A flexible generalization of the skew normal distribution based on a weighted normal distribution

The skew normal distribution of Azzalini (Scand J Stat 12:171–178, 1985) has been found suitable for unimodal density but with some skewness present. Through this article, we introduce a flexible extension of the Azzalini (Scand J Stat 12:171–178, 1985) skew normal distribution based on a symmetric component normal distribution (Gui et al. in J Stat Theory Appl 12(1):55–66, 2013). The proposed model can efficiently capture the bimodality, skewness and kurtosis criteria and heavy-tail property. The paper presents various basic properties of this family of distributions and provides two stochastic representations which are useful for obtaining theoretical properties and to simulate from the distribution. Further, maximum likelihood estimation of the parameters is studied numerically by simulation and the distribution is investigated by carrying out comparative fitting of three real datasets.     

Maximal autocorrelation functions in functional data analysis

This paper proposes a new factor rotation for the context of functional principal components analysis. This rotation seeks to re-express a functional subspace in terms of directions of decreasing smoothness as represented by a generalized smoothing metric. The rotation can be implemented simply and we show on two examples that this rotation can improve the interpretability of the leading components.     

New recursive estimators of the time-average variance constant

Estimation of the time-average variance constant (TAVC) of a stationary process plays a fundamental role in statistical inference for the mean of a stochastic process. Wu (2009) proposed an efficient algorithm to recursively compute the TAVC with \(O(1)\) memory and computational complexity. In this paper, we propose two new recursive TAVC estimators that can compute TAVC estimate with \(O(1)\) computational complexity. One of them is uniformly better than Wu’s estimator in terms of asymptotic mean squared error (MSE) at a cost of slightly higher memory complexity. The other preserves the \(O(1)\) memory complexity and is better then Wu’s estimator in most situations. Moreover, the first estimator is nearly optimal in the sense that its asymptotic MSE is \(2^{10/3}3^{-2} \fallingdotseq 1.12\) times that of the optimal off-line TAVC estimator.     

Approximate Bayesian computation with composite score functions

Both approximate Bayesian computation (ABC) and composite likelihood methods are useful for Bayesian and frequentist inference, respectively, when the likelihood function is intractable. We propose to use composite likelihood score functions as summary statistics in ABC in order to obtain accurate approximations to the posterior distribution. This is motivated by the use of the score function of the full likelihood, and extended to general unbiased estimating functions in complex models. Moreover, we show that if the composite score is suitably standardised, the resulting ABC procedure is invariant to reparameterisations and automatically adjusts the curvature of the composite likelihood, and of the corresponding posterior distribution. The method is illustrated through examples with simulated data, and an application to modelling of spatial extreme rainfall data is discussed.     

Computing the log concave NPMLE for interval censored data

In analyzing interval censored data, a non-parametric estimator is often desired due to difficulties in assessing model fits. Because of this, the non-parametric maximum likelihood estimator (NPMLE) is often the default estimator. However, the estimates for values of interest of the survival function, such as the quantiles, have very large standard errors due to the jagged form of the estimator. By forcing the estimator to be constrained to the class of log concave functions, the estimator is ensured to have a smooth survival estimate which has much better operating characteristics than the unconstrained NPMLE, without needing to specify a parametric family or smoothing parameter. In this paper, we first prove that the likelihood can be maximized under a finite set of parameters under mild conditions, although the log likelihood function is not strictly concave. We then present an efficient algorithm for computing a local maximum of the likelihood function. Using our fast new algorithm, we present evidence from simulated current status data suggesting that the rate of convergence of the log-concave estimator is faster (between \(n^{2/5}\) and \(n^{1/2}\)) than the unconstrained NPMLE (between \(n^{1/3}\) and \(n^{1/2}\)).     

On smoothness of Tukey depth contours

The smoothness of Tukey depth contours is a regularity condition often encountered in asymptotic theory, among others. This condition ensures that the Tukey depth fully characterizes the underlying multivariate probability distribution. In this paper we demonstrate that this regularity condition is rarely satisfied. It is shown that even well-behaved probability distributions with symmetrical, smooth and (strictly) quasi-concave densities may have non-smooth Tukey depth contours, and that the smoothness behaviour of depth contours is fairly unpredictable.     

Managing The Lactating Body: The Breast-Feeding Project and Privileged Motherhood

Drawing on interviews with twenty-five mostly white, educated, work-force experienced and class-privileged mothers, this paper explores how these women construct the lactating body as a carefully managed site and breast-feeding as a project—a task to be researched, planned, implemented, and assessed, with reliance on expert knowledge, professional advice, and consumption. The framing of breast-feeding as a project contrasts with the emphases on pleasure, embodied subjectivity, relationality, and empowerment that characterizes much of the recent breast-feeding literature across the humanities and social sciences. I argue that the project frame sheds light on the amount of work and self-discipline involved in compliance with broader middle-class mothering standards set in the consumerist, technological, medicalized, and professionalized contexts that shape parenting in late capitalist America.

Myths of Women and Their Reflection in a Therapy Group

One essential dilemma for modern clinical social work involves the relationship between the processes taking place inside the self and the social, cultural, and political developments affecting a person from the outside. The group-analysis approach focuses on four levels of relationships and communication within the group, among others a primordial level of shared myths, archetypical images, and the collective unconscious as an important component of psychotherapy. This article describes group-analysis therapy with women, analyzing a therapeutic process that used social myths to explore the formative institutionalization processes participants had undergone, thereby expanding themselves, growing, and changing.

Passing Encounters East and West: Comparing Japanese and American Pedestrian Interactions

This study examined the microinteractions of pedestrians in Japan and in the United States as they walked past a confederate. Specifically, the effects of culture, condition (avoid, look-only, and look plus smile) and sex of confederate on glances, smiles, nods, and greetings by passing pedestrians were examined in a field study on over 1000 participants. The hypotheses of (1) lower responsiveness in Japanese pedestrians than in American pedestrians and (2) increased responsiveness as a function of condition were supported in a series of log-linear analyses of pedestrian glances, smiles, nods, and greetings. Both of these main effects were, however, qualified by Culture X Condition interactions on smiles, nods, and greetings, with the large condition effects present in the American pedestrians, but absent in the Japanese pedestrians. The results are discussed in terms of the functions of glances, smiles, nods, and greetings in these brief encounters and how differing cultural norms affect Japanese and American responsiveness. Finally, the limitations of this study and the broader utility of this research paradigm are discussed.