18.
Sangyeol Lee Okyoung Na Seongryong Na 《Annals of the Institute of Statistical Mathematics》2003,55(3):467-485
In this paper we consider the problem of testing for a variance change in nonstationary and nonparametric time series models.
The models under consideration are the unstable AR(q) model and the fixed design nonparametric regression model with a strong mixing error process. In order to perform a test,
we employ the cusum of squares test introduced by Inclán and Tiao (1994,J. Amer. Statist. Assoc.,89, 913–923). It is shown that the limiting distribution of the test statistic is the sup of a standard Brownian bridge as seen
in iid random samples. Simulation results are provided for illustration. 相似文献
19.
Yizao Wang 《Extremes》2012,15(2):175-196
We provide a necessary and sufficient condition for the ratio of two jointly α-Fréchet random variables to be regularly varying. This condition is based on the spectral representation of the joint distribution
and is easy to check in practice. Our result motivates the notion of the ratio tail index, which quantifies dependence features that are not characterized by the tail dependence index. As an application, we derive the asymptotic behavior of the quotient correlation coefficient proposed in Zhang (Ann Stat
36(2):1007–1030, 2008) in the dependent case. Our result also serves as an example of a new type of regular variation of products, different from
the ones investigated by Maulik et al (J Appl Probab 39(4):671–699, 2002). 相似文献
20.
R. A. Abusev 《Journal of Mathematical Sciences》1995,75(1):1378-1382
The extensive use of maximum likelihood estimates underscores the importance of the problem of statistical estimation of their
errors. These estimates are of utmost importance in cases where the family of normal distributions and the families related
to the normal distributions are considered [1, 2, 4]. The mean square errors of the maximum likelihood estimates of the normal density were investigated in the author's paper
[3]. The mean square errors of statistical estimates of some families of densities related to the normal distributions were
considered in the papers [4–6]. In the present paper, we obtain an asymptotic expansion of the mean square error of the maximum likelihood estimates of
the densities of the joint distribution of sufficient statistics of the family of multivariate normal distributions. The results
obtained allow us to construct the mean square errors of the maximum likelihood estimates for the chi-square density and Wishart's
density.
Translated fromStatisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 4–11, Perm. 1990. 相似文献