Mathematische Statistik I

On the Optimization of Side-Channel Attacks by Advanced Stochastic Methods

“…It provides concrete formulae that characterize the optimal decision strategy. Although Theorem 1 can be deduced from more general theorems (e.g., Hilfssatz 2.137 and Satz 2.138(i) in [20] immediately imply assertion (i)) we give an elementary proof (cf. Theorem 2.48 in [20] for the special case t = 2) in order to illustrate the background.…”

“…Although Theorem 1 can be deduced from more general theorems (e.g., Hilfssatz 2.137 and Satz 2.138(i) in [20] immediately imply assertion (i)) we give an elementary proof (cf. Theorem 2.48 in [20] for the special case t = 2) in order to illustrate the background. We restricted our attention to the case |Θ| < ∞ and left out mathematical difficulties as the concept of σ-algebras and measurability.…”

“…Let κ: Ω × P(A) → [0, 1] denote any randomized decision strategy (cf. [20], for instance). Fubini's Theorem implies…”

“…minimax problems) it is reasonable to consider the more general class of r andomized decision strategies where the statistician decides randomly (quantified by a probability measure) between various alternatives when observing a particular ω ( [20]). In our context we may restrict our attention to the deterministic decision strategies (cf.…”

Bowker's test for symmetry and modifications within the algebraic framework

“…It can be shown that Witting (1985), Korollar 3.20). We will be interested in the set of all data sets with the same value of the sufficient statistic t =…”