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The Law of Large Numbers for U-statistics Under Absolute Regularity
Law of large numbers U-statistics absolute regularity
2009/5/8
We prove the law of large numbers for U-statistics whose underlying sequence of random variables satisfies an absolute regularity condition ($beta$-mixing condition) under suboptimal conditions.
Asymptotics for Products of Sums and U-statistics
central limit theorem lognormal distribution products of sums records U-statistics
2009/4/29
The product of subsequent partial sums of independent, identically distributed, square integrable, positive random variables is asymptotically lognormal. The result extends in a rather routine way to ...
Poisson Statistics for the Largest Eigenvalues of Wigner Random Matrices with Heavy Tails
random matrices largest eigenvalues Poisson statistics
2009/4/28
We study large Wigner random matrices in the case when the marginal distributions of matrix entries have heavy tails. We prove that the largest eigenvalues of such matrices have Poisson statistics.
Large and Moderate Deviations for Hotelling's T^2-Statistics
largedeviation moderate deviation self-normalized partial sums law of the iterated logarithm
2009/4/22
Let X , X1, X 2 , ... be i.i.d. R d-valued random variables. We prove large and moderate deviations for Hotelling's T2-statistic when X is in the generalized domain of attraction of the normal law.
Large and Moderate Deviations for Hotelling's T^2-Statistics
random variable deviation normal law Hotelling's T^2-Statistics
2009/4/1
Let X , X1, X 2 , ... be i.i.d. R d-valued random variables. We prove large and moderate deviations for Hotelling's T2-statistic when X is in the generalized domain of attraction of the normal law.
Edgeworth Expansions of Some Statistics Including the LB-statistic and V-statistic
Edgeworth expansion linear combination of U-statistics V-statistic
2009/3/10
As an estimator of an estimable parameter, Toda and Yamato (2001) introduced a linear combination Yn of U-statistics which includes V-statistic and LB-statistic. We give the Edgeworth expansions of th...
Asymptotic Representation of Ratio Statistics and Their Mean Squared Errors
asymptotic mean squared error asymptotic U-statistics bias correction coefficient of variation correlation coefficient H-decomposition
2009/3/9
Some statistics in common use take a form of a ratio of two statistics such as sample correlation coefficient, Pearson’s coefficient of variation and so on. In this paper, obtaining an asymptotic repr...
A Convex Combination of Two-Sample U-Statistics
convex combination two-sample U-statistic two-sample V-statistic
2009/3/6
A convex combination of one-sample U-statistics was introduced by Toda and Yamato (2001) and its Edgeworth expansion was derived by Yamato et al. (2003). We introduce a convex combination of two-sampl...
Distributions and the Bootstrap Method of Some Statistics in Principal Canonical Correlation Analysis
canonical correlation analysis perturbation method principal component
2009/3/5
We investigate the canonical correlation of the principal components from two populations, and attain the limiting distribution using the perturbation expansion of the canonical correlation estimate. ...
Conditions for Robustness to Nonnormality on Test Statistics in a GMANOVA Model
actual test size asymptotic expansion Bartlett correction chi-square approximation general multivariate linear hypothesis modified Bartlett correction
2009/3/5
This paper presents the conditions for robustness to the nonnormality on\break three test statistics for a general multivariate linear hypothesis, which were proposed under the normal assumption in a ...
APPLICATION OF ROBUST STATISTICS TO ASSET ALLOCATION MODELS
robust statistics asset allocation FAST-MCD bivariate Winsorization penalization
2009/2/25
Many strategies for asset allocation involve the computation of the expected value and
the covariance matrix of the returns of financial instruments. How much of each instrument
to own is determined...
Improving small area estimation by combining surveys：new perspectives in regional statistics
composite estimator complementary survey mean squared error official statistics regional statistics small areas
2009/2/23
A national survey designed for estimating a specific population quantity is sometimes used for
estimation of this quantity also for a small area, such as a province. Budget constraints do not allow a...
Wavelet methods in statistics：Some recent developments and their applications
curve smoothing density estimation wavelet thresholding penalized least-squares robust regression partial linear models mixed effects models inverse regression time series prediction
2009/2/11
The development of wavelet theory has in recent years spawned applications in signal processing, in fast algorithms for integral transforms, and in image and function representation methods. This last...
Special section on statistics in the atmospheric sciences
Meteorology precipitation forecasting Markov models dataassimilation air pollution climate change
2010/3/17
With the possible exception of gambling, meteorology, particularly precipitation
forecasting, may be the area with which the general public is most
familiar with probabilistic assessments of uncerta...
Statistics of extremes by oracle estimation
Nonparametric adaptive estimation extreme values Hill estimator probabilities of rare events high quantiles
2010/4/30
We use the fitted Pareto law to construct an accompanying approximation
of the excess distribution function. A selection rule of
the location of the excess distribution function is proposed based on...