On bahadur's representation of quantiles in nonregular cases

The paper considers Bahadur’s representation of quantiles (see Bahadur (1966), Ann. Math. Statist., 37, 577-580) in cases where the usual assumptions regarding the existence and boundedness of the derivatives of the distribution function in a neighbourhood of the population quantile(s) of interest are not met. Following Kiefer((1967), Ann. Math. Statist., 38, 1323-1342) we provide an exact order of the remainder term in Bahadur’s representation. A weaker result regarding the order of the remainder term is also provided under weaker regularity assumptions.     

Asian images portrayed in the websites of US higher education institutions

Using a purposive sample of 265 US colleges and universities, the analysis identified 378 Asian models from 8,319 human models. Results showed Asian students to be under-represented on the web compared to their proportion in the student body, whereas African Americans were proportionately represented. Instead of stereotypical portrayals, Asians appeared neutral in terms of power positions.     

知识分类理论与学生书面表达障碍分析

基于对学生书面语言表达障碍进行的心理分析,通过知识分类理论,作者发现,目前大学生英语作文能力的表现在写作的各个环节都不同程度地存在陈述性知识缺乏,从而影响运用程序性知识解决作文过程中面临的种种具体问题。提出进行以阅读为中心的多方位的陈述性知识教学和控制半开放的程序性知识训练,使大学英语作文教学做到有的放矢。     

Exact Non-parametric Confidence Intervals for Quantiles with Progressive Type-II Censoring

It is shown how various exact non-parametric inferences based on order statistics in one or two random samples can be generalized to situations with progressive type-II censoring, which is a kind of evolutionary right censoring. Ordinary type-II right censoring is a special case of such progressive censoring. These inferences include confidence intervals for a given parent quantile, prediction intervals for a given order statistic of a future sample, and related two-sample inferences based on exceedance probabilities. The proposed inferences are valid for any parent distribution with continuous distribution function. The key result is that each observable uncensored order statistic that becomes available with progressive type-II censoring can be represented as a mixture with known weights of underlying ordinary order statistics. The importance of this mixture representation lies in that various properties of such observable order statistics can be deduced immediately from well-known properties of ordinary order statistics.     

Tracking Edges, Corners and Vertices in an Image

Abstract.  In a range of imaging problems, particularly those where the images are of man-made objects, edges join at points which comprise three or more distinct boundaries between textures. In such cases the set of edges in the plane forms what a mathematician would call a planar graph. Smooth edges in the graph meet one another at junctions, called 'vertices', the 'degrees' of which denote the respective numbers of edges that join there. Conventional image reconstruction methods do not always draw clear distinctions among different degrees of junction, however. In such cases the algorithm is, in a sense, too locally adaptive; it inserts junctions without checking more globally to determine whether another configuration might be more suitable. In this paper we suggest an alternative approach to edge reconstruction, which combines a junction classification step with an edge-tracking routine. The algorithm still makes its decisions locally, so that the method retains an adaptive character. However, the fact that it focuses specifically on estimating the degree of a junction means that it is relatively unlikely to insert multiple low-degree junctions when evidence in the data supports the existence of a single high-degree junction. Numerical and theoretical properties of the method are explored, and theoretical optimality is discussed. The technique is based on local least-squares, or local likelihood in the case of Gaussian data. This feature, and the fact that the algorithm takes a tracking approach which does not require analysis of the full spatial data set, mean that it is relatively simple to implement.     

Approximate Representation of Estimators in Constrained Regression Problems

The estimators of inequality-constrained regression problems can be computed by iterative algorithms of mathematical programming, but they do not have analytical expressions in terms of the given data. This situation brings obstacles to further studies on the constrained regression. In this paper we derive approximate representations of the estimators with a remainder of magnitude ( N ⁻¹ log log N )^1/2. From these representations one can clearly see the concrete structure of the estimators of these problems. It will be very helpful for further regression analysis.     

Robust modeling using the generalized epsilon-skew-t distribution

In this paper, an alternative skew Student-t family of distributions is studied. It is obtained as an extension of the generalized Student-t (GS-t) family introduced by McDonald and Newey [10]. The extension that is obtained can be seen as a reparametrization of the skewed GS-t distribution considered by Theodossiou [14]. A key element in the construction of such an extension is that it can be stochastically represented as a mixture of an epsilon-skew-power-exponential distribution [1] and a generalized-gamma distribution. From this representation, we can readily derive theoretical properties and easy-to-implement simulation schemes. Furthermore, we study some of its main properties including stochastic representation, moments and asymmetry and kurtosis coefficients. We also derive the Fisher information matrix, which is shown to be nonsingular for some special cases such as when the asymmetry parameter is null, that is, at the vicinity of symmetry, and discuss maximum-likelihood estimation. Simulation studies for some particular cases and real data analysis are also reported, illustrating the usefulness of the extension considered.     

Geometric approach to the skewed normal distribution

The representations of the skewed normal distribution given in Propositions 1–4 in Genton (Ed., 2004) are considered here from a unified geometric point of view and are, based upon this, generalized in two respects. On the one hand, the four concrete representations motivate us for a unified and much more general algebraic–geometric representation of the skewed normal distribution (Theorems 1 and 2 as well as Remarks 2 and 3); on the other hand, the mentioned representations are generalized to the elliptically contoured case (Propositions and Corollaries 1c–4c).     

Defending the American Dream: Coverage of the Jonathan Pollard Spy Case

This article contemplates the journalistic coverage of American espionage as an attempt to maintain consonance with broader cultural discourses about what it means to be an American. Tracking the American press coverage of the Jonathan Pollard spy case, the article demonstrates that the press turns espionage into a phenomenon upholding fundamental American beliefs in openness, sincerity, and straightforwardness. It shows that, rather than represent espionage as a phenomenon embodying deceit, secrecy, and immoral action, the press turns espionage into a phenomenon that communicates that one is what one says one is and that one's self presentation reflects one's insides. Ultimately, however, this representation of espionage undermines a full understanding of how—and why—spying works in culture.     

Ranking sets additively in decisional contexts: an axiomatic characterization

Ranking finite subsets of a given set X of elements is the formal object of analysis in this article. This problem has found a wide range of economic interpretations in the literature. The focus of the article is on the family of rankings that are additively representable. Existing characterizations are too complex and hard to grasp in decisional contexts. Furthermore, Fishburn (1996), Journal of Mathematical Psychology 40, 64–77 showed that the number of sufficient and necessary conditions that are needed to characterize such a family has no upper bound as the cardinality of X increases. In turn, this article proposes a way to overcome these difficulties and allows for the characterization of a meaningful (sub)family of additively representable rankings of sets by means of a few simple axioms. Pattanaik and Xu’s (1990), Recherches Economiques de Louvain 56, 383–390) characterization of the cardinality-based rule will be derived from our main result, and other new rules that stem from our general proposal are discussed and characterized in even simpler terms. In particular, we analyze restricted-cardinality based rules, where the set of “focal” elements is not given ex-ante; but brought out by the axioms.