We investigate barycenters of probability measures on proper Alexandrov spaces of curvature bounded below, and show that they enjoy several properties relevant to or different from those in metric spaces of curvature bounded above. We prove the reverse variance inequality, and show that the push forward of a measure to the tangent cone at its barycenter has the flat support.

We show that that the jackknife variance estimator vjack and the the infinitesimal jackknife variance estimator are asymptotically equivalent if the functional of interest is a smooth function of the mean or a smooth trimmed L-statistic. We calculate the asymptotic variance of vjack for these functionals.

Since the ideas of arbitrage free pricing were born, finance has changed radically both in theory and practice. Derivatives markets have evolved and options serve nowadays as underlyings and as hedging instruments. In this thesis, we consider some markets for equity derivatives. We start by statistical analysis of the markets for European options and variance swaps because these products are im...

Data on weight productivity of 1023 ewes of the D’Man breed calculated using an original file on growth performances of 2026 lambs of the same breed were used in this study. All the lambs were born and raised in Tunisia between 1994 and 1999 in the north of the country (Mateur, Kef) and in the south under an oasian environment (Gabès). The studied variables included weights of the litter at 10,...

We introduce covariance reducing models for studying the sample covariance matrices of a random vector observed in different populations. The models are based on reducing the sample covariance matrices to an informational core that is sufficient to characterize the variance heterogeneity among the populations. They possess useful equivariance properties and provide a clear alternative to spectr...

Temperature microstructure is mapped in two dimensions for a section 6.7 km long and 150 m deep in water which is 200 m deep. The section is located on the continental shelf southeast of Point Conception on the southern California coast. Regions of mixing activity are composed of numerous individual events, some of which are observed to collapse onto isopycnal surfaces when plotted in a distanc...

We analyse the covariance of the one-dimensional mass power spectrum along lines of sight. The covariance reveals the correlation between different modes of fluctuations in the cosmic density field and gives the sample variance error for measurements of the mass power spectrum. For Gaussian random fields, the covariance matrix is diagonal. As expected, the variance of the measured one-dimension...

We consider the Generalised Normal Variance-Mean (GNVM) model in which the mixing random variable is Gamma distributed for financial return data. This model generalises the popular Variance-Gamma (VG) distribution. This GNVM model can be interpreted as the addition of noise to a (skew) VG base. In this presentation, we will not only discuss the parameter estimation of the general model, but als...

It has been argued that the frequency domain accuracy of high model-order estimates obtained on the basis of closed loop data is largely invariant to whether direct or indirect approaches are used. The analysis underlying this conclusion has employed variance expressions that are asymptotic both in the data length and the model order, and hence are approximations when either of these are finite...

Consider the multicolored urn model where after every draw, balls of the different colors are added to the urn in proportion determined by a given stochastic replacement matrix. We consider some special replacement matrices which are not irreducible. For three and four color urns, we derive the asymptotic behavior of linear combinations of number of balls. In particular, we show that certain li...