Recursive estimation of the conditional geometric median in Hilbert spaces

Efficient and fast estimation of the geometric median in Hilbert spaces with an averaged stochastic gradient algorithm

With the progress of measurement apparatus and the development of automatic sensors it is not unusual anymore to get large samples of observations taking values in high dimension spaces such as functional spaces. In such large samples of high dimensional data, outlying curves may not be uncommon and even a few individuals may corrupt simple statistical indicators such as the mean trajectory. We...

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

The Geometric Tools of Hilbert Spaces

TR Multivariate Conditional Median Estimation

An affine equivariant version of the nonparametric spatial conditional median (SCM) is constructed, using an adaptive transformation-retransformation (TR) procedure. The relative performance of SCM estimates, computed with and without applying the TR—procedure, are compared through simulation. Also included is the vector of coordinate conditional, kernelbased, medians (VCCMs). The methodology i...

On the Decomposition of Hilbert Spaces

Basic relation between numerical range and Davis-Wielandt shell of an operator $A$ acting on a Hilbert space with orthonormal basis $xi={e_{i}|i in I}$ and its conjugate $bar{A}$ which is introduced in this paper are obtained. The results are used to study the relation between point spectrum, approximate spectrum and residual spectrum of $A$ and $bar{A}$. A necessary and sufficient condition fo...