Christos P. Kitsos

Recent Advances in Nonlinear Experimental Design

A microwave hybrid made up of a section of trough waveguide, rectangular waveguide and coaxial transmission lines is provided. The rectangular waveguide and the trough waveguide are joined end to end. The side walls of the trough waveguide form a continuous structure with the broad walls of the rectangular waveguide. The bottom wall of the trough waveguide forms a continuous structure with a narrow wall of the rectangular waveguide. Near the junction region of the trough waveguide and the rectangular section are coupled a pair of coaxial transmission lines with the inner conductor of one of the coaxial transmission lines extending through a first of the side walls of the trough waveguide and the inner conductor of the other coaxial transmission line extending through the second opposite side wall of the trough waveguide.

An optimal design problem in rhythmometry.

A trigonometric regression model is assumed for a problem involving circadian rhythm exhibited by peak expiratory flow. Experimental designs are sought with a view to estimating a particular nonlinear function of the parameters. Both optimal and nonoptimal, but more practicable, designs are derived and their relative efficiencies are established.

Logarithmic Sobolev Inequalities for Information Measures

For <i>alpha</i> <i>ges</i> <i>1</i>, the new Vajda-type information measure <i>J</i> _alpha <i>(X</i>) is a quantity generalizing Fishers information (FI), to which it is reduced for <i>alpha</i> <i>=</i> <i>2</i> . In this paper, a corresponding generalized entropy power <i>N</i> _alpha <i>(X</i>) is introduced, and the inequality <i>N</i> _alpha <i>(X</i>) <b>J</b> _alpha(<i>X</i>) ges <i>n</i> is proved, which is reduced to the well-known inequality of Stam for <i>alpha</i> <i>=</i> <i>2</i>. The cases of equality are also determined. Furthermore, the Blachman-Stam inequality for the FI of convolutions is generalized for the Vajda information <i>J</i> _alpha <i>(X</i>) and both families of results in the context of measure of information are discussed. That is, logarithmic Sobolev inequalities (LSIs) are written in terms of new more general entropy-type information measure, and therefore, new information inequalities are arisen. This generalization for special cases yields to the well known information measures and relative bounds.

Fully sequential procedures in nonlinear design problems

Abstract In nonlinear design problems the major difficulty to overcome is the dependence of the optimal design points on the true vector θ of the parameters. Batch-sequential designs take advantage of the inflow of new information about θ. In this paper fully sequential procedures are discussed for any optimality criterion φ, say. Simulation studies encourange the use of a fully-sequential procedure instead of one-stage method which produce locally optimal designs.

Robust Linear Calibration

We regard the simple linear calibration problem where only the response y of the regression line y = β0 + β1 t is observed with errors. The experimental conditions t are observed without error. For the errors of the observations y we assume that there may be some gross errors providing outlying observations. This situation can be modeled by a conditionally contaminated regression model. In this model the classical calibration estimator based on the least squares estimator has an unbounded asymptotic bias. Therefore we introduce calibration estimators based on robust one-step-M-estimators which have a bounded asymptotic bias. For this class of estimators we discuss two problems: The optimal estimators and their corresponding optimal designs. We derive the locally optimal solutions and show that the maximin efficient designs for non-robust estimation and robust estimation coincide.

New Information Measures for the Generalized Normal Distribution

We introduce a three-parameter generalized normal distribution, which belongs to the Kotz type distribution family, to study the generalized entropy type measures of information. For this generalized normal, the Kullback-Leibler information is evaluated, which extends the well known result for the normal distribution, and plays an important role for the introduced generalized information measure. These generalized entropy type measures of information are also evaluated and presented.

Quasi-Sequential Procedures for the Calibration Problem

The calibration problem has been discussed widely, by many authors adopting different lines of thought: Classical, Bayesian, Structural. We face the problem of a monlinear experimental design problem and we introduce a quasi-sequential procedure to overcome the poor initial knowledge about the parameters we want to estimate. A simulation study provides empirical evidence that significant improvements can be achieved.

New entropy type information measures

The target of his paper is to introduce new entropy type measures of information. The defined measure yields to an extension of the multivariate normal, the hyper multivariate normal distribution

A COMPILATION OF THE D-OPTIMAL DESIGNS IN CHEMICAL KINETICS

This paper links the chemical kinetic models that obey the framework of nonlinear statistical models with optimal design theory. We provide the appropriate optimal designs for them, so that the involved parameters can be estimated as well as possible. Therefore, the D-optimality criterion is adopted, under the optimal design approach, for a number of models used in chemical kinetic applications. In the tables, the collected results are presented for 15 models.

Optimal Designs for Estimating the Percentiles of the Risk in Multistage Models of Carcinogenesis

The multistage carcinogenesis models describe a process by which a normal cell becomes malignant and gives rise to a tumor. This paper aims at evaluating the percentiles of the risk function derived as dose-response relationship in a multi-stage model. These percentiles have been known as virtual safe dose levels or risk specific dose levels. The optimal design theory is applied to estimate the appropriate percentile and the sequential approach of design is adopted through a stochastic approximation scheme. If the initial design is D-optimal the limit design is D-optimal as well and it is the one with the minimum entropy.