Quadratic error of unbiased estimator of density of joint distribution of sufficient statistics of multidimensional normal distribution

1991 ◽  
Vol 56 (3) ◽  
pp. 2403-2406 ◽  
Author(s):  
R. A. Abusev
Keyword(s):  
Normal Distribution ◽  
Unbiased Estimator ◽  
Joint Distribution ◽  
Quadratic Error ◽  
Sufficient Statistics ◽  
Multidimensional Normal Distribution

Limit theorems for uniform distributions on spheres in high-dimensional euclidean spaces

1982 ◽  
Vol 19 (01) ◽  
pp. 221-228 ◽  
Author(s):  
A. J. Stam
Keyword(s):  
Normal Distribution ◽  
Uniform Distribution ◽  
Total Variation ◽  
Joint Distribution ◽  
Limit Theorems ◽  
Geometric Probability ◽  
High Dimensional ◽  
Standard Normal Distribution ◽  
Uniform Distributions ◽  
Standard Normal

If X = (X 1, · ··, Xn ) has uniform distribution on the sphere or ball in ℝ with radius a, then the joint distribution of , ···, k, converges in total variation to the standard normal distribution on ℝ. Similar results hold for the inner products of independent n-vectors. Applications to geometric probability are given.

scholarly journals On n/p-Asymptotic Distribution Of Vector Of Weighted Traces Of Powers Of Wishart Matrices

2018 ◽  
Vol 33 ◽  
pp. 24-40 ◽  
Author(s):  
Jolanta Pielaszkiewicz ◽  
Dietrich Von Rosen ◽  
Martin Singull
Keyword(s):  
Normal Distribution ◽  
Covariance Matrix ◽  
Asymptotic Distribution ◽  
Joint Distribution ◽  
Recursive Formula ◽  
Multivariate Normal ◽  
Wishart Matrices ◽  
The Matrix ◽  
Matrix Normal ◽  
Matrix Normal Distribution

The joint distribution of standardized traces of $\frac{1}{n}XX'$ and of $\Big(\frac{1}{n}XX'\Big)^2$, where the matrix $X:p\times n$ follows a matrix normal distribution is proved asymptotically to be multivariate normal under condition $\frac{{n}}{p}\overset{n,p\rightarrow\infty}{\rightarrow}c>0$. Proof relies on calculations of asymptotic moments and cumulants obtained using a recursive formula derived in Pielaszkiewicz et al. (2015). The covariance matrix of the underlying vector is explicitely given as a function of $n$ and $p$.

scholarly journals A Sufficient Statistics Characterization of the Normal Distribution

1970 ◽  
Vol 41 (3) ◽  
pp. 1086-1090 ◽  
Author(s):  
Douglas Kelker ◽  
Ted K. Matthes
Keyword(s):  
Normal Distribution ◽  
Sufficient Statistics

Limit theorems for uniform distributions on spheres in high-dimensional euclidean spaces

1982 ◽  
Vol 19 (1) ◽  
pp. 221-228 ◽  
Author(s):  
A. J. Stam
Keyword(s):  
Normal Distribution ◽  
Uniform Distribution ◽  
Total Variation ◽  
Joint Distribution ◽  
Limit Theorems ◽  
Geometric Probability ◽  
High Dimensional ◽  
Standard Normal Distribution ◽  
Uniform Distributions ◽  
Standard Normal

If X = (X1, · ··, Xn) has uniform distribution on the sphere or ball in ℝ with radius a, then the joint distribution of , ···, k, converges in total variation to the standard normal distribution on ℝ. Similar results hold for the inner products of independent n-vectors. Applications to geometric probability are given.

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