Hans Nyquist

Optimal Designs of Discrete Response Experiments in Contingent Valuation Studies

Optimal designs for estimating model parameters and other characteristics such as mean and median willingness-to-pay are discussed.when a logistic or a probit regression model is used for analyzing a contingent valuation study with discrete questions. A numerical example, related to a study of the value of preserving some virgin forests in Sweden, illustrates the efficiencies of different designs and how a sequential procedure can be applied. Copyright 1992 by MIT Press.

Least orthogonal absolute deviations

Minimizing the sum of absolute values of orthogonal deviations from the regression line is introduced as an approach to the errors-in-variables problem. The absolute value of the estimate of the slope coefficient is shown to be bounded below and above by the absolute values of the estimates when the sum of absolute values of vertical deviations and horizontal deviations are minimized, respectively. Computational aspects are discussed, and a connection to the projection pursuit approach to estimation of multivariate dispersion is pointed out.

Effects on the eigenstructure of a data matrix when deleting an observation

Abstract The paper considers relationships between the eigenstructures of a complete data matrix and the data matrix after removal of a single observation. Eigenstructures are characterized in terms of eigenvalues, eigenvectors, and principal components. An approximation to the eigenvalues of the data matrix after removal of an observation is proposed and its use is illustrated in two numerical examples. Some results on the accuracy of the approximation are proved.

The Influence of Sex, Education and Age on Test Scores on the Swedish Scholastic Aptitude Test.

Abstract This study describes the effects of sex, education and age on the total test score on the Swedish Scholastic Aptitude Test (SweSA T), a test used in the selection process to colleges and universities in Sweden since 1977. Its use has so far been limited to one of four quota groups consisting of applicants 25 years or older and with more than four years of work experience. Statistical methods used in this study are regression models with dummy variables and estimated with a corner‐point parameterization. The results indicate rather genuine differences in every variable studied. Test takers with a higher education obtain a higher mean score than those with a lower education and older test takers obtain a higher mean score on the subtests vocabulary (WORD) and general information (GI) than younger persons. The mean test score for men is higher than the corresponding score for women, even if differences in education and age are controlled for. Finally some statistical problems related to the analysis...

Frechet distance as a tool for diagnosing multivariate data

Abstract Outliers can have dramatic effects on results from statistical analyses and on conclusions based on statistical analyses. It is therefore important to detect outliers and influential points. Methods for detecting outliers in multivariate data may be based on assessments of changes in the estimate of the mean vector or changes in the estimate of the scatter matrix as data points are perturbed. Here we propose a method based on the Frechet distance between the observed empirical distributions of the unperturbed and perturbed data. As these distributions involve both the mean vector and the scatter matrix, the resulting diagnostics are functions of both mean and scatter. The proposed diagnostics are illustrated by two examples.

Applications of the jackknife procedure in ridge regression

Abstract Three aspects of the application of the jackknife technique to ridge regression are considered, viz. as a bias estimator, as a variance estimator, and as an indicator of observations influence on parameter estimates. The ridge parameter is considered non-stochastic. The jackknifed ridge estimator is found to be a ridge estimator with a smaller value on the ridge parameter. Hence it has a smaller bias but a larger variance than the ridge estimator. The variance estimator is expected to be robust against heteroscedastic error variance as well as against outliers. A measure of observations influence on the estimates of regression parameters is proposed.

Computation of Optimum in Average Designs for Experiments with Finite Design Space

Abstract For Generalized Linear Models (GLM) optimum designs generally depend on the true but unknown parameter values. If a prior distribution for the parameters is available, it is possible to use a design that is optimum in average. If, in particular, the prior is uniform, the corresponding optimum design is termed a Laplace design. The purpose of this article is to indicate a Newton-Raphson procedure for computation of optimum in average designs for inference about parameters in a GLM when the design space is finite and to study the efficiency properties of Laplace designs in comparison with designs that use a uniform allocation of observations. Three numerical examples are presented, viz. two control group experiments and a Latin square experiment. The efficiency comparisons in these examples indicate that the Laplace designs are likely to be more efficient, when the prior information about the parameters is correct.

On the conditioning problem in generalized linear models

When weights are assigned to a data matrix, as in the iterative least squares estimator of a generalized linear model, the condition of the data matrix is changed. In this paper a geometrical appro ...

Applications of robust estimation techniques in demand analysis

This paper addresses the problems associated with applying robust estimaion techniques to demand analysis. Three questions are considered: (1) How well do alternative robust techniques perform in comparison with traditional least-squares techniques? In nearly all cases these estimators outperform the least-squares estimator. (2) How fragile is the distributional assumption of normality in demand analysis? Our study presents evidence which indicates that a proper demand equation specification should in certain cases include both fat- and thin-tailed alternatives to the normal distribution. The degree of quantitative sensitivity in results is on an even keel with traditional movements caused by changes in functional form or explanatory variables. (3) What is the relationship between assumptions about the distribution of the error process and resultant elasticity measures? Elasticity estimates derived from our demand equations are found to change by orders of magnitude when distributional assumption in a nei...

Further theoretical results and a comparison between two methods for approximating eigenvalues of perturbed covariance matrices

Covariance matrices, or in general matrices of sums of squares and cross-products, are used as input in many multivariate analyses techniques. The eigenvalues of these matrices play an important role in the statistical analysis of data including estimation and hypotheses testing. It has been recognized that one or few observations can exert an undue influence on the eigenvalues of a covariance matrix. The relationship between the eigenvalues of the covariance matrix computed from all data and the eigenvalues of the perturbed covariance matrix (a covariance matrix computed after a small subset of the observations has been deleted) cannot in general be written in closed-form. Two methods for approximating the eigenvalues of a perturbed covariance matrix have been suggested by Hadi (1988) and Wang and Nyquist (1991) for the case of a perturbation by a single observation. In this paper we improve on these two methods and give some additional theoretical results that may give further insight into the problem. We also compare the two improved approximations in terms of their accuracies.