In this paper, the estimation of a scale parameter t under a new and bounded loss function, based on a reflection of the gamma density function, is discussed. The best scale-invariant estimator of tis obtained and the admissibility of all linear functions of the sufficient statistic, for estimating t in the absence of a nuisance parameter, is investigated

The expected supremum of a Gaussian process indexed by the image of an index set under a function class is bounded in terms of separate properties of the index set and the function class. The bound is relevant to the estimation of nonlinear transformations or the analysis of learning algorithms whenever hypotheses are chosen from composite classes, as is the case for multi-layer models.

We study universal prediction w.r.t. an indexed class of sources (e.g., parametric families) and general loss functions. We explore the centrality of the self-information loss function (log-loss) in the theory of universal prediction by showing that under certain assumptions, the feasibility of universal prediction w.r.t. the log-loss function, over an indexed class of sources (that is, univers...

Let No be Conway’s class of surreal numbers. I will make explicit the notion of a function f on No recursively defined over some family of functions. Under some ‘tameness’ and uniformity conditions, f must satisfy some interesting properties; in particular, the supremum of the class ̆ x ∈ No : f (x) ≥ 0 ̄ is actually an element of No. As an application, I will prove that concatenation function x ...

In this talk, the class of multivariate extended skew normal distributions is introduced. The properties of this class of distributions, such as, the moment generating function, probability density function, conditional probability density functions and independence are discussed. The definition of extended noncentral skew chi-square distribution is given. The necessary and sufficient condition...

The stochastic properties of p-random sequences are studied in this paper. It is shown that the law of the iterated logarithm holds for p-random sequences. This law gives a quantitative characterization of the density of p-random sets. When combined with the invari-ance property of p-random sequences, this law is also useful in proving that some complexity classes have p-measure 0.