Robert G. Staudte

A Robust Version of Mallows's C P

Abstract We present a robust version of Mallowss C P for regression models. It is defined by RC P = W Pσ2 - (U P - V P), where W P = ω i ω2 i r 2 i is a weighted residual sum of squares computed from a robust fit of model P, σ2 is a robust and consistent estimator of σ2 in the full model, and U P and V P are constants depending on the weight function and the number of parameters in model P. Good subset models are those with RC P close to V P or smaller than V P. When the weights are identically 1, W P becomes the residual sum of squares of a least squares fit, and RC P reduces to Mallowss C P. The robust model selection procedure based on RC P allows us to choose the models that fit the majority of the data by taking into account the presence of outliers and possible departures from the normality assumption on the error distribution. Together with the classical C P, the robust version suggests several models from which we can choose.

Water-soluble (1→3), (1→4)-β-d-glucans from barley (Hordeum vulgare) endosperm. III. Distribution of cellotriosyl and cellotetraosyl residues

Abstract Cellotriosyl and cellotetraosyl residues, linked by single (1→3)-β-linkages, account for more than 90% of the 40°C water-soluble (1→3), (1→4)-β- d -glucan from barley flour. We have analysed their sequence dependence by treating the polymer as a two-state Markov chain with stationary distribution. Quantitation of the penultimate oligosaccharides released during hydrolysis of the (1→3), (1→4)-β- d -glucan with (1→3), (1→4)-β- d -glucan 4-glucanohydrolase (EC 3.2.1.73) by analytical gel filtration chromatography enabled the relative abundance of two adjacent cellotriosyl, two adjacent cellotetraosyl and adjacent cellotetraosyl/cellotriosyl residues to be estimated and the sequence dependence to be evaluated. Within the theoretical and practical constraints of the method it is concluded that the cellotriosyl and cellotetraosyl residues are arranged in an essentially independent (random) fashion. Thus, any mechanism proposed for the biosynthesis of the molecule should explain this apparently random distribution of cellotriosyl and cellotetraosyl residues as well as the presence, in relatively low frequency, of blocks of up to 10 or more adjacent (1→4)-linkages.

The bifurcating autoregression model in cell lineage studies.

A model for cell lineage data is presented and analysed. The model is an extension of the classical first-order autoregression, used in time-series studies, to bifurcating data trees of general size and shape. Maximum likelihood theory is developed and compared with an extensive simulation study. Some properties of moment estimators are also presented.

Variance components models for dependent cell populations

Cells grown in culture can be tracked for several generations and measurements taken on size or age at division and other cell characteristics. The observations for the offspring of each cell form a family tree of dependent data. Such cell lineage data are here modeled as repeated measurements on different family trees arising from individual ancestor cells selected at random from a population of cultured cells. The bifurcating autoregression model is embedded in a process that allows for measurement error and variation from tree to tree. Robust methods are presented that accommodate outliers in this time-dependent and branching environment while allowing the statistician to interactively build a variance components model for the process. The methodology is illustrated on a substantial data set of 41 trees of EMT6 cells, with the surprising conclusion that after removing measurement error, sister-cell lifetimes are nearly identical.

Influence Functions of Iteratively Reweighted Least Squares Estimators

Abstract The iteratively reweighted least squares algorithm is routinely employed to evaluate robust regression estimates. The importance of beginning the algorithm with a robust estimator of the unknown parameters is often stressed. The precise influence of the initial estimator on subsequent iterates or the limit of such estimators, however, does not seem to have been calculated previously. Because robust regression involves the downweighting of specific points having large rescaled residuals and/or large leverages in the design space, it is natural to think in terms of the weights themselves, rather than some less intuitive function such as the η function of generalized M estimators. Therefore, we consider multiple linear regression by the method of weighted least squares, where the weights are estimated quantities depending on both position in the design space and the residual relative to an initial regression estimator. The influence function of the weighted least squares estimator is shown to depend...

Additive models for dependent cell populations

We propose an additive model for cell population growth which allows for positive correlation between sister cell lifetimes but arbitrary correlations between mother and daughter cell lifetimes. In the model each cell lifetime is the sum of two independent components, one of which is shared with its sister cell and which is also a function of the components of the lifetime of their mother. Assuming that the components follow a gamma distribution, the model is fitted to cell lifetime data of EMT6 cells obtained by the method of time-lapse cinematography.

Power Approximations in Testing for Unequal Means in a One-Way ANOVA Weighted for Unequal Variances

Abstract The classical F-test for unequal means in a one-way ANOVA is known to be misleading when the populations have different variances. To overcome this (James, G. S. (1951). The comparison of several groups of observations when the ratios of the population variances are unknown. Biometrika 38:324–329 and Welch, B. L. (1951). On the comparison of several mean values: an alternative approach. Biometrika 38:330–336.) weighted the terms in the numerator sum of squares by the respective inverses of the sample mean variances, and they proposed equivalent tests based on F or χ 2 approximations to the null distribution of the weighted sum of squares for moderate sample sizes. We provide approximations for the nonnull distributions of their weighted statistics which are found to be useful in obtaining approximations to the power of the Welch F-test.

Cell lineage analysis: Variance Components Models for Dependent Cell Populations

Abstract Cells grown in culture can be tracked for several generations and measurements taken on size or age at division and other cell characteristics. The observations for the offspring of each cell form a family tree of dependent data. Such cell lineage data are here modeled as repeated measurements on different family trees arising from individual ancestor cells selected at random from a population of cultured cells. The bifurcating autoregression model is embedded in a process that allows for measurement error and variation from tree to tree. Robust methods are presented that accommodate outliers in this time-dependent and branching environment while allowing the statistician to interactively build a variance components model for the process. The methodology is illustrated on a substantial data set of 41 trees of EMT6 cells, with the surprising conclusion that after removing measurement error, sister-cell lifetimes are nearly identical.

Variance Stabilizing the Difference of Two Binomial Proportions

The article studies estimation of Δ = p1 − p2, the difference of two proportions p1 and p2, based on two independent Binomial experiments of size n1 and n2. The usual estimator, the difference between the two sample proportions, is variance stabilized conditionally on a weighted average of p1 and p2. When using this variance stabilized statistic as a test, a new family of confidence intervals for Δ is found. We show with a simulation study that these confidence intervals compare favorably in coverage accuracy and width to two other popular intervals proposed by Newcombe and Agresti and Caffo. Because no additional study weights need estimating, the variance stabilized statistic is also well-suited for combining results from independent studies. This meta analysis is also explained in the article.

Interval estimates of weighted effect sizes in the one-way heteroscedastic ANOVA

A framework for comparing normal population means in the presence of heteroscedasticity and outliers is provided. A single number called the weighted effect size summarizes the differences in population means after weighting each according to the difficulty of estimating their respective means, whether the difficulty is due to unknown population variances, unequal sample sizes or the presence of outliers. For an ANOVA weighted for unequal variances, we find interval estimates for the weighted effect size. In addition, the weighted effect size is shown to be a monotone function of a suitably defined weighted coefficient of determination, which means that interval estimates of the former are readily transformed into interval estimates of the latter. Extensive simulations demonstrate the accuracy of the nominal 95% coverage of these intervals for a wide range of parameters.