Functional boxplots based on epigraphs and hypographs

Functional boxplot is an attractive technique to visualize data that come from functions. We propose an alternative to the functional boxplot based on depth measures. Our proposal generalizes the usual construction of the box-plot in one dimension related to the down-upward orderings of the data by considering two intuitive pre-orders in the functional context. These orderings are based on the epigraphs and hypographs of the data that allow a new definition of functional quartiles which is more robust to shape outliers. Simulated and real examples show that this proposal provides a convenient visualization technique with a great potential for analyzing functional data and illustrate its usefulness to detect outliers that other procedures do not detect.     

Institutional constraints on executive greed: stratification systems in American art museums

This paper examines the stratification systems of over 200 organisations, individually represented by the internal income distributions of each organisation, in turn seen as products of executive decision-making. As a first principle, I assume that in any decision-making situation in which organisational leaders must choose between their own welfare and the welfare of their employees, they will almost always select the selfish course of action. In accordance with this axiom of executive greed, the majority of intra-organisational income distributions exhibit a substantial positive or right skew (that is, many people in the lower income levels and very few in the highest). Yet there is sufficient variation to suggest that there are forces which constrain executive greed. Combining the new structuralist perspective on stratification with resource dependency and organisational fields models, the paper examines hypotheses which maintain that the shape of internal distributive systems is affected by: (i) organisational properties, such as size and structural complexity, which empower the employee in labour relations with management; and (ii) highly-institutionalised resource dependencies which constrain income disbursement decisions. Data are taken from a US sample of art museums. The results of the analyses seriously contradict the new structuralist's empowerment accounts of the effects of size and structural complexity on stratification, and suggest that their propositions have been posed at a level which may be far too general. Certain highly-institutionalised resource dependencies are found to promote equality in internal distributive systems.I thank Ann Rotchford, Charles Perrow, Helmut Anheier and three anonymous reviewers for the useful comments that they provided on an earlier version of this paper. I am grateful to Ann Rotchford for her help in preparing the Appendix.     

The Validity of Observational Measures in Detecting Optimal Maternal Communication Styles: Evidence from European Americans and Latinos

This study examined the sensitivity of an observational coding system for assessing positive and negative maternal behaviors of Latino and European American mothers toward their adolescent children. Ninety Latino (54 Spanish speaking and 35 English speaking) and 20 European American mother–adolescent dyads participated in an observational study of conversations about sexuality, AIDS, and conflicts. Associations were examined between observed maternal positive and negative behaviors and adolescent‐reported relationship quality. Results indicated that maternal negative responsiveness was negatively associated with relationship quality for all ethnic/language groups. However, maternal positive responsiveness was related to relationship quality for European Americans but not for Latinos. These findings suggest a need for a broader definition of positive parenting in Latino families.     

On the explosion rate of maximum-bias functions

The maxbias function B_T() contains much information about the robustness properties of the estimate T. This function satisfies B_T(0)=0 and B_T()<for all 0<<whereis the breakdown point of T. Hampel (1974)pioneered the study of the limiting behaviour of B_T(?) where ? → 0. He computed and optimized the rate γ at which B_T(?) approaches 0 when ? → 0. This rate is now called the contamination sensitivity of T, and constitutes one of the cornerstones of the theory of robustness. We show that much can also be learned from the study of the limiting behaviour of B_T(?) when ? → ?*. A new robustness measure, called the relative explosion rate, can be obtained by studying the limiting relative maxbias behaviour of two extimates when approaches their common breakdown point ?*. Like the contamination sensitivity, the relative explosion rate can be readily derived from the estimate's score function. General formulae are given for M-estimates of scale and S-, MM- and τ-estimates of regression. We also show that the maxbias behaviour for large ? is largely determined by the curvature of the estimate's score function near zero. This motivates our definition and study of the local order of a score function.     

Homogeneity test for functional data

In the context of functional data analysis, we propose new sample tests for homogeneity. Based on some well-known depth measures, we construct four different statistics in order to measure distance between the two samples. A simulation study is performed to check the efficiency of the tests when confronted with shape and magnitude perturbation. Finally, we apply these tools to measure the homogeneity in some samples of real data, and we obtain good results using this new method.