Donald G. Watts

Why is Introductory Statistics Difficult to Learn? And What Can We Do to Make it Easier?

and notes of interest to teachers of the first mathematical statistics course intended specifically for the section, should be useful to a substantial and of applied statistics courses. The department includes the Accent on number of teachers of the indicated types of courses or should have the Teaching Materials section; suitable contents for the section are described potential for fundamentally affecting the way in which a course is taught.

A Quadratic Design Criterion for Precise Estimation in Nonlinear Regression Models

D-optimal experimental designs for precise estimation in nonlinear regression models are obtained by minimizing the determinant of the approximate variance–covariance matrix of the parameter estimates. This determinant may not give a true indication of the volume of a joint inference region for the parameters, however, because of intrinsic and parameter-effects nonlinearity. In this article, we investigate experimental designs that minimize a second-order volume approximation. Unlike D-optimal designs, these designs depend on the noise and confidence levels, and on the parameterization used, and when used sequentially, quadratic designs depend on the residuals from previous experiments and on the type of inference. Quadratic designs appear to be less sensitive to variations in initial parameter values used for design.

A Relative Off set Orthogonality Convergence Criterion for Nonlinear least Squares

An orthogonality convergence criterion using relative offset is proposed. This criterion is compared to currently used criteria and its advantages are discussed.

Multiresponse Estimation With Special Application to Linear Systems of Differential Equations

We present a multiresponse estimation procedure for parameters of systems described by ⋅ = As. The procedure features a generalized Gauss–Newton algorithm for optimizing the determinant criterion, efficient evaluation of the expectation function and its derivatives directly from the reaction network or compartment diagram, automatic determination of starting values, and eficient computational procedures for handling linear constraints on the responses.

Comparing graphical and statistical methods for analysing dielectric dispersions of polymers represented in the complex plane

Abstract The expression proposed by Havriliak and Negami to represent the dielectric relaxation data of polymers is combined with multi-response statistical methods to provide objective parameter estimates and measures of precision. The graphical and multi-response methods are compared using the data for twelve polymers. The temperature dependence of the relaxation parameters for poly(vinyl acetate) is also treated with the multi-response techniques and compared with those previously reported. The statistical techniques lead to a much quicker, objective estimation of parameters, and permit sensitive analysis of residuals to reveal important sources of discrepancy.

Meaningful Multicollinearity Measures

Problems of multicollinearity in regression analysis are considered and numerical measures established to assess the extent of multicollinearity in a set of regression data with respect to parameter confidence regions and tests of hypotheses, the effective sample size, and predictability.

Using An Hyperbola as a Transition Model to Fit Two-Regime Straight-Line Data

In a recent paper [1] a general form of transition model was suggested to describe data which appear to follow two different straight line relationships on opposite sides of an undetermined join point. An alternative model is now considered, the familiar hyperbola, parameterized in a geometrically meaningful form. The two models are fitted to two sets of experimental data for purposes of comparison. In one of the examples account is taken of autocorrelated errors using a procedure suggested by Sredni [13].

A generalized Guass-Newton procedure for multi-response parameter estimation

A method is presented for calculating the gradient and an approximate Hessian of the Box-Draper multi-response parameter estimation criterion using only the first-order derivatives of the model functions. This is an analogue of the Gauss-Newton iterative procedure for nonlinear least squares. We also describe an implementation based on a

Model building in chemistry using profile t and trace plots

QR

Randomized trial of prostacyclin infusion in acute myocardial infarction

decomposition of the residual matrix which allows incorporation of a regularization procedure similar to the Levenburg-Marquardt method in nonlinear least squares.The method incorporates a convergence criterion based on a comparison of the increment size to the statistical variability of the estimates.