Bump hunting with non-Gaussian kernels

It is well known that the number of modes of a kernel density estimator is monotone nonincreasing in the bandwidth if the kernel is a Gaussian density. There is numerical evidence of nonmonotonicity in the case of some non-Gaussian kernels, but little additional information is available. The present paper provides theoretical and numerical descriptions of the extent to which the number of modes is a nonmonotone function of bandwidth in the case of general compactly supported densities. Our results address popular kernels used in practice, for example, the Epanechnikov, biweight and triweight kernels, and show that in such cases nonmonotonicity is present with strictly positive probability for all sample sizes n\geq3. In the Epanechnikov and biweight cases the probability of nonmonotonicity equals 1 for all n\geq2. Nevertheless, in spite of the prevalence of lack of monotonicity revealed by these results, it is shown that the notion of a critical bandwidth (the smallest bandwidth above which the number of modes is guaranteed to be monotone) is still well defined. Moreover, just as in the Gaussian case, the critical bandwidth is of the same size as the bandwidth that minimises mean squared error of the density estimator. These theoretical results, and new numerical evidence, show that the main effects of nonmonotonicity occur for relatively small bandwidths, and have negligible impact on many aspects of bump hunting.Comment: Published at http://dx.doi.org/10.1214/009053604000000715 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Understanding Workday Housework Participation: Testing Three Theories

In this study we examine the usefulness of three theories (time availability theory, gender ideology theory, and relative resources) in predicting workday housework performance among partnered and married mothers and fathers. In doing so, we incorporate an extended version of time availability theory that considers the use of flexible scheduling and the presence of nonstandard work hours in addition to number of hours worked. Our hypotheses are addressed with data from a nationally representative sample of employed adults. Our results show that none of the theories are useful in predicting fathers’ workday housework performance; however, two theories are beneficial for predicting mothers’ performance. Specifically, mothers with more traditional gender ideologies (in support of gender ideology theory) along with mothers who work fewer hours than their partners (in support of time availability theory) perform more workday housework. Additionally, and in support of an extended version of time availability theory, we find the use of flexible scheduling among mothers is associated with higher levels of workday housework performance. Implications of the study are discussed

Dealing with Label Switching in Mixture Models Under Genuine Multimodality

The fitting of finite mixture models is an ill-defined estimation problem as completely different parameterizations can induce similar mixture distributions. This leads to multiple modes in the likelihood which is a problem for frequentist maximum likelihood estimation, and complicates statistical inference of Markov chain Monte Carlo draws in Bayesian estimation. For the analysis of the posterior density of these draws a suitable separation into different modes is desirable. In addition, a unique labelling of the component specific estimates is necessary to solve the label switching problem. This paper presents and compares two approaches to achieve these goals: relabelling under multimodality and constrained clustering. The algorithmic details are discussed and their application is demonstrated on artificial and real-world data

Maximum likelihood kernel density estimation: On the potential of convolution sieves

Methods for improving the basic kernel density estimator include variable locations, variable bandwidths and variable weights. Typically these methods are implemented separately and via pilot estimation of variation functions derived from asymptotic considerations. The starting point here is a simple maximum likelihood procedure which allows (in its greatest generality) variation of all these quantities at once, bypassing asymptotics and explicit pilot estimation. One special case of this approach is the density estimator associated with nonparametric maximum likelihood estimation (NPMLE) in a normal location mixture model. Another, closely associated with the NPMLE, is a kernel convolution sieve estimator proposed in 1982 but little used in practice to date. Simple algorithms are utilised, a simulation study is reported on, a method for bandwidth selection is investigated and an illustrative example is given. The simulations and other considerations suggest that the kernel convolution sieve provides an especially promising framework for further practical utilisation and development. And the method has a further advantage: it automatically reduces, where appropriate, to a few-component mixture model which indicates and initialises parametric mixture modelling of the data

A computational framework to emulate the human perspective in flow cytometric data analysis

Background: In recent years, intense research efforts have focused on developing methods for automated flow cytometric data analysis. However, while designing such applications, little or no attention has been paid to the human perspective that is absolutely central to the manual gating process of identifying and characterizing cell populations. In particular, the assumption of many common techniques that cell populations could be modeled reliably with pre-specified distributions may not hold true in real-life samples, which can have populations of arbitrary shapes and considerable inter-sample variation. <p/>Results: To address this, we developed a new framework flowScape for emulating certain key aspects of the human perspective in analyzing flow data, which we implemented in multiple steps. First, flowScape begins with creating a mathematically rigorous map of the high-dimensional flow data landscape based on dense and sparse regions defined by relative concentrations of events around modes. In the second step, these modal clusters are connected with a global hierarchical structure. This representation allows flowScape to perform ridgeline analysis for both traversing the landscape and isolating cell populations at different levels of resolution. Finally, we extended manual gating with a new capacity for constructing templates that can identify target populations in terms of their relative parameters, as opposed to the more commonly used absolute or physical parameters. This allows flowScape to apply such templates in batch mode for detecting the corresponding populations in a flexible, sample-specific manner. We also demonstrated different applications of our framework to flow data analysis and show its superiority over other analytical methods. <p/>Conclusions: The human perspective, built on top of intuition and experience, is a very important component of flow cytometric data analysis. By emulating some of its approaches and extending these with automation and rigor, flowScape provides a flexible and robust framework for computational cytomics

Family-based clusters of cognitive test performance in familial schizophrenia

BACKGROUND: Cognitive traits derived from neuropsychological test data are considered to be potential endophenotypes of schizophrenia. Previously, these traits have been found to form a valid basis for clustering samples of schizophrenia patients into homogeneous subgroups. We set out to identify such clusters, but apart from previous studies, we included both schizophrenia patients and family members into the cluster analysis. The aim of the study was to detect family clusters with similar cognitive test performance. METHODS: Test scores from 54 randomly selected families comprising at least two siblings with schizophrenia spectrum disorders, and at least two unaffected family members were included in a complete-linkage cluster analysis with interactive data visualization. RESULTS: A well-performing, an impaired, and an intermediate family cluster emerged from the analysis. While the neuropsychological test scores differed significantly between the clusters, only minor differences were observed in the clinical variables. CONCLUSIONS: The visually aided clustering algorithm was successful in identifying family clusters comprising both schizophrenia patients and their relatives. The present classification method may serve as a basis for selecting phenotypically more homogeneous groups of families in subsequent genetic analyses

Zero-Hour Contracts and Stress in UK Domiciliary Care Workers

UK domiciliary care workers play a vital role in maintaining and improving the lives of service users who have a variety of needs. Around 60% of these employees work under zero-hours contracts but, while it is known that conditions such as temporary and shift working can influence employee health and performance, zero-hours have not been widely investigated. This project sought to firstly investigate the stress associated with working as a domiciliary care worker, as well as comparing the experiences of employees contracted to zero hours with those contracted to at least 16 hours per week. Twenty-nine semi-structured interviews (15 zero-hour, 14 contracted hours) were conducted in the West Midlands of the UK and analysed using thematic analysis. Across all participants, four predominant stressors were found. Firstly, level of pay for what is a job with high levels of responsibility were poor. Secondly, participants described struggling to maintain an adequate work-life balance due to the varied timings of visits, as well as rude and aggressive behaviour from both service users and their families. Lastly, a lack of peer support and poor care from peers was discussed. However, every respondent described the positive relationships that they develop with service users being a distinct stress-reliever. Zero-hours respondents discussed two further stressors. Power refers to the relationship between employee and management, with respondents describing the balance of power being with management. Uncertainty reflected respondents not having set hours of work or pay, and thus not being able to plan in their personal lives and sometimes not being able to pay bills. Findings suggest that domiciliary care workers are exposed to a range of stressors, with zero-hours adding to these. Further research should look into methods to improve both the job role for workers, and redress the power relationships for those with zero-hours contracts

Company-level family policies: Who has access to it and what are some of its outcomes

Despite the increase in number of studies that examine the cross-national variation in the policy configuration that allow a better work-family integration, very few look beyond the national levels. It is also crucial to examine occupational level welfare since companies may restrict or expand the existing national level regulations, defining the “final availability” workers actual have towards various arrangements. In addition, companies may provide various additional arrangements through occupational policies which are not set out in the national level agreements that are crucial in addressing reconciliation needs of workers. This chapter examines what types of arrangements are provided at the company level to address work-family demands of workers. It further provides a synthesis of studies that examine both national level contexts and individual level characteristics that explain who gets access to company level family-friendly policies, which is linked to the possible outcomes of these policies