Theory of Statistical Estimation

Some statistical estimation problems in ruin theory

Much research in ruin theory in insurance mathematics focuses on the behaviour of various quantities of interest, such as the probability of ruin or the ruin-time moments, for a particular risk model in insurance. In practice, precise knowledge of the risk model is available only via observed data. In this presentation, the problem of statistical estimation of the quantities of interest, given ...

Asymptotic Theory of Statistical Estimation 1 Jiantao Jiao

Estimation of non-statistical uncertainty using fuzzy-set theory

A novel method using a fuzzy practicable interval to characterize non-statistical uncertainty in dynamic measurement is proposed. The method permits the uncertainty being estimated under the conditions that the number of measurements is very small and the probability distribution unknown. The feasibility of the method is validated by computer-simulation experiments.

Quantal Response Statistical Equilibrium in Economic Interactions: Theory and Estimation

Social science addresses systems in which the individual actions of participants interacting in complex, non-additive ways through institutional structures determine social outcomes. In many cases, the institutions incorporate enough negative feedback to stabilize the resulting outcome as an equilibrium. We study a particular type of such equilibria, quantal response statistical equilibrium (QR...

Linking Approximation Theory and Statistical Estimation in Wavelet Image Processing

Decomposition in a basis: (b j) j∈J basis of L 2 ([0, 1]). ∀f ∈ L 2 ([0, 1], f = j∈J f, b j b j with f, b j = 1 0 f (t)b j (t)dt. The Parseval-Bessel norm energy conservation equality yields f 2 = j∈J |f, b j | 2 1.2 Linear and non linear approximation For any I ∈ P(J), one defines f |I by f |I = j∈I f, b j b j. The question is now how to select " a good subset " of a given size M. A first poss...