Quadratic Approximation via the SCAD Penalty with a Diverging Number of Parameters

The high-dimensional data arises in diverse fields of sciences, engineering and humanities. Variable selection plays an important role in dealing with high dimensional statistical modelling. In this article, we study the variable selection of quadratic approximation via the smoothly clipped absolute deviation (SCAD) penalty with a diverging number of parameters. We provide a unified method to select variables and estimate parameters for various of high dimensional models. Under appropriate conditions and with a proper regularization parameter, we show that the estimator has consistency and sparsity, and the estimators of nonzero coefficients enjoy the asymptotic normality as they would have if the zero coefficients were known in advance. In addition, under some mild conditions, we can obtain the global solution of the penalized objective function with the SCAD penalty. Numerical studies and a real data analysis are carried out to confirm the performance of the proposed method.     

耶律阿保机对世选制的调整与利用

阿保机时代是契丹社会大变革的时代,阿保机变革旧制的一个内容就是对传统世选制的改造。经过他的努力,从理论意义上实现了契丹可汗世选向皇位世袭的转变,也对官吏的世选作了重大的调整。值得重视的是,阿保机的政治智慧在变革世选制过程中有所体现。     

Self‐Construal,Career Decision Self‐Efficacy,and Perceived Barriers Predict Mexican American Women's Life Satisfaction

This study used the social cognitive theory of well‐being (SCTW; Lent, 2004 ) to examine the role of career decision self‐efficacy (CDSE), perceived educational barriers, and independent self‐construal on the life satisfaction of 176 Mexican American college women. A 3‐step hierarchical regression analysis indicated that independent self‐construal, CDSE, and fewer perceived educational barriers significantly predicted greater life satisfaction among Mexican American college women above and beyond the influence of socioeconomic status and generational status. These findings are consistent with SCTW and highlight the need for counselors and researchers to be aware of the role that self‐construal, CDSE, and perceived educational barriers can have on Mexican American women's life satisfaction. Implications for practice at the secondary‐school and university levels are discussed.     

A Method to Handle Zero Counts in the Multinomial Model

In the context of an objective Bayesian approach to the multinomial model, Dirichlet(a, …, a) priors with a < 1 have previously been shown to be inadequate in the presence of zero counts, suggesting that the uniform prior (a = 1) is the preferred candidate. In the presence of many zero counts, however, this prior may not be satisfactory either. A model selection approach is proposed, allowing for the possibility of zero parameters corresponding to zero count categories. This approach results in a posterior mixture of Dirichlet distributions and marginal mixtures of beta distributions, which seem to avoid the problems that potentially result from the various proposed Dirichlet priors, in particular in the context of extreme data with zero counts.     

Searching for self in a world of labels

Searching for Self is a performance poetry piece that demonstrates the difficulties of identity construction in contemporary life. The author challenges the ‘self’ and ‘other’ dichotomy, and in so doing she attempts to reduce the distance between the ‘client’ and ‘expert’; the researcher and researched; the service provider and service user; and theory and practice. The poems are linked to the authors’ experiences of being labeled with a disability.     

Transductive versions of the LASSO and the Dantzig Selector

Transductive methods are useful in prediction problems when the training dataset is composed of a large number of unlabeled observations and a smaller number of labeled observations. In this paper, we propose an approach for developing transductive prediction procedures that are able to take advantage of the sparsity in the high dimensional linear regression. More precisely, we define transductive versions of the LASSO (Tibshirani, 1996) and the Dantzig Selector (Candès and Tao, 2007). These procedures combine labeled and unlabeled observations of the training dataset to produce a prediction for the unlabeled observations. We propose an experimental study of the transductive estimators that shows that they improve the LASSO and Dantzig Selector in many situations, and particularly in high dimensional problems when the predictors are correlated. We then provide non-asymptotic theoretical guarantees for these estimation methods. Interestingly, our theoretical results show that the Transductive LASSO and Dantzig Selector satisfy sparsity inequalities under weaker assumptions than those required for the “original” LASSO.     

Model Checks in Inverse Regression Models with Convolution‐Type Operators

Abstract. We consider the problem of testing parametric assumptions in an inverse regression model with a convolution‐type operator. An L ₂ ‐type goodness‐of‐fit test is proposed which compares the distance between a parametric and a non‐parametric estimate of the regression function. Asymptotic normality of the corresponding test statistic is shown under the null hypothesis and under a general non‐parametric alternative with different rates of convergence in both cases. The feasibility of the proposed test is demonstrated by means of a small simulation study. In particular, the power of the test against certain types of alternative is investigated. Finally, an empirical example is provided, in which the proposed methods are applied to the determination of the shape of the luminosity profile of the elliptical galaxy NGC 5017.     

The social experience of physically disabled Australian university students

Research on the university experience of disabled students has focused on barriers in learning and teaching, while the social world of university has as yet gained little attention as a distinctive object of study. Here we examine social experience and socially imposed restrictions through the lenses of social capital and self-concept. A qualitative study investigated the formation of social capital and changes in self-concept amongst physically disabled Australian university students. Data were collected through semi-structured interviews and analysed using a grounded theory approach. The study found weak social attachments at university, but stronger attachments outside. Self-concept did not appear to be structured in any direct way by university-generated social capital, partly as a consequence of its weakness.     

Quantile regression and variable selection for the single-index model

In this paper, we propose a new full iteration estimation method for quantile regression (QR) of the single-index model (SIM). The asymptotic properties of the proposed estimator are derived. Furthermore, we propose a variable selection procedure for the QR of SIM by combining the estimation method with the adaptive LASSO penalized method to get sparse estimation of the index parameter. The oracle properties of the variable selection method are established. Simulations with various non-normal errors are conducted to demonstrate the finite sample performance of the estimation method and the variable selection procedure. Furthermore, we illustrate the proposed method by analyzing a real data set.