Last corrections 24 April 2000.

Titles

• Profile Methods (1996); (version presented at Compstat96)
• Semiparametric Testing of the Link Function in Models For Binary Outcomes (1994)
• Modeling Mortality and Morbidity of Newborns (1994) --- Journal Version
• Exploratory Analysis of Mortality and Morbidity of Newborns (1995) --- Discussion Paper Version (extended)
• Pitfalls of Normal-Gamma Stochastic Frontier Models (1994)
• Another Look at the American Electrical Utility Data (1994)
• Profile Methods (1993) ; (old version)
• Statistical Analysis of ESCA Spectra (1993)
• Modern Inference for Nonlinear Models (1992)
• A Comparison of Approaches to Inference for Nonlinear Models (1991)

Titles, Coauthors and Abstracts

• Profile Methods (1996)

Compstat96, Barcelona.

Abstract:

In this paper, we describe uses of profile methods in statistics. Our goal is to identify {\em profiling} as a useful task common to many statistical analyses going beyond simple normal approximations and to encourage its inclusion in standard statistical software. Therefore, our approach is broader than deep and, although we touch on a wide variety of areas of interest, we do not present fundamental research in any of them and we do not claim our use of profiles is optimal. Our contribution lies in the realization that profiling is a general task and that it can be automated to a large extent.

• Semiparametric Testing of the Link Function in Models For Binary Outcomes (1994)

Discussion Paper 9415 by I. Proenca and C. Ritter .

Abstract: This work stands in the larger context of tests of parametric models against semiparametric alternatives. A semiparametric statistic proposed by Horowitz and Haerdle, which we call the H-H statistic, can be used to construct a test for unknown deviations from a hypothesized link function in a parametric single index model which rejects for large values of the statistic. Here we study empirically the finite sample performance of this statistic for the important special case of logistic regression for binary data. We show that its asymptotic distribution is not a good approximation for the finite sample distribution up to sample sizes of several thousand observations. For the chosen examples the value of the test statistic for finite sample sizes tends to be smaller than what would be expected under the asymptotic approximation, thus reducing the power of the test based on asymptotic critical values. Moreover, the finite sample variance of the statistic depends on the bandwidth, which also render asymptotic critical values unsuitable. We propose a modified statistic that reduces considerably both the bias and bandwidth dependency.

• Modeling Mortality and Morbidity of Newborns (1994)

Statistics in Medicine (in press) by C. Ritter, A. Bouckaert, M. Van Lierde, and I. Theunissen.

Abstract:

Data of 11053 births collected over a ten year period at a single hospital are analyzed and models linking birthweight and gestational age with mortality and morbidity defined by low Apgar scores are constructed and compared for singleton births. Based on these models, charts of mortality and morbidity are drawn and compared with common charts of birthweight centiles. Classification rules for newborns at risk are defined by iso-mortality contours, marginal birthweight centiles, and birthweight centiles adjusted by gestational age respectively, and compared using receiver operating characteristic (ROC) curves. The results suggest that, as far as neonatal mortality is concerned, classification rules based on simple marginal birthweight centiles perform almost as well as iso-mortality contours and considerably better than birthweight centiles adjusted for gestational age.

• Exploratory Analysis of Mortality and Morbidity of Newborns (1995) --- Discussion Paper Version (extended)

Discussion paper 95?? C. Ritter, A. Bouckaert, M. Van Lierde, and I. Theunissen.

Abstract: same as above.

• Pitfalls of Normal-Gamma Stochastic Frontier Models (1994)

Discussion paper 9417 by C. Ritter and L. Simar.

Abstract:

Although conceptually pleasing, normal-gamma frontier models lead to difficult estimation problems. It is shown here that unless the sample size reaches several thousands of observations the shape parameter of the gamma density is hard to estimate, and that this carries over to estimates of the stochastic frontier, the individual inefficiencies, and the allocation of the overall variance to the stochastic frontier and to the inefficiencies.%

Keywords: Identifiability, least squares, likelihood, profile, simulation.

• Another Look at the American Electrical Utility Data (1994)

Discussion paper 9401 by C. Ritter and L. Simar.

Abstract:

The American electric utility data, which are frequently analyzed in the context of frontier models, can be explained by a linear model without inefficiencies. The observed maximum likelihood for this linear model is very mildly smaller than the maximum likelihood for more flexible stochastic frontier models and the the log-likelihood-ratio statistic for an approximate chi-square test of the simple least squares model against normal-exponential and normal-gamma stochastic frontier models is far from significant.

• Profile Methods (1993) (old version with a few mistakes in it)

Discussion paper 9323 by C. Ritter and D.M. Bates.

Abstract:

We begin by describing profile methods, such as profile values, profile traces, profile transformations, and profile diagnostic plots, in a general setting and point out an interesting feature of profile transforms, the boxing property. We then discuss profile methods in the specific contexts of likelihood and Bayesian inference and make links with approximate Bayesian marginalization, with Jeffrey's prior, and with importance sampling. We conclude by investigating profile transforms for posterior distributions and point out some peculiarities.

• Statistical Analysis of ESCA Spectra (1993)

Discussion paper 9324 by C. Ritter .

Abstract:

ESCA (Electron Spectroscopy for Chemical Analysis) is a key technique in the study of modified material surfaces. Analysis of the resulting spectra consists in decomposing multiple peaks into sub-peaks, whose functional form is known up to a few parameters. Statistical inference consists in estimation of these parameters and of derived quantities, such as peak-area ratios, and in assessing the accuracies of these estimates. Purely likelihood based peak decomposition is notorious for identifiability problems. In practice, however, additional knowledge exists about some of the parameters and can, when incorporated in the model as an informative prior, produce unique decompositions. Modern tools for Bayesian statistics, such as profile diagnostics, Laplacian approximations of marginals, and Markov chain algorithms for sampling from the posterior, can then be employed to obtain inference reaching beyond point estimates and approximate standard errors.

• Modern Inference for Nonlinear Models (1992)

Ph.D. Thesis. (University of Wisconsin)

Abstract:

The potential of several modern statistical methods, including profiling, approximate marginalization, importance sampling, and Markov chain simulation, for nonlinear least squares regression is studied. These methods can all be adapted to nonlinear regression and employed to enhance inference, but the most significant benefit is achieved by combining them. The combined power of the new methods is demonstrated on two case studies, the analysis of pharmacokinetic data with a multiexponential model and the decomposition of ESCA spectra.

• A Comparison of Approaches to Inference for Nonlinear Models (1991)

Invited paper to the Interface-91 conference by C. Ritter , S. Bisgaard, and D.M. Bates.

Abstract:

As greater computing power becomes routinely available to researchers, analyses based on Bayesian or likelihood methods become easier to perform, especially since the increase in computing power has been accompanied by development of inventive statistical algorithms for inference. We consider here the nonlinear regression model but these approaches to inference are applicable in more general circumstances and we feel the comparisons will remain useful. Several methods can be used for inference in nonlinear regression: propagation of errors, likelihood profiles, approximate marginal likelihoods and posteriors, and Monte Carlo methods such as importance sampling and the Gibbs sampler. These methods vary in computing intensity and in their ability to handle poorly conditioned situations. Furthermore, since some of these methods have only been recently developed, it is not easy for the practitioner to compare them and choose between them because they are not widely implemented. We demonstrate the respective merits of these methods in a small but instructive example.