Some results on two-level factorial designs with dependent observations

There are many situations in which observations in factorial experiments may be dependent. When this is so, run orders are needed that result in efficient estimates of contrasts. The Cheng and Steinberg reverse foldover algorithm, which gives a maximal number of level changes, is known to produce very efficient main-effects two-level designs using the D-criterion, but less is known about other designs, models and criteria. We present some further theoretical results, and give another statistic of importance in predicting efficiency under strong dependence. The theory is illustrated using some 16-run designs.     

New results on the likelihood ratio and score tests for the von Mises distribution

In this paper, we derive Bartlett and Bartlett-type corrections [G.M. Cordeiro and S.L.P. Ferrari 1991, A modified score test statistic having chi-squared distribution to order n ^?1 , Biometrika 78 (1991), pp. 573–582] to improve the likelihood ratio and Rao's score statistics for testing the mean parameter and the concentration parameter in the von Mises distribution. Simple formulae are suggested for the corrections valid for small and large values of the concentration parameter that do not depend on the modified Bessel functions and can be useful in practical applications.     

Estimation of nonseparable models with censored dependent variables and endogenous regressors

In this article we develop a nonparametric estimator for the local average response of a censored dependent variable to endogenous regressors in a nonseparable model where the unobservable error term is not restricted to be scalar and where the nonseparable function need not be monotone in the unobservables. We formalize the identification argument put forward in Altonji, Ichimura, and Otsu (2012 Altonji, J. G., Ichimura, H., Otsu, T. (2012). Estimating derivatives in nonseparable models with limited dependent variables. Econometrica 80:1701–1719.[Crossref], [Web of Science ®] , [Google Scholar]), construct a nonparametric estimator, characterize its asymptotic property, and conduct a Monte Carlo investigation to study its small sample properties. Identification is constructive and is achieved through a control function approach. We show that the estimator is consistent and asymptotically normally distributed. The Monte Carlo results are encouraging.     

Some results on optimality in models with heteroscedastic errors from partial optimum designs

This paper studies optimum designs for linear models when the errors are heteroscedastic. Sufficient conditions are given in order to obtainD-, A- andE-optimum designs for a complete regression model from partial optimum designs for some sub-parameters. A result about optimality for a complete model from the optimality for the submodels is included. Supported by Junta de Andalucía, research group FQM244.     

Constructing optimal router bit life sequential experimental designs: New results with a case study

Consider the experiment to improve router bit life as reported in Phadke (1986 Phadke, M. S. 1986. Design optimization case studies. AT &; T Technical Journal 65:51–68.[Crossref], [Web of Science ®] , [Google Scholar]). The goal of the experiment was to increase the life of the router bit before it gets dull, which causes excessive dust formation and consequent expensive cleaning operation to smooth the edges of the boards. A 32-run experimental design was used including seven two-level factors and two four-level factors (cf. Table 1). In this experiment and others, factorial designs with a mixture of two-level and μ( > 2)-level factors may be adopted. Sequential experiments composed of initial experiments and follow-up experiments are widely used to resolve ambiguities involving the aliasing of factorial effects. This article investigates the construction and theoretical properties of optimal designs for sequential experiments with a mixture of α two-level and β μ-level factors for the first time. Constructing optimal design for the router bit life sequential experiment will be discussed for a practical use. From the numerical results, it is found that using a uniform design as the initial experimental design for the router bit life experiment is highly recommended to get an efficient router bit life sequential experimental design. The novelty and significance of the work are evaluated by comparing our results to the existing literature.     

Some results on coverings of galois spaces with ovoids and related bib designs

Some different coverings of Galois planes with ovoids are obtained and a three-dimensional example is also introduced. The regularity of these structures is put in evidence by constructing related BIB designs.     

Mean shift and influence measures in linear measurement error models with stochastic linear restrictions

We present influence diagnostics for linear measurement error models with stochastic linear restrictions using the corrected likelihood of Nakamura in 1990. The case deletion and mean shift outlier models are developed to identify outlying and influential observations. We derive a corrected score test statistic for outlier detection based on mean shift outlier models. The analogs of Cook's distance and likelihood distance are proposed to determine influential observations based on case deletion models. A parametric bootstrap procedure is used to obtain empirical distributions of the test statistics and a simulation study has been used to evaluate the performance of the proposed estimators based on the mean squares error criterion and the score test statistic. Finally, a numerical example is given to illustrate the theoretical results.     

A note on sequential ML estimates and their asymptotic covariances

A marginal and sequential maximum likelihood estimation method is described which can be used instead of full information maximum likelihood estimation if the latter method is unfeasible. It is shown that the sequential procedure yields strongly consistent and asymptotically normal estimates under relatively general regularity conditions. It is shown that the covariance matrix of the sequential ML estimator does not coincide with the inverse of the Fisher information matrix. Hence, the corrected covariance matrix is derived. The application of the sequential procedure to the multivariate probit model with dichotomous, ordered categorical, single-sided censored and double-sided censored endogenous variables is included. This research was partially supported by a dissertation grant of theStudienstiftung des Deutschen Volkes. Comments and suggestions on earlier drafts by Gerhard Arminger, Giorgio Calzolari, Bernd Kortzen and an anonymous referee are gratefully acknowledged.     

On correlation analysis of many‐to‐many observations: an alternative to Pearson's correlation coefficient and its application to an ecotoxicological study

Correlation studies are an important hypothesis‐generating and testing tool, and have a wide range of applications in many scientific fields. In ecological studies in particular, multiple environmental variables are often measured in an attempt to determine relationships between chemical, physical and biological factors. For example, one may wish to know whether and how soil properties correlate with plant physiology. Although correlation coefficients are widely used, their properties and limitations are often imperfectly understood. This is especially the case when one is interested in correlations between, say, trace element content in sediments and in marine organisms, where no one‐to‐one correspondence exists. We show that evaluating Pearson's correlation coefficient for either site‐specific means or composite samples results in biased estimates, and we propose an alternative estimator. We use simulation studies to demonstrate that our estimator generally has a much smaller bias and mean squared error. We further illustrate its use in a case study of the correlation between trace element content in sediments and in mussels in Lyttelton Harbour, New Zealand.     

The effect of interaction and rounding error in two-way ANOVA: example of impact on testing for normality

A key issue in various applications of analysis of variance (ANOVA) is testing for the interaction and the interpretation of resulting ANOVA tables. In this note it is demonstrated that for a two-way ANOVA, whether interactions are incorporated or not may have a dramatic influence when considering the usual statistical tests for normality of residuals. The effect of numerical rounding is also discussed.     

Some results on dependent random variables and a connection with the multivariate s-increasing convex order

In this paper, some new concepts of dependence are introduced that generalize the concepts of positive and negative association. The new concepts of dependence are linked to the multivariate s-increasing convex order. Furthermore, a Kolmogorov-type inequality and a Hàjek–Rènyi inequality are proven that lead to an asymptotic result for these new random objects.     

Balancing type I and type II error probabilities: further comments on proof of safety vs proof of hazard

This paper elaborates on earlier contributions of Bross (1985) and Millard (1987) who point out that when conducting conventional hypothesis tests in order to “prove” environmental hazard or environmental safety, unrealistically large sample sizes are required to achieve acceptable power with customarily-used values of Type I error probability. These authors also note that “proof of safety” typically requires much larger sample sizes than “proof of hazard”. When the sample has yet to be selected and it is feared that the sample size will be insufficient to conduct a reasonable.     

A Note on Sufficient Conditions for Valid Unmodified t Testing in Correlation Analysis with Autocorrelated and Heteroscedastic Sample Data

Traditionally, sphericity (i.e., independence and homoscedasticity for raw data) is put forward as the condition to be satisfied by the variance–covariance matrix of at least one of the two observation vectors analyzed for correlation, for the unmodified t test of significance to be valid under the Gaussian and constant population mean assumptions. In this article, the author proves that the sphericity condition is too strong and a weaker (i.e., more general) sufficient condition for valid unmodified t testing in correlation analysis is circularity (i.e., independence and homoscedasticity after linear transformation by orthonormal contrasts), to be satisfied by the variance–covariance matrix of one of the two observation vectors. Two other conditions (i.e., compound symmetry for one of the two observation vectors; absence of correlation between the components of one observation vector, combined with a particular pattern of joint heteroscedasticity in the two observation vectors) are also considered and discussed. When both observation vectors possess the same variance–covariance matrix up to a positive multiplicative constant, the circularity condition is shown to be necessary and sufficient. “Observation vectors” may designate partial realizations of temporal or spatial stochastic processes as well as profile vectors of repeated measures. From the proof, it follows that an effective sample size appropriately defined can measure the discrepancy from the more general sufficient condition for valid unmodified t testing in correlation analysis with autocorrelated and heteroscedastic sample data. The proof is complemented by a simulation study. Finally, the differences between the role of the circularity condition in the correlation analysis and its role in the repeated measures ANOVA (i.e., where it was first introduced) are scrutinized, and the link between the circular variance–covariance structure and the centering of observations with respect to the sample mean is emphasized.     

Autocovariance Estimation in Regression with a Discontinuous Signal and m‐Dependent Errors: A Difference‐Based Approach

We discuss a class of difference‐based estimators for the autocovariance in nonparametric regression when the signal is discontinuous and the errors form a stationary m‐dependent process. These estimators circumvent the particularly challenging task of pre‐estimating such an unknown regression function. We provide finite‐sample expressions of their mean squared errors for piecewise constant signals and Gaussian errors. Based on this, we derive biased‐optimized estimates that do not depend on the unknown autocovariance structure. Notably, for positively correlated errors, that part of the variance of our estimators that depend on the signal is minimal as well. Further, we provide sufficient conditions for ‐consistency; this result is extended to piecewise Hölder regression with non‐Gaussian errors. We combine our biased‐optimized autocovariance estimates with a projection‐based approach and derive covariance matrix estimates, a method that is of independent interest. An R package, several simulations and an application to biophysical measurements complement this paper.     

A New Lens on High School Dropout: Use of Correspondence Analysis and the Statewide Longitudinal Data System

The combination of log-linear models and correspondence analysis have long been used to decompose contingency tables and aid in their interpretation. Until now, this approach has not been applied to the education Statewide Longitudinal Data System (SLDS), which contains administrative school data at the student level. While some research has been conducted using the SLDS, its primary use is for state education administrative reporting. This article uses the combination of log-linear models and correspondence analysis to gain insight into high school dropouts in two discrete regions in Kentucky, Appalachia and non-Appalachia, defined by the American Community Survey. The individual student records from the SLDS were categorized into one of the two regions and a log-linear model was used to identify the interactions between the demographic characteristics and the dropout categories, push-out and pull-out. Correspondence analysis was then used to visualize the interactions with the expanded push-out categories, boredom, course selection, expulsion, failing grade, teacher conflict, and pull-out categories, employment, family problems, illness, marriage, and pregnancy to provide insights into the regional differences. In this article, we demonstrate that correspondence analysis can extend the insights gained from SDLS data and provide new perspectives on dropouts. Supplementary materials for this article are available online.     

Diagnostics on nonlinear model with scale mixtures of skew-normal and first-order autoregressive errors

In this work, we develop some diagnostics for nonlinear regression model with scale mixtures of skew-normal (SMSN) and first-order autoregressive errors. The SMSN distribution class covers symmetric as well as asymmetric and heavy-tailed distributions, which offers a more flexible framework for modelling. Maximum-likelihood (ML) estimates are computed via an expectation–maximization-type algorithm. Local influence diagnostics and score test for the correlation are also derived. The performances of the ML estimates and the test statistic are investigated through Monte Carlo simulations. Finally, a real data set is used to illustrate our diagnostic methods.     

Joint analysis of occurrence and time to stability after entrance into the Italian labour market: an approach based on a Bayesian cure model with structured stochastic search variable selection

Precarious employment is a serious social problem, especially in those countries, such as Italy, where there are limited benefits from social security. We investigate this phenomenon by analysing the initial part of the career of employees starting with unstable contracts for a panel of Italian workers. Our aim is to estimate the probability of getting a stable job and to detect factors influencing both this probability and the duration of precariousness. To answer these questions, we use an ad hoc mixture cure rate model in a Bayesian framework.