9 papers
The joint density of top k sample eigenvectors and principal subspace inference
Koki Shimizu, Haoming Wang
In this paper, the exact joint density of the top sample eigenvectors is derived for any population covariance matrix , sample size , and $1 \l…
Real gamma distribution on analytic bundles of flag varieties
Haoming Wang
This paper introduces four matrix normal distributions on analytic bundles of flag varieties, extending the separable covariance with potentially variable…
Martingale Problem and Quadratic Family
Haoming Wang
Assuming uniqueness of the martingale problem for Markov processes of generators in a quadratic family like \[q_t(i,j) = a_t(i) q_0(i,j)^2 + b_t(i) q_0(i,j) - \frac{a_t(i)}{N…
On incomplete Gamma and Beta integrals
Haoming Wang
This paper discusses the incomplete Gamma and Beta integrals involving the generalised hypergeometric function. The distribution of the largest and the smallest roots of a ratio ar…
Glivenko-Cantelli for -divergence
Haoming Wang, Lek-Heng Lim
We extend the celebrated Glivenko-Cantelli theorem, sometimes called the fundamental theorem of statistics, from its standard setting of total variation distance to all -diverge…
An explicit formula for zonal polynomials
Haoming Wang
The derivation of zonal polynomials involves evaluating the integral \[ \exp\left( - \frac{1}{2} \operatorname{tr} D_β Q D_{l} Q \right) \] with respect to orthogonal matrices \(Q\…
On non-central distribution of the matrix ratio
Haoming Wang
We derive the distribution of the ratio of a non-central mean matrix and a sample covariance matrix. This aligns with the confluent term in the non-central uni-variate St…
Factorization of a prime matrix in even blocks
Haoming Wang
In this paper, a matrix is said to be prime if the row and column of this matrix are both prime numbers. We establish various necessary and sufficient conditions for developing mat…
On minimal predictable intensity of point processes
Haoming Wang
An adapted, right-continuous, non-decreasing, integer-valued process with unit jumps and starting at zero has a minimal predictable intensity if and only if it is a standard Poisso…