Many nonparametric regression techniques (such as kernels, nearest neighbors, and smoothing splines) estimate the conditional mean of Y given X = z by a weighted sum of observed Y values, where observations with X values near z tend to have larger weights. In this report the weights are taken to represent a finite signed measure on the space of Y values. This measure is studied as an estimate o...

Let X be a Markov process characterized as the solution of a martingale problem with generator A, and let Y be a related observation process. The conditional distribution πt of X(t) given observations of Y up to time t satisfies certain martingale properties, and it is shown that any probability-measure-valued process with the appropriate martingale properties can be interpreted as the conditio...

Department of Mathematical Statistics and Actuarial Science University of Bern, Sidlerstrasse 5 CH-3012 Bern, Switzerland October 8, 2008 Abstract: Let (S1, S2) = (R cos(Θ), R sin(Θ)) be a bivariate random vector with associated random radius R which has distribution function F being further independent of the random angle Θ. In this paper we investigate the asymptotic behaviour of the conditio...

Default loss distribution of corporate portfolios plays a crucial role in CDO tranche pricing, tracking error calculation and profit/loss assessment of corporation systems. This work gives an efficient algorithm to calculate the default loss distribution based on Hull-White probability bucketing approach and importance sampling method. The Gaussian copula model is assumed to calculate the condi...

A Bayesian network (from now on BN) of a set of variables X = {X1, . . . , Xn} represents a joint probability distribution over those variables. It consists of a network structure that encodes assertions of conditional independence in the distribution and a set of conditional probability distributions corresponding to that structure. It is graphically represented by directed acyclic graphs, who...

The uniformly minimum variance unbiased (UMVU), maximum likelihood, percentile (PC), least squares (LS) and weighted least squares (WLS) estimators of the probability density function (pdf) and cumulative distribution function are derived for the generalized Rayleigh distribution. This model can be used quite effectively in modelling strength data and also modeling general lifetime data. It has...