The Instrumental Weighted Variables. Part III. Asymptotic Representation

The robust version of the classical instrumental variables, called Instrumental Weighted Variables (IWV) and the conditions for its square root of n-consistency as given in the Part I and II of this paper are recalled. Of course, the reasons why the classical instrumental variables as well as IWV were introduced and the idea of implicit weighting the residuals (firstly employed by the Least Weighted Squares, see Víšek (2000)) are also very briefly recalled (details were discussed in Part I of this paper). Then asymptotic representation and normality of all solutions of the corresponding normal equations is proved.Robustness; instrumental variables; implicit weighting; square root of n-consistency of estimate by means of instrumental weighted variables; asymptotic representation of the estimate and its normality

The Instrumental Weighted Variables. Part II. Square root of n-consistency

The definition of Instrumental Weighted Variables (IWV) (which is a robust version of the classical Instrumental Variables) and conditions for the weak consistency as given in the Part I of this paper are recalled. The reasons why the classical Instrumental Variables were introduced as well as the idea of implicit weighting the residuals (firstly employed by the Least Weighted Squares, see Víšek (2000)) are also recalled. Then square root of n-consistency of all solutions of the corresponding normal equations is proved.Robustness; instrumental variables; implicit weighting; square root of n-consistency of estimate by means of instrumental weighted variables

BSA - exact algorithm computing LTS estimate

The main result of this paper is a new exact algorithm computing the estimate given by the Least Trimmed Squares (LTS). The algorithm works under very weak assumptions. To prove that, we study the respective objective function using basic techniques of analysis and linear algebra.Comment: 18 pages, 1 figur

The least trimmed squares. Part III: Asymptotic normality

summary:Asymptotic normality of the least trimmed squares estimator is proved under general conditions. At the end of paper a discussion of applicability of the estimator (including the discussion of algorithm for its evaluation) is offered

Simulation of Hyperthermic Treatment Using the Matrix of Stripline Applicators

This paper describes the design of a microwave stripline applicator for hyperthermic treatment, and the design of an anatomically based biological model, which is a necessary part of hyperthermia treatment planning for measuring the distribution of SAR. In this paper we compare the SAR distribution in a cylindrical homogeneous agar phantom (which has similar characteristics to biological tissue) and in an anatomically based biological model of the femur (which has been developed from a computer tomography scan) using a matrix of two applicators of the same type