In mathematical statistics courses, students learn that the quadratic function is minimized when x mean of random variable X, and graphs this for any two distributions X are simply translates each other. We focus on problem minimizing defined by in context mixtures probability discrete, absolutely continuous, singular continuous types. This important, example, Bayesian statistics, one attempts ...

let x be a random variable from a normal distribution with unknown mean θ and known variance σ2. in many practical situations, θ is known in advance to lie in an interval, say [−m,m], for some m > 0. as the usual estimator of θ, i.e., x under the linex loss function is inadmissible, finding some competitors for x becomes worthwhile. the only study in the literature considered the problem of min...

‎consider an estimation problem in a one-parameter non-regular distribution when both endpoints of the support depend on a single parameter‎. ‎in this paper‎, ‎we give sufficient conditions for a generalized bayes estimator of a parametric function to be admissible‎. ‎some examples are given‎. ‎

The purpose of this note is to demonstrate that in the Fourier expansion of a quasistationary random continuous process with continuous covariance function, the amplitudes of the frequency components do not possess the desirable property of being mutually uncorrelated unless the process degenerates to a single random variable in its range of definition. Specifically we consider a real-valued co...

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...

The regret bound of an optimization algorithms is one of the basic criteria for evaluating the performance of the given algorithm. By inspecting the differences between the regret bounds of traditional algorithms and adaptive one, we provide a guide for choosing an optimizer with respect to the given data set and the loss function. For analysis, we assume that the loss function is convex and it...

General principles of supercritical fluid extraction technology to raise efficiency are summarized and concluded in this paper. It generalized the present domestic situation of relative research and developed proposals towards kind of charging and discharging continuous components by a new supercritical fluid extraction .It also introduced structures and working principles of device. Keywords— ...