The problem of estimating the parameter ?, when it is restricted to an interval of the form , in a class of discrete distributions, including Binomial Negative Binomial discrete Weibull and etc., is considered. We give necessary and sufficient conditions for which the Bayes estimator of with respect to a two points boundary supported prior is minimax under squared log error loss function....

 Minimax estimation problems with restricted parameter space reached increasing interest within the last two decades Some authors derived minimax and admissible estimators of bounded parameters under squared error loss and scale invariant squared error loss In some truncated estimation problems the most natural estimator to be considered is the truncated version of a classic...

Consider the problem of classification. Modern-day solutions have looked toward problem formulations where the search space is convex. Such formulations guarantee that a minimization of the objective function is found. But, in order to achieve that guarantee, such formulations treat outliers somewhat overzealously. Many classification objectives can be viewed as minimizing a loss funciton. For ...

We investigate robustness properties for a broad class of support vector machines with non-smooth loss functions. These kernel methods are inspired by convex risk minimization in infinite dimensional Hilbert spaces. Leading examples are the support vector machine based on the ε-insensitive loss function, and kernel based quantile regression based on the pinball loss function. Firstly, we propos...

This paper presents a new formulation of the regularized image up-sampling problem that incorporates models of the image acquisition and display processes. This approach leads to a new data fidelity term that has been coupled with a bounded-total-variation regularizer to yield our objective function. This objective function is minimized using the level-set method with two types of motion that i...

In robust parameter design, the quadratic loss function is commonly used. However, this loss function is not always realistic and the expected loss may not exist in some cases. This paper proposes the use of a general class of bounded loss functions that are cumulative distribution functions and probability density functions. New loss functions are investigated and the loss functions are shown ...

In the present paper, among other results, a decomposition formula is given for the w-bounded continuous negative definite functions of a topological *-semigroup S with a weight function w into a proper H*-algebra A in terms of w-bounded continuous positive definite A-valued functions on S. A generalization of a well-known result of K. Harzallah is obtained. An earlier conjecture of the author ...

In this lecture we will consider a general loss function and a general regression model where Y is not necessarily a binary variable. For the binary classification problem, we then used the followings: • Hoeffding’s inequality: it requires boundedness of the loss functions. • Bounded difference inequality: again it requires boundedness of the loss functions. • VC theory: it requires binary natu...