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S Algebraically, principal components can be defined as the eigenvalues and eigenvectors of a covariance or correlation matrix, but they are statistically meaningful as successive projections of the multivariate data in the direction of maximal variability. An attractive alternative in robust principal component analysis is to replace the classical(More)
The study of precise large deviations for random sums is an important topic in insurance and finance. In this paper, we extend recent results of Tang (2006) and Liu (2009) to random sums in various situations. In particular, we establish a precise large deviation result for a nonstandard renewal risk model in which innovations, modelled as real-valued(More)
In this paper we consider the probabilities of …nite-and in…nite-time absolute ruin in the renewal risk model with constant premium rate and constant force of interest. In the particular case of compound Poisson model, explicit asymptotic expressions for the …nite-and in…nite-time absolute ruin probabilities are given. For the general renewal risk model, we(More)
By inverting the Bayes formula in a point-wise manner, we develop measures quantifying the information gained by the Bayesian process, in reference to the Fisher information. Simple examples are used for focused illustrations of the ideas. Numerical computation for the measures is discussed with formulae. By extending the information gain concept to the(More)
  • Kai Wang Ng
  • 2011
} be two distinct partitions of the sample space, or equivalently two sets of events satisfying three properties: (i) each event is non-void, (ii) events in the same set are mutually exclusive (i.e. P (H j ∪ H k) = P (H j) + P (H k) for j = k), and (iii) each set is collectively exhaustive, (i.e. P (∪ m i=1 H j) = 1). The Bayes formula in general form is,