In this paper, we use the bootstrap technique to obtain prediction errors for different claim reserving methods, namely methods based on the chain ladder technique and on generalised linear models. We discuss several forms of performing the bootstrap and illustrate the different solutions using the data set from Taylor and Ashe (1983) which has already been used by several authors.

Generalized Linear Models (GLZ) are an extension of the linear modeling process that allows models to be fit to data that follow probability distributions other than the Normal distribution, such as the Poisson, Binomial, Multinomial, and etc. Generalized Linear Models also relax the requirement of equality or constancy of variances that is required for hypothesis tests in traditional linear mo...

In this paper the data of a forest health inventory are analysed. Since 1983 the degree of defoliation (damage), together with various explanatory variables (covariates) concerning stand, site, soil and weather, are recorded by the second of the two authors, in the forest district Rothenbuch (Spessart, Bavaria). The focus is on the space and time dependencies of the data. The mutual relationshi...

B. Roynette, P. ValloisM. Yor (3) 26/05/2008 (1) Institut Elie Cartan, Université Henri Poincaré, B.P. 239, 54506 Vandoeuvre les Nancy Cedex (2) Laboratoire de Probabilités et Modèles Aléatoires, Université Paris VI et VII, 4 place Jussieu Case 188 F 75252 Paris Cedex 05 (3) Institut Universitaire de France Abstract This paper consists of three parts : in the first part, we describe a family of...

Let 2 be a finite thick dual polar space of rank 3. We say that a hyperplane H of 2 is locally singular (respectively, quadrangular or ovoidal) if H & Q is the perp of a point (resp. a subquadrangle or an ovoid) of Q for every quad Q of 2. If H is locally singular, quadrangular, or ovoidal, then we say that H is uniform. It is known that if H is locally singular, then either H is the set of poi...

Loss functions are central to machine learning because they are the means by which the quality of a prediction is evaluated. Any loss that is not proper, or can not be transformed to be proper via a link function is inadmissible. All admissible losses for n-class problems can be obtained in terms of a convex body in Rn. We show this explicitly and show how some existing results simplify when vi...

We study in this paper a generalized coupon collector problem, which consists in analyzing the time needed to collect a given number of distinct coupons that are drawn from a set of coupons with an arbitrary probability distribution. We suppose that a special coupon called the null coupon can be drawn but never belongs to any collection. In this context, we prove that the almost uniform distrib...

Let k be a field, L ⊂ Zn be a lattice such that L∩Nn = {0}, and IL ⊂ k[x1, . . . , xn] the corresponding lattice ideal. We present the generalized Scarf complex of IL and show that it is indispensable in the sense that it is contained in every minimal free resolution of R/IL.

Partial correlation is used in many epidemiological studies and clinical trials when a researcher investigates an association involving some potential confounding factors. Partial correlation is a method used to describe the relationship between two variables when controlling for effects of one or more variables in this relationship. In SAS, several procedures such as PROC CORR, PROC REG, and P...