Nonparametric density estimates consistent of the order of <Emphasis Type="Italic">n</Emphasis><Superscript>−1/2</Superscript> in the <Emphasis Type="Italic">L</Emphasis><Subscript>1</Subscript>–norm

We introduce an approximate minimum Kolmogorov distance density estimate of a probability density f₀ on the real line and study its rate of consistency for n. We define a degree of variations of a nonparametric family of densities containing the unknown f₀. If this degree is finite then the approximate minimum Kolmogorov distance estimate is consistent of the order of n^–1/2 in the L₁-norm and also in the expected L₁-norm. Comparisons with two other criteria leading to the same order of consistency are given.Received June 2002     

The primary schools (<Emphasis Type="Italic">sibyans</Emphasis>) in Ottoman Cyprus during the Tanzimat <Emphasis Type="Italic">reform</Emphasis> era (1839–1878)

The nineteenth century is a century of reform for the Ottoman state. The Tanzimat reforms hold a unique place in the Ottoman history of modernization. During the Tanzimat period (1839–1878), the state underwent a restructuring process in almost all of its institutions to establish a centralized modern state and many new institutions were established. The Ottomans paid special attention to education to train the new generation required for the continuity of modernization and the centralized bureaucratic structure. While they opened modern high schools and higher education institutions, they attempted to reform the existing s?byan schools, which were the primary education institutions. This process of restructuring education was also carried out in Cyprus, which had been an Ottoman island since 1571. These attempts remained restricted to efforts to increase the number of s?byan schools in Cyprus. There was a failure to replace the religious education given at schools with a secular program, curriculum or modern education system based on education management. This situation also adversely affected the quality of education at the Rü?tiye School in Nicosia, the first and only modern secondary school of the period and which was opened in Nicosia in 1864.     

Hotelling’s <Emphasis Type="Italic">T</Emphasis><Superscript>2</Superscript> control chart with two adaptive sample sizes

Some quality control schemes have been developed when several related quality characteristics are to be monitored. The familiar multivariate process monitoring and control procedure is the Hotelling’s T ² control chart for monitoring the mean vector of the process. It is a direct analog of the univariate shewhart [`(x)]{\bar{x}} chart. As in the case of univariate, the ARL improvements are very important particularly for small process shifts. In this paper, we study the T ² control chart with two-state adaptive sample size, when the shift in the process mean does not occur at the beginning but at some random time in the future. Further, the occurrence time of the shift is assumed to be exponentially distributed random variable.     

Balancing Employee Rights and Responsibilities in Sexual Harassment Cases Following <Emphasis Type="Italic">Faragher</Emphasis> and <Emphasis Type="Italic">Ellerth</Emphasis>: An Employer’s Perspective

In 1998, the United States Supreme Court issued two opinions that delicately balanced the responsibilities of employers and employees in fulfilling Title VIIs goal of eliminating discrimination in the workplace. Those two opinions—Faragher v. City of Boca Raton and Burlington Industries,Inc. v. Ellerth—require employers to implement measures to prevent harm to their employees, but also require employees to take advantage of those measures to avoid harm. Numerous articles have evaluated the responsibilities of the employer under Faragher and Ellerth. But little, ifany, emphasis has been placed on the responsibilities of the employee. This article evaluates the role of the employee in avoiding harm and, analyzing recent decisions from the Second and Third Circuits, argues that the employees responsibilities shouldplay an integral part in evaluating sexual harassment liability.     

Elfving’s method for <Emphasis Type="Italic">m</Emphasis>-dimensional models

Elfvings method is a well known graphical procedure for obtaining c-optimal designs. Although the method is valid for any dimension it is rarely used for more than two parameters. Its usefulness seems to be constrained by the difficulty on the construction of the Elfving set. In this paper a computational procedure for finding c-optimal designs using Elfvings method for more than two dimensions is provided. It is suitable for any model, achieving an efficient performance for three or four dimensional models. The procedure can be implemented in most programming languages.Acknowledgments. The authors would like to thank Dr. Torsney for his helpful comments. This research was supported by a grant from JCyL SA004/01.     

An empirical analysis of the <Emphasis Type="Italic">Wall Street Journal’s</Emphasis> SmartMoney fund screen

We examine mutual funds that appeared in the Wall Street Journal’s SmartMoney Fund Screen column from September 2004 through July 2009. We find that the majority of funds listed do not have Morningstar’s highest five star rating. Regardless of Morningstar rating, the average prepublication performance of the funds is significantly higher than the benchmarks used to measure performance. Post publication, fund performance declines, and the decline is statistically significant across our performance measures. However, additional tests indicate that the SmartMoney funds which have a three or four star rating from Morningstar are better investment values than corresponding five star Morningstar funds with the same prospectus objective and expense ratio.     

The <Emphasis Type="Italic">K</Emphasis><Subscript>ϕ</Subscript>-Divergence Statistic for Categorical Data Problems

In this work a new family of statistics based on K _ϕ -divergence (Burbea and Rao (1982) On the convexity of divergence measures based on entropy function. IEEE Trans Inf Theory 28, 489–495) are obtained by either replacing both distributions involved in the argument by their samples estimates or replacing one distribution and considering the other as given. Asymptotic distributions of these statistics are obtained and test for goodness-of-fit and for homogeneity with a known distribution, can be constructed on the basis of these results     

Preliminary test ridge regression estimators with student’s <Emphasis Type="Italic">t</Emphasis> errors and conflicting test-statistics

The preliminary test ridge regression estimators (PTRRE) based on the Wald (W), Likelihood Ratio (LR) and Lagrangian Multiplier (LM) tests for estimating the regression parameters has been considered in this paper. Here we consider the multiple regression model with student t error distribution. The bias and the mean square errors (MSE) of the proposed estimators are derived under both null and alternative hypothesis. By studying the MSE criterion, the regions of optimality of the estimators are determined. Under the null hypothesis, the PTRRE based on LM test has the smallest risk followed by the estimators based on LR and W tests. However, the PTRRE based on W test performs the best followed by the LR and LM based estimators when the parameter moves away from the subspace of the restrictions. The conditions of superiority of the proposed estimators for both shrinkage parameter, k and the departure parameter, are provided. Some tables for the maximum and minimum guaranteed efficiency of the proposed estimators have been given, which allows us to determine the optimum level of significance corresponding to the optimum estimator. Finally, we conclude that the estimator based on Wald test dominates the other two estimators in the sense of having highest minimum guaranteed efficiency.     

Using <Emphasis Type="Italic">K</Emphasis>-means method and spectral clustering technique in an outfitter’s value analysis

This study applies K-means method and spectral clustering technique in the customer data analysis of an outfitter in Taipei City, Taiwan. The data set contains transaction records of 551 customers from April 2004 to March 2006. The differences between the two clustering techniques mentioned here are significant. K-means method is more capable of dealing with linear separable input, while spectral clustering technique might have the advantage in non-linear separable input. Thus, it would be of interest to know which clustering technique performs better in a real-world case of evaluating customer value when the type of input space is unknown. By using cluster quality assessment, this study found that spectral clustering technique performs better than K-means method. To summarize the analysis, this study also suggests marketing strategies for each cluster based on the results generated by spectral clustering technique.     

Gender as a moderator of the relationship between Facebook<Superscript>®</Superscript> addiction and self-efficacy for learning in a college sample: the mediating effect of deliberative belief

The present study explores the mediating role of deliberative belief and the moderating role of gender on the relationships between Facebook^® addiction and self-efficacy for learning among 690 college students. Self-administered questionnaires, including a Facebook^® Addiction Scale, a Deliberative Belief Scale and a Self-efficacy for Learning Scale were utilized to collect the data. The results indicated that there was a negatively significant relationship between Facebook^® addiction and deliberative belief (β = ? 0.25, p < .001) and a positively significant relationship between deliberative belief and self-efficacy for learning (β = + 0.53, p < .001). A multigroup analysis using structure equation modeling also demonstrated that gender moderated the relationship between Facebook^® addiction and deliberative belief. The findings revealed that high Facebook^® addiction was associated with decreased deliberative belief, which was further associated with decreased self-efficacy for learning. Moreover, Facebook^® addiction tends to significantly reduce the self-efficacy for learning for male students but not for female students.