ON STANDARD NORMAL CONVERGENCE OF THE MULTIVARIATE STUDENT t-STATISTIC FOR SYMMETRIC RANDOM VECTORS

نویسنده

  • EVARIST GINÉ
چکیده

It is proved that if the multivariate Student t-statistic based on i.i.d. symmetric random vectors is asymptotically standard normal, then these random vectors are in the generalized domain of attraction of the normal law. Uniform integrability is also considered, even in the absence of symmetry.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The distance correlation t-test of independence in high dimension

AMS subject classifications: primary 62G10 secondary 62H20 Keywords: dCor dCov Multivariate independence Distance covariance Distance correlation High dimension a b s t r a c t Distance correlation is extended to the problem of testing the independence of random vectors in high dimension. Distance correlation characterizes independence and determines a test of multivariate independence for rand...

متن کامل

Approximating the Distributions of Singular Quadratic Expressions and their Ratios

Noncentral indefinite quadratic expressions in possibly non- singular normal vectors are represented in terms of the difference of two positive definite quadratic forms and an independently distributed linear combination of standard normal random variables. This result also ap- plies to quadratic forms in singular normal vectors for which no general representation is currently available. The ...

متن کامل

Hessian Stochastic Ordering in the Family of multivariate Generalized Hyperbolic Distributions and its Applications

In this paper, random vectors following the multivariate generalized hyperbolic (GH) distribution are compared using the hessian stochastic order. This family includes the classes of symmetric and asymmetric distributions by which different behaviors of kurtosis in skewed and heavy tail data can be captured. By considering some closed convex cones and their duals, we derive some necessary and s...

متن کامل

Exact Convergence Rate and Leading Term in Central Limit Theorem for Student ’ S T Statistic

The leading term in the normal approximation to the distribution of Student’s t statistic is derived in a general setting, with the sole assumption being that the sampled distribution is in the domain of attraction of a normal law. The form of the leading term is shown to have its origin in the way in which extreme data influence properties of the Studentized sum. The leading-term approximation...

متن کامل

Master Thesis Multivariate Skew-Normal Distributions and their Extremal Properties

In this master thesis we explore skewed distributions extended from the normal distribution. A transition from the symmetric to an asymmetric setting is formulated for the univariate as well as the multivariate case. This is done by introducing an additional infinite-dimensional parameter, namely a skewing function π. Our main focus is on the extremal behavior of such skewed random vectors. For...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2004