On estimating the dimensionality in discriminant analysis

In discriminant analysis, the dimension of the hyperplane which population mean vectors span is called the dimensionality. The procedures commonly used to estimate this dimension involve testing a sequence of dimensionality hypotheses as well as model fitting approaches based on (consistent) Akaike's method, (modified) Mallows' method and Schwarz's method. The marginal log-likelihood (MLL) method is developed and the asymptotic distribution of the dimensionality estimated by this method for normal populations is derived. Furthermore a modified marginal log-likelihood (MMLL) method is also considered. The MLL method is not consistent for large samples and two modified criteria are proposed which attain asymptotic consistency. Some comments are made with regard to the robustness of this method to departures from normality. The operating characteristics of the various methods proposed are examined and compared.     

Non-parametric estimation of population size from capture–recapture data when the capture probability depends on a covariate

Summary.  In capture–recapture experiments the capture probabilities may depend on individual covariates such as an individual's weight or age. Typically this dependence is modelled through simple parametric functions of the covariates. Here we first demonstrate that misspecification of the model can produce biased estimates and subsequently develop a non-parametric procedure to estimate the functional relationship between the probability of capture and a single covariate. This estimator is then incorporated in a Horvitz–Thompson estimator to estimate the size of the population. The resulting estimators are evaluated in a simulation study and applied to a data set on captures of the Mountain Pygmy Possum.     

Statistical methodology for assessing homology of intronic regions of genes

We consider the problem of statistically evaluating the similarity of DNA intronic regions of genes. Present algorithms are based on matching a sequence of interest with known DNA sequences in a gene bank and are designed primarily to assess homology among exonic regions of genes. Most research focuses on exonic regions because they have a clear biological significance, coding for proteins, and therefore tend to be more conserved in evolution than intronic regions. To investigate whether the intronic features of genes whose expression is highly sensitive to environmental perturbations differ from genes that have a more constant expression, a collection of oncogenes, tumor suppressor genes, and nonregulatory genes involved in energy metabolism are compared. An analysis of the features of these genes' intronic regions result in clustering by regulatory group. In addition, Billingsley's test for Markov structure (1961) suggests that 67% of the intronic regions in this collection of genes show evidence of nonrandom structure, indicating the possibility of a biological function for these regions. The result of Billingsley's test for homology is used as input to a clustering algorithm. The biological significance of this methodology lies in the identification of groups based on the intronic regions from genes of unknown function. With the advent of rapid sequencing techniques, there is a great need for statistical techniques to help identify the purpose of poorly understood portions of genes. These methods can be utilized to assess the functional group to which such a gene might possibly belong.     

Disabled people,choices and collective organisation: examining the potential of cooperatives in future social support

Major shifts in funding, demography, personal expectations and the rise of a global disabled people’s movement require new and creative solutions to the choices and rights agenda into the twenty-first century. Direct payments and the individual employment of personal assistants is one clear and recognised path to independent living. However, there have been some reservations about the nature, process and impact of the broader personalisation agenda more generally within which direct payments and personal budgets are located. Some commentators point to the loss of the collective impulse in personalised approaches – ideas that were central to the development of the independent living movement and its founding principles. Some countries have seen the rise of collective responses to direct payment developments. This is explicable in terms of a suspicion of individualist underpinnings of personalisation coupled with a collective vision of social life. This article is based on an exploratory study of collective approaches in the field of direct payments where choice and social solidarity are being combined. Drawing on developments in Sweden, England and Wales, the article aims to inform possible future debates about direct payments and cooperative approaches and argues that greater user-control is not inimical to enhanced collective action.     

Guilt and Shame in Chinese Culture: A Cross-cultural Framework from the Perspective of Morality and Identity

Olwen Bedford and Kwang-Kuo Hwang, Guilt and Shame in Chinese Culture: A Cross-cultural Framework from the Perspective of Morality and Identity, pp. 127–144.
This article formulates a cross-cultural framework for understanding guilt and shame based on a conceptualization of identity and morality in Western and Confucian cultures. First, identity is examined in each culture, and then the relation between identity and morality illuminated. The role of guilt and shame in upholding the boundaries of identity and enforcing the constraints of morality is then discussed from the perspective of each culture. The developed framework is then applied the emotions of guilt and shame in Chinese culture drawing on previous field research. Implications for future research are discussed.     

Risk aversion and the relationship between Nash's solution and subgame perfect equilibrium of sequential bargaining

This article presents some new, intuitive derivations of several results in the bargaining literature. These new derivations clarify the relationships among these results and allow them to be understood in a unified way. These results concern the way in which the risk posture of the bargainers affects the outcome of bargaining as predicted by Nash's (axiomatic) solution of a static bargaining model (Nash, 1950) and by the subgame perfect equilibrium of the infinite horizon sequential bargaining game analyzed by Rubinstein (1982). The analogous, experimentally testable predictions for finite horizon sequential bargaining games are also presented.     

Making the familiar strange and making the strange familiar: understanding Korean children’s experiences of living with an autistic sibling

Based on the findings of a small‐scale study using visual ethnographic techniques with nine South Korean children, this article explores the role of culture in understanding autism. While autism is embedded within the ‘strange’ and ‘unfamiliar’, linked to exclusion and discrimination in Korean society, the children focussed on reframing their experiences of living with autism as ‘ordinary’. Despite the limitations of the small sample, the richness and depth of data generated by children themselves offers new insights into children’s interpretations and experiences of autism and raises interesting questions for cross cultural research in the field of disability.     

The rank distribution of the maximin in a random matrix

Let S be a set of tm distinct real numbers and R a random t × m matrix of these tm numbers with rows {r_i} and columns (c_i}. Define b = Max Min x. l≤i≤t x?r_i. Let c be the event Max Min x = Min Max x. l≤i≤t x?r_i l≤i≤m x?c_i. This paper derives the probability distribution of the rank of b in S, as well as the same distribution conditional on c.     

On the number of separable partitions

Consider partitions of a given set A of n distinct points in general position in ℝ ^d into parts where each pair of parts can be separated by a hyperplane that contains a given set of points E. We consider the problem of counting and generating all such partitions (correcting a classic 1967 result of Harding about the number of such partitions into two parts). Applications of the result to partition problems are presented.     

Structural and Individual Determinants of Outmarriage Among Chinese-, Filipino-, and Japanese-Americans in California*

This study combines structural factors of intergroup relations with personal assimilation factors to examine Asian American intermarriage in California, We conduct a multilevel logistic regression analysis of outmarriage among Chinese, Filipinos, and Japanese in 14 California metropolitan statistical areas with high con centrations of Asian Americans by using the 1980 Census Public-Use Microdata Sample. The results show that Asian intermarriage is affected by both assimilation and structural determinants. Some theoretically unexpected findings are discussed that hint at alternative interpretations.