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The Laplace transform of the first exit time from a finite interval by a regular spectrally negative α-stable Ornstein-Uhlenbeck process is provided in terms of the Wright's generalized hypergeometric...
The Laplace transform of the first exit time from a finite interval by a regular spectrally negative α-stable Ornstein-Uhlenbeck process is provided in terms of the Wright's generalized hypergeometric...
Metric entropy of the class of probability distribution functions on [0,1] with a k-monotone density is studied through its connection with the small ball probability of k-times integrated Brownian mo...
From the decision-theoretic viewpoint, using a weighted loss we compare the risks of testing procedures in the location and scale parameter cases. We also get numerically the minimax solution of Bayes...
Shape estimation and object reconstruction are common problems in image analysis. Mathematically,viewing objects in the image plane as random sets reduces the problem of shape estimation to inference ...
The problem of estimating linear functions of ordered scale parameters of two Gamma distributions is considered under entropy loss. A necessary and sufficient condition for the maximum likelihood esti...
We consider in the following the problem of robust spectral density estimation.Unfortunately, conventional spectral density estimators are not robust in the presence of additive outliers (cf. [18]). I...
The choice and design of loss functions is discussed. Particularly when computational methods like cross-validation are applied, there is no need to stick to “standard” loss functions such as the L2...
Aggregation functions are generally defined and used to combine several numerical values into a single one, so that the final result of the aggregation takes into account all the individual values i...
We define zonal polynomials of quaternion matrix argument and deduce some important formulae of zonal polynomials and hypergeometric functions of quaternion matrix argument. As an application, we gi...
A function  : [0,∞)→(0, 1] is a completely monotonic function if and only if (kxk2) is positive definite on Rd for all d and thus it represents the correlation function of a weakly stationary and is...
The joint cumulative distribution function for order statistics arising from several different populations is given in terms of the distribution function of the populations. The computational cost o...
Suppose that a target function f0 : Rd → R is monotonic, namely, weakly increasing, and an original estimate ˆ f of the target function is available, which is not weakly increasing. Many common...
In this paper we discuss a closed-form approximation of the likelihood functions of an arbitrary diffusion process. The approximation is based on an exponential ansatz of the transition probability ...

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