Estimating Multivariate Variance and Covariance Components Using Quadratic and Bilinear Forms

Specialization of Quadratic and Symmetric Bilinear Forms

• Chapters III and IV are in preparation. Preface A Mathematician Said Who Can Quote Me a Theorem that's True? For the ones that I Know Are Simply not So, When the Characteristic is Two! This pretty limerick first came to my ears in May 1998 during a talk by T.Y. Lam on field invariants from the theory of quadratic forms. 1 It is – poetic exaggeration allowed – a suitable motto for this monogra...

Estimating quadratic variation using realised variance

This paper looks at some recent work on estimating quadratic variation using realised variance (RV) — that is sums of M squared returns. This econometrics has been motivated by the advent of the common availability of high frequency financial return data. When the underlying process is a semimartingale we recall the fundamental result that RV is a consistent (as M → ∞) estimator of quadratic va...

Association Schemes of Quadratic Forms and Symmetric Bilinear Forms

Let Xn and Yn be the sets of quadratic forms and symmetric bilinear forms on an n-dimensional vector space V over Fq , respectively. The orbits of GLn(Fq ) on Xn × Xn define an association scheme Qua(n, q). The orbits of GLn(Fq ) on Yn × Yn also define an association scheme Sym(n, q). Our main results are: Qua(n, q) and Sym(n, q) are formally dual. When q is odd, Qua(n, q) and Sym(n, q) are iso...

Multivariate Analysis of Variance Using Patterned Covariance Matrices

On Multivariate Hermitian Quadratic Forms

Quantifier elimination over real closed fields (real QE) is an important area of research for various fields of mathematics and computer science. Though the cylindrical algebraic decomposition (CAD) algorithm introduced by G. E. Collins [4] and improved by many successive works has been considered as the most efficient method for a general real QE problem up to the present date, we may have a m...