Nonparametric product partition models for multiple change-points analysis

ABSTRACT

We propose an extension of parametric product partition models. We name our proposal nonparametric product partition models because we associate a random measure instead of a parametric kernel to each set within a random partition. Our methodology does not impose any specific form on the marginal distribution of the observations, allowing us to detect shifts of behaviour even when dealing with heavy-tailed or skewed distributions. We propose a suitable loss function and find the partition of the data having minimum expected loss. We then apply our nonparametric procedure to multiple change-point analysis and compare it with PPMs and with other methodologies that have recently appeared in the literature. Also, in the context of missing data, we exploit the product partition structure in order to estimate the distribution function of each missing value, allowing us to detect change points using the loss function mentioned above. Finally, we present applications to financial as well as genetic data.     

Multivariate Kendall's tau for change‐point detection in copulas

Statistical procedures for the detection of a change in the dependence structure of a series of multivariate observations are studied in this work. The test statistics that are proposed are $L_1$ , $L_2$ , and $L_{\infty }$ distances computed from vectors of differences of Kendall's tau; two multivariate extensions of Kendall's measure of association are used. Since the distributions of these statistics under the null hypothesis of no change depend on the unknown underlying copula of the vectors, a procedure based on the multiplier central limit theorem is used for the computation of p‐values; the method is shown to be valid both asymptotically and for moderate sample sizes. Alternative versions of the tests that take into account possible breakpoints in the marginal distributions are also investigated. Monte Carlo simulations show that the tests are powerful under many scenarios of change‐point. In addition, two estimators of the time of change are proposed and their efficiency is carefully studied. The methodologies are illustrated on simulated series from the Canadian Regional Climate Model. The Canadian Journal of Statistics 41: 65–82; 2013 © 2012 Statistical Society of Canada     

Random translation of discrete order statistics

We investigate the existence and uniqueness of a discrete parent distribution supported on the integers whose order statistics are related by a random translation. We also provide some examples using the constructive method that we propose.     

Hypothesis test for paired samples in the presence of missing data

Missing data are present in almost all statistical analysis. In simple paired design tests, when some subject has one of the involved variables missing in the so-called partially overlapping samples scheme, it is usually discarded for the analysis. The lack of consistency between the information reported in the univariate and multivariate analysis is, perhaps, the main consequence. Although the randomness on the missing mechanism (missingness completely at random) is an usual and needed assumption for this particular situation, missing data presence could lead to serious inconsistencies on the reported conclusions. In this paper, the authors develop a simple and direct procedure which allows using the whole available information in order to perform paired tests. In particular, the proposed methodology is applied to check the equality among the means from two paired samples. In addition, the use of two different resampling techniques is also explored. Finally, real-world data are analysed.     

Projection Measures And Estimation Variances Of Intensities

The paper investigates random processes of geometrical objects in Euclidean spaces. General properties of the measure of total projections are derived by means of Palm distribution. Explicit formulas for variances of the projection measure are obtained for Poisson point processes of compact sets.

Intensity estimators of fibre (surface) processes are then studied by means of projection measures. Classification of direct and indirect probes is introduced. The indirect sampling design of vertical sections and projections is generalized and its statistical properties derived.     

Patterns of individual change and program satisfaction in a positive parenting program for parents at psychosocial risk

Despite the evidence of effectiveness of positive parenting programs, little is known about the typology of changes that parents at psychosocial risk undergo after an intervention. We compared individual patterns of change in three parenting outcomes in 256 at risk parents with young children attending the group‐based Growing Up Happily in the Family program delivered in municipal social services. We identified four clusters of individual change: Cluster 1 (30.6%) had negative changes in parental child‐rearing attitudes and parenting stress, Cluster 2 (27.7%) had positive changes in child‐rearing attitudes and negative results in parental perceived competence, and Cluster 3 (24.1%) and Cluster 4 (17.6%) showed overall better results. Residential area, type of social support, and quality of implementation characterized cluster membership. Participants in clusters with better results were more satisfied with the program than those with worse results. Practical recommendations are provided for the successful implementation of group parenting programs in family preservation services.     

Developing an Index to Measure Sub-municipal Level Urban Sprawl

The present study aims to develop an index composed of different spatial variables to measure the urban sprawl levels of a municipality located in Southern Spain. According to the findings, urban sprawl can be measured not only on the metropolitan level but also on a more detailed and precise level, such as sub-municipal. A group of experts chosen for their suitability in measuring urban sprawl select six spatial variables (population density, net residential density, coverage ratio, land use types, percentage of residential land use, and average year of construction). These variables are aggregated using Choquet integral, a technique that combines interactions between those variables providing greater coherence to the complexity that is inherent in the creation of composite sprawl indexes. This methodology has been demonstrated to be valid and appropriate in evaluating urban expansion at sub-municipal level, but can also be applied to other scales once it is clearly a phenomenon in which interaction between criteria exists. The resulting composite index allows the assignment of different levels of sprawl to the urban areas consistent with their morphology and landscape.     

Dirty money? The politics of representation in Cuban revolutionary banknotes

This article examines the visual politics of Cuban postrevolutionary banknotes, focusing on the series minted in 1961. It is argued that the iconography of this series – which stresses the revolutionary merits of Fidel Castro and his movement, and associates the latter with the independence wars – portrays the Castro-led Cuban Revolution as the fulfilment of the nation’s aspiration to sovereignty. The article maintains that the design of the 1961 banknote series articulates tropes that convey a fidelista imaginary, presenting the visual rhetoric of currencies as a mechanism of propaganda and persuasion.