Regression from another angle

This paper presents a simply viewed framework that brings together various concepts of regression, prediction, and principal components. Several new concepts related to prediction are introduced, and then the interrelationships of these concepts are established. The generalizations are examined in detail and are illustrated in the context of a well known data set.     

A property of coefficients of variation for ordered bivariate log-normal variables

This paper considers the maximum and minimum of a pair of log-normal variables with equal mean. It shows that either order statistic has a smaller coefficient of variation than the two original log-normal variables provided the latter are of equal variance. When the variances are unequal, as the variance ratio increases, the minimum (maximum), has a smaller coefficient of variation if the correlation coefficient of the log-normal variables is small (small) and the variances are large (small).     

Exact permutation inference for two sample repeated measures data

Experiments in which very few units are measured many times sometimes present particular difficulties. Interest often centers on simple location shifts between two treatment groups, but appropriate modeling of the error distribution can be challenging. For example, normality may be difficult to verify, or a single transformation stabilizing variance or improving normality for all units and all measurements may not exist. We propose an analysis of two sample repeated measures data based on the permutation distribution of units. This provides a distribution free alternative to standard analyses. The analysis includes testing, estimation and confidence intervals. By assuming a certain structure in the location shift model, the dimension of the problem is reduced by analyzing linear combinations of the marginal statistics. Recently proposed algorithms for computation of two sample permutation distributions, require only a few seconds for experiments having as many as 100 units and any number of repeated measures. The test has high asymptotic efficiency and good power with respect to tests based on the normal distribution. Since the computational burden is minimal, approximation of the permutation distribution is unnecessary.     

A Bootstrap Stationarity Test for Predictive Regression Invalidity

In order for predictive regression tests to deliver asymptotically valid inference, account has to be taken of the degree of persistence of the predictors under test. There is also a maintained assumption that any predictability in the variable of interest is purely attributable to the predictors under test. Violation of this assumption by the omission of relevant persistent predictors renders the predictive regression invalid, and potentially also spurious, as both the finite sample and asymptotic size of the predictability tests can be significantly inflated. In response, we propose a predictive regression invalidity test based on a stationarity testing approach. To allow for an unknown degree of persistence in the putative predictors, and for heteroscedasticity in the data, we implement our proposed test using a fixed regressor wild bootstrap procedure. We demonstrate the asymptotic validity of the proposed bootstrap test by proving that the limit distribution of the bootstrap statistic, conditional on the data, is the same as the limit null distribution of the statistic computed on the original data, conditional on the predictor. This corrects a long-standing error in the bootstrap literature whereby it is incorrectly argued that for strongly persistent regressors and test statistics akin to ours the validity of the fixed regressor bootstrap obtains through equivalence to an unconditional limit distribution. Our bootstrap results are therefore of interest in their own right and are likely to have applications beyond the present context. An illustration is given by reexamining the results relating to U.S. stock returns data in Campbell and Yogo (2006 Campbell, J. Y. and Yogo, M. (2006), “Efficient Tests of Stock Return Predictability,” Journal of Financial Economics, 81, 27–60.[Crossref], [Web of Science ®] , [Google Scholar]). Supplementary materials for this article are available online.     

Interrogating Mixed-Race: A Crisis of Ambiguity?

In many respects, issues surrounding ‘mixed-race’ identities rupture and dislocate much current thinking within post-race and new ethnicities paradigms. This article seeks to critically engage with what is arguably a marginalized and diverse ‘community’. An evaluation of theories emanating from the UK and USA seeks to challenge hybrid degenerative theories, and more recent attempts at explaining how such identities are negotiated in complex social arenas. What emerges is that some theories are underpinned by static and linear behavioural patterns, which appear oversimplified. Key questions are raised in order to further explore whether ‘mixed-race’ identities are genuinely marginalized and remain ambiguous in a range of physical, social, emotional and ideological contexts. Reflecting upon such issues seeks to prompt questions as to whether there can be a more sophisticated and sensitive understanding of the unique experiences (both positive and negative) of ‘mixed-race’ individuals. By doing so, it is hoped that such a topic becomes more central to considerations of how prejudice and discrimination operate across and within a wide variety of settings.     

Identity,difference and community in Southern Irish Protestantism: The Protestants of West Cork

This article looks at how the Protestants of West Cork came to terms with Irish independence, and how they have responded to the major social and political changes of the past decades. West Cork Protestants are geographically peripheral to the Southern Protestant population as a whole, and have a weaker socio-economic profile. They live in an area that saw some of the fiercest fighting and worst atrocities in the war of independence and civil war. Their experience throws considerable light on issues of whether Protestants were a privileged or oppressed minority, and whether and how they integrated into the new state. Extensive in-depth interviews are used to show how West Cork Protestants reconstructed their identity, defined their differences from Catholics and maintained community in the years since independence.     

Inference in hybrid Bayesian networks using dynamic discretization

We consider approximate inference in hybrid Bayesian Networks (BNs) and present a new iterative algorithm that efficiently combines dynamic discretization with robust propagation algorithms on junction trees. Our approach offers a significant extension to Bayesian Network theory and practice by offering a flexible way of modeling continuous nodes in BNs conditioned on complex configurations of evidence and intermixed with discrete nodes as both parents and children of continuous nodes. Our algorithm is implemented in a commercial Bayesian Network software package, AgenaRisk, which allows model construction and testing to be carried out easily. The results from the empirical trials clearly show how our software can deal effectively with different type of hybrid models containing elements of expert judgment as well as statistical inference. In particular, we show how the rapid convergence of the algorithm towards zones of high probability density, make robust inference analysis possible even in situations where, due to the lack of information in both prior and data, robust sampling becomes unfeasible.     

Bandwidth-based nonparametric inference

Nonparametric curve estimation is an extremely common statistical procedure. While its primary purpose has been exploratory, some advances in inference have been made. This paper provides a critical review of inferential tests that make fundamental use of a key element of nonparametric smoothing, the bandwidth, to determine the significance of certain features. A major focus is on two important problems that have been tackled using bandwidth-based inference: testing for the multimodality of a density and testing for the monotonicity of a regression curve. Early research in bandwidth-based inference is surveyed, as well as recent theoretical advances. Possible future directions in bandwidth-based inference are discussed.