Goodness-of-Fit Tests Based on Correcting Moments of Entropy Estimators

In this article, we consider the entropy estimator introduced by Alizadeh Noughabi and Arghami (2010) and derive the nonparametric distribution function corresponding to our estimator as a piece-wise uniform distribution. We use the results to introduce goodness-of-fit tests for the normal and the exponential distributions. The critical values and powers for some alternatives are obtained by simulation. The powers of the proposed tests under various alternatives are compared with the competitors.     

Hybrid test for the hypothesis of symmetry

In recent years, McWilliams and Tajuddin have proposed new and more powerful non-parametric tests of symmetry for continuous distributions about a known center. In this paper, we propose a simple non-parametric two-stage procedure based on the sign test and a percentile-modified two-sample Wilcoxon test. The small-sample properties of this test, Tajuddin's test, McWilliams' test and a modified runs test of Modarres and Gastwirth are investigated in a Monte Carlo simulation study. The simulations indicate that, for a wide variety of asymmetric alternatives in the lambda family, the hybrid test is more powerful than are existing tests in the literature.     

Effects of Class Positions of Parents on Educational Attainment of Daughters and Sons*

Cet article évalue les effets de l'appartenance de la mère et du père à une classe - déterminée selon la théorie marxiste des classes -sur le niveau d'instruction de leurs enfants, garçons et filles, au Canada. Les données sont tirées d'un échantillon représentatif de Canadiens et de Canadiennes. Les analyses multivariables mon-trent que l'appartenance du père et de la mère à une classe influe sur le niveau d'instruction des enfants des deux sexes. Que le père ou la mère soit issu de la bourgeoisie, de la classe des dirigeants ou de la classe des spécialistes, l'enfant aura un niveau d'instruction plus élevé que celui dont les parents appartiennent à une autre classe. On a toutefois observé que seuls certains effets de l'appartenance à une classe étaient directs; les effets liés à l'appartenance à une classe semblent ne se manifester que partiellement dans les differences de niveau d'instruction des parents, qui sont liées à la classe à laquelle ils appartiennent. Les niveaux d'instruction de la mere et du père influent directement sur le niveau d'instruction des enfants des deux sexes, une fois neutralisés les effets de l'appartenance sociale des parents. De plus, les effets du niveau d'instruction du père et de la mère ont tendance à différer selon le sexe de l'enfant (le niveau d'études de la mère influe davantage sur celui de la fille et à l'inverse celui du père influe davantage sur celui du fils). Toutefois, cette tendance ne se vérifie pas en ce qui concerne les effets de l'appartenance des parents à une classe. Les analyses qui comparent les sous-échantillons d'âges indiquent que la double influence de l'appartenance des parents à une classe et de leur niveau d'instruction a diminué après les années soixante compara-tivement aux années précédentes. Les résultats sont interprétés à la lumière de la théorie du capital culturel. This paper assesses the effects of mothers' and fathers' class positions—measured in terms of Marxist class categories—on the educational attainment of male and female offspring in Canada. Our data are from a national representative sample of Canadians. Multivariate analyses show that, for offspring of both genders, the class positions of fathers and mothers influence educational attainment. Where either parent was a member of the bourgeois, managerial or expert class categories, this meant more education for the offspring than other class backgrounds. Only some proportions of the class effects were direct; the effects of class background appear to partially operate through differences in educational attainment of parents that are associated with parents' class positions. Mothers' and fathers' education levels continue to have comparatively strong positive relationships with educational attainment for offspring of both genders after controls for class categories of parents. Further, the effects of paternal and maternal education tend to be “same-sex directed” (mothers' education levels have stronger effects for daughters than for sons and vice versa for fathers' education). However, a similar pattern does not hold for the effects of parental class positions. Analyses comparing age sub-samples indicate that the influences of both parental class positions and parental education levels upon educational attainment of offspring have decreased in the post-1960 period compared with earlier years. The results are interpreted in terms of the theory of cultural capital.     

Change Point Estimation of Multivariate Linear Profiles Under Linear Drift

In this paper, maximum likelihood estimators (MLE) for both step and linear drift changes in the regression parameters of multivariate linear profiles are developed. Performance of the proposed estimators is compared under linear drift changes in the regression parameters when a combined MEWMA and Chi-square control charts method signals an out-of-control condition. The effect of smoothing parameter of MEWMA control charts, missing data, and multiple drift changes on the performance of the both estimators is also evaluated. The application of the proposed estimators is also investigated thorough a numerical example resulted from a real case.     

Identification of outlying height and weight data in the Iranian National Health Survey 1990-92

Data on the weights and heights of children 2-18 yeas old in Iran were obtained in a National Health Survey of 10 660 families in 1990-92. Data were 'cleaned' in 1 year age groups. After excluding gross outliers by inspection of bivariate scatter plots, Box-Cox power transformations were used to normalize the distributions of height and weight. If a multivariate Box-Cox power transformation to normality exists, then it is equivalent to normalizing the data variable by variable. After excluding gross outliers, exclusions based on the Mahalanobis distance were almost identical to those identified by Hadi's iterative procedure, because the percentages of outliers were small. In all, 1% of the observations were gross outliers and a further 0.4% were identified by multivariate analysis. Review of records showed that the outliers identified by multivariate analysis resulted from data-processing errors. After transformation and 'cleaning', the data quality was excellent and suitable for the construction of growth charts.     

Procrustes shape analysis of triangulations of a two coloured point pattern

Consider a set of points in the plane with Gaussian perturbations about a regular mean configuration in which a Delaunay triangulation of the mean of the process is comprised of equilateral triangles of the same size. The points are labelled at random as black or white with variances of the perturbations possibly dependent on the colour. By investigating triangle subsets (with four sets of possible colour labels for the vertices) in detail we propose various test statistics based on a Procrustes shape analysis. A simulation study is carried out to investigate the relative merits and the adequacy of the approximations used in the distributional results, as well as a comparison with simulation methods based on nearest-neighbour distances. The methodology is applied to an investigation of regularity in human muscle fibre cross-sections.     

Nonparametric mixture analysis of rock crab of the genus Leptograpsus

A nonparametric mixture analysis has been applied to study morphological characteristics of Leptograpsus crab. Two Gaussian models were also considered, one with the assumption of independent components and one with arbitrary relationship between the components. The three models then fitted to several combination of variables based on selecting different morphological characteristics. It has been observed that the nonparametric method gave the best result overall.     

An Information Theoretic Framework for Exploratory Multivariate Market Segmentation Research*

State-of-the-art market segmentation often involves simultaneous consideration of multiple and overlapping variables. These variables are studied to assess their relationships, select a subset of variables which best represent the subgroups (segments) within a market, and determine the likelihood of membership of a given individual in a particular segment. Such information, obtained in the exploratory phase of a multivariate market segmentation study, leads to the construction of more parsimonious models. These models have less stringent data requirements while facilitating substantive evaluation to aid marketing managers in formulating more effective targeting and positioning strategies within different market segments. This paper utilizes the information-theoretic (IT) approach to address several issues in multivariate market segmentation studies. A marketing data set analyzed previously is employed to examine the suitability and usefulness of the proposed approach [12]. Some useful extensions of the IT framework and its applications are also discussed.     

Correction to: The Weibull Fréchet distribution and its applications

Afify et al. [The Weibull Fréchet distribution and its applications, J. Appl. Stat., 43 (2016), pp. 2608–2626] defined and studied a new four-parameter lifetime model called the Weibull Fréchet distribution. They made some mistakes in presenting the log-likelihood function and the components of score vector. In this note, we will correct them.     

Majorization and the spectral radius of starlike trees

A starlike tree is a tree with exactly one vertex of degree greater than two. The spectral radius of a graph G, that is denoted by \(\lambda (G)\), is the largest eigenvalue of G. Let k and \(n_1,\ldots ,n_k\) be some positive integers. Let \(T(n_1,\ldots ,n_k)\) be the tree T (T is a path or a starlike tree) such that T has a vertex v so that \(T{\setminus } v\) is the disjoint union of the paths \(P_{n_1-1},\ldots ,P_{n_k-1}\) where every neighbor of v in T has degree one or two. Let \(P=(p_1,\ldots ,p_k)\) and \(Q=(q_1,\ldots ,q_k)\), where \(p_1\ge \cdots \ge p_k\ge 1\) and \(q_1\ge \cdots \ge q_k\ge 1\) are integer. We say P majorizes Q and let \(P\succeq _M Q\), if for every j, \(1\le j\le k\), \(\sum _{i=1}^{j}p_i\ge \sum _{i=1}^{j}q_i\), with equality if \(j=k\). In this paper we show that if P majorizes Q, that is \((p_1,\ldots ,p_k)\succeq _M(q_1,\ldots ,q_k)\), then \(\lambda (T(q_1,\ldots ,q_k))\ge \lambda (T(p_1,\ldots ,p_k))\).