Density Estimation: Deals with the problem of estimating probability density functions (PDFs) based on some data sampled from the PDF. May use assumed forms of the distribution, parameterized in some way (parametric statistics); or May avoid making assumptions about the form of the PDF (nonparametric statistics). We are concerned more here with the non-parametric case (see Roger Barlow’s lectur...

This paper presents an algorithm for solving Bi-criteria Minimum Cost Dynamic Flow (BiCMCDF) problem with continuous flow variables. The approach is to transform a bi-criteria problem into a parametric one by building a single parametric linear cost out of the two initial cost functions. The algorithm consecutively finds efficient extreme points in the decision space by solving a series of mini...

We characterize the boundary ∂Σ of the solution set Σ of a parametric linear system A(p)x = b(p) where the elements of the n×n matrix and the right-hand side vector depend on a number of parameters p varying within interval bounds. The characterization of ∂Σ is by means of pieces of parametric hypersurfaces, the latter represented by their coordinate functions depending on corresponding subsets...

Most existing works on specification testing assume that we have direct observations from the model of interest. We study specification testing for Markov models based on contaminated observations. The evolving model dynamics of the unobservable Markov chain is implicitly coded into the conditional distribution of the observed process. To test whether the underlying Markov chain follows a param...

— The paper uses the LU-parametric representation of fuzzy numbers and fuzzy-valued functions, to obtain valid approximations of fuzzy generalized derivative and to solve fuzzy differential equations. The main result is that a fuzzy differential initial-value problem can be translated into a system of in nitely many ordinary differential equations and, by the LU-parametric representation, the i...