Test of Independence for Baker’s Bivariate Distributions

Baker (2008 Baker, R. (2008). An order-statistics-based method for constructing multivariate distributions with fixed marginals. Journal of Multivariate Analysis 99: 2312–2327.[Crossref], [Web of Science ®] , [Google Scholar]) introduced a new method for constructing multivariate distributions with given marginals based on order statistics. In this paper, we provide a test of independence for a pair of absolutely continuous random variables (X, Y) jointly distributed according to Baker’s bivariate distributions. Our purpose is to test the hypothesis that X and Y are independent versus the alternative that X and Y are positively (negatively) quadrant dependent. The asymptotic distribution of the proposed test statistic is investigated. Also, the powers of the proposed test and the class of distribution-free tests proposed by Kochar and Gupta (1987 Kochar, S. G., Gupta, R. P. (1987). Competitors of Kendall-tau test for testing independence against positive quadrant dependence. Biometrika 74(3): 664–666.[Crossref], [Web of Science ®] , [Google Scholar]) are compared empirically via a simulation study.     

Beall’s List and Cabell’s Blacklist: A Comparison of Two Lists of Predatory OA Journals

Abstract

This study uses systematic random sampling to compare the content of “Beall’s List of Predatory Journals and Publishers” and “Cabell’s Blacklist” of journals. The Beall’s List data was generated from its new site that maintains a new list besides the original list. It found that 28.5% Beall’s List sample publishers are out of business, some Cabell’s Blacklist journals have become ceased. The main takeaway is that among the Beall’s List sample publishers with a working website for journal publishing, only 31.8% can be found on Cabell’s Blacklist.     

Efficiency and robustness of hogg’s adaptive trimmed means

The adaptive trimmed means of Hogg (1974) and modified by De Wet and van Wvk (1978) are studied in this paper for finite samples. They are shown to have good intervals and afficiency Properties for Sample sizes 20 and larger Confidence intervals pased on these estimator are also considered and found to be fairly ro-bust for sample sizes 40 and larger.     

Forecasting Study of Shanghai’s and Shenzhen’s Stock Markets Using a Hybrid Forecast Method

In this article, a novel hybrid method to forecast stock price is proposed. This hybrid method is based on wavelet transform, wavelet denoising, linear models (autoregressive integrated moving average (ARIMA) model and exponential smoothing (ES) model), and nonlinear models (BP Neural Network and RBF Neural Network). The wavelet transform provides a set of better-behaved constitutive series than stock series for prediction. Wavelet denoising is used to eliminate some slight random fluctuations of stock series. ARIMA model and ES model are used to forecast the linear component of denoised stock series, and then BP Neural Network and RBF Neural Network are developed as tools for nonlinear pattern recognition to correct the estimation error of the prediction of linear models. The proposed method is examined in the stock market of Shanghai and Shenzhen and the results are compared with some of the most recent stock price forecast methods. The results show that the proposed hybrid method can provide a considerable improvement for the forecasting accuracy. Meanwhile, this proposed method can also be applied to analysis and forecast reliability of products or systems and improve the accuracy of reliability engineering.     

Notes on Kolassa’s Method for Estimating the Power of Wilcoxon–Mann–Whitney Test

The Kolassa method implemented in the nQuery Advisor software has been widely used for approximating the power of the Wilcoxon–Mann–Whitney (WMW) test for ordered categorical data, in which Edgeworth approximation is used to estimate the power of an unconditional test based on the WMW U statistic. When the sample size is small or when the sizes in the two groups are unequal, Kolassa’s method may yield quite poor approximation to the power of the conditional WMW test that is commonly implemented in statistical packages. Two modifications of Kolassa’s formula are proposed and assessed by simulation studies.     

Tail Probability Ratios of Normal and Student’s t Distributions

The ratio of normal tail probabilities and the ratio of Student’s t tail probabilities have gained an increased attention in statistics and related areas. However, they are not well studied in the literature. In this paper, we systematically study the functional behaviors of these two ratios. Meanwhile, we explore their difference as well as their relationship. It is surprising that the two ratios behave very different to each other. Finally, we conclude the paper by conducting some lower and upper bounds for the two ratios.     

Bayesian Analysis on a Noncentral Fisher–Student’s Hypersphere

Fisher succeeded early on in redefining Student’s t-distribution in geometrical terms on a central hypersphere. Intriguingly, a noncentral analytical extension for this fundamental Fisher–Student’s central hypersphere h-distribution does not exist. We therefore set to derive the noncentral h-distribution and use it to graphically illustrate the limitations of the Neyman–Pearson null hypothesis significance testing framework and the strengths of the Bayesian statistical hypothesis analysis framework on the hypersphere polar axis, a compact nontrivial one-dimensional parameter space. Using a geometrically meaningful maximal entropy prior, we requalify the apparent failure of an important psychological science reproducibility project. We proceed to show that the Bayes factor appropriately models the two-sample t-test p-value density of a gene expression profile produced by the high-throughput genomic-scale microarray technology, and provides a simple expression for a local false discovery rate addressing the multiple hypothesis testing problem brought about by such a technology.     

Probabilistic rounding and Sheppard’s correction

When rounded data are used in place of the true values to compute the variance of a variable or a regression line, the results will be distorted. Under suitable smoothness conditions on the distribution of the variable(s) involved, this bias, however, can be corrected with very high precision by using the well-known Sheppard’s correction. In this paper, Sheppard’s correction is generalized to cover more general forms of rounding procedures than just simple rounding, viz., probabilistic rounding, which includes asymmetric rounding and mixture rounding.     

Analysis of mutual funds’ management styles: a modeling,ranking and visualizing approach

A method to rank mutual funds according to their investment style measured with respect to the returns of a reference portfolio (benchmark) is introduced. It is based on a style analysis model estimating a mutual fund portfolio composition as well as the benchmark one. Starting from such compositions, it computes a proximity measure based on the L ₁ or L ₂ norm to assess the similarity between each mutual fund portfolio returns and the benchmark returns as well as between the returns of each benchmark constituent and that of the corresponding mutual fund constituent. To this purpose the mean integrated absolute error and the mean integrated squared error are computed to derive both a global ranking of mutual fund management styles and partial rankings expressing the over- (under-) weighting of each portfolio constituent. A visual inspection of the results emphasizing main differences in management styles is provided, using a parallel coordinates plot. Since a modeling, a ranking and a visualizing approach are integrated, the method is named MoRaViA. From the practitioners’ point of view, it allows the identification of a specific management style for each mutual fund, discriminating active management funds from passive management ones. To evaluate the effectiveness of MoRaViA, many sets of artificial portfolios are generated and an application on a set of equity funds operating in the European market is presented.     

A Generalization of Turnbull’s Estimator for Interval-Censored and Doubly Truncated Data

Nonparametric estimates of the conditional distribution of a response variable given a covariate are important for data exploration purposes. In this article, we propose a nonparametric estimator of the conditional distribution function in the case where the response variable is subject to interval censoring and double truncation. Using the approach of Dehghan and Duchesne (2011), the proposed method consists in adding weights that depend on the covariate value in the self-consistency equation of Turnbull (1976), which results in a nonparametric estimator. We demonstrate by simulation that the estimator, bootstrap variance estimation and bandwidth selection all perform well in finite samples.     

Modelling and research on manufacturer’s capacity of remanufacturing and recycling in closed-loop supply chain

This paper introduces and analyses the present situation of the electronic waste recycling at home and abroad. Involving manufacturers in the recycling process of supply chain as the dominant party and establishing the closed-loop supply chain system structure model of the waste electronic products recycling, the effects of remanufacturing capacity and recycling coefficient on the closed-loop supply chain recycling network are analysed by using system dynamics method. The simulation results show that, compared with the traditional supply chain, the total revenue of the supply chain under the recycling mode dominated by manufacturers has improved, that the increase of the remanufacturing capacity has promoted the growth of the electronic product's sales rate, which reaches a equilibrium when remanufacturing capacity is set as 0.36, and that the recycling efficiency of e-waste has improved significantly as the e-waste recycling coefficient constantly increased.     

Shuffle of min’s random variable approximations of bivariate copulas’ realization

The comonotonicity and countermonotonicity provide intuitive upper and lower dependence relationship between random variables. This paper constructs the shuffle of min’s random variable approximations for a given Uniform [0, 1] random vector. We find the two optimal orders under which the shuffle of min’s random variable approximations obtained are shown to be extensions of comonotonicity and countermonotonicity. We also provide the rate of convergence of these random vectors approximations and apply them to compute value-at-risk.     

Construction of closed interval for process capability indices Cpu,Cpl, and Spk based on Boole’s inequality and de Morgan’s laws

ABSTRACT

Considerable effort has been spent on the development of confidence intervals for process capability indices (PCIs) based on the sampling distribution of the PCI or the transferred PCI. However, there is still no definitive way to construct a closed interval for a PCI. The aim of this study is to develop closed intervals for the PCIs C_pu, C_pl, and S_pk based on Boole's inequality and de Morgan's laws. The relationships between different sample sizes, the significance levels, and the confidence intervals of the PCIs C_pu, C_pl, and S_pk are investigated. Then, a testing model for interval estimation for the PCIs C_pu, C_pl, and S_pk is built as a powerful tool for measuring the quality performance of a product. Finally, an applied example is given to demonstrate the effectiveness and applicability of the proposed method and the testing model.     

Simultaneous estimation of Cronbach’s alpha coefficients

The simultaneous estimation of Cronbachs alpha coefficients from q populations under the compound symmetry assumption is considered. In a multi-sample scenario, it is suspected that all the Cronbachs alpha coefficients are identical. Consequently, the inclusion of non-sample information (NSI) on the homogeneity of Cronbachs alpha coefficients in the estimation process may improve precision. We propose improved estimators based on the linear shrinkage, preliminary test, and the Steins type shrinkage strategies, to incorporate available NSI into the estimation. Their asymptotic properties are derived and discussed using the concepts of bias and risk. Extensive Monte-Carlo simulations were conducted to investigate the performance of the estimators.     

Critical values of Mandel’s h and k, the Grubbs and the Cochran test statistic

According to ISO 5725-2 (1994), measurement results obtained in an interlaboratory experiment are inspected for consistency by plotting Mandel’s h and k statistics and for outliers by application of the Grubbs test and the Cochran test. Critical values of these statistics for significance levels α=5% and α=1% and for some numbers p of laboratories and n of repeated measurements in the laboratories are supplied in ISO 5725-2 without reference to methods for their calculation. In this paper, exact formulae for the critical values of Mandel’s h and k and approximate formulae for the critical values of the Single Grubbs test, the Double Grubbs test and the Cochran test are derived.     

Lag Order and Critical Values of the Augmented Dickey–Fuller Test

Response surface analysis is used to obtain approximate finite-sample critical values for the augmented Dickey–Fuller (ADF) test. Previous studies estimating the critical values for the test have generally ignored their possible dependence on the lag order. This study shows that the lag order, in addition to the sample size, can affect the finite-sample behavior of the test. The result points to the importance of correcting for the effect of lag order in applying the ADF test.     

Lombardy’s local labour systems and foreign immigrants

The analysis highlights the relationship between the territorial distribution of foreigners in Lombardy and the economic space they occupy, territorially defined by the Local Labour Systems. In particular, using these units the study assesses the importance of ethnic networks and local labour market conditions in defining the varying concentration of foreign nationalities living in the territory.The research was partially supported by grants from CNR (99.01522.CT10). Preliminary findings have been presented at SIS (Societá Italiana di Statistica) Annual Meeting, Milano Bicocca, 2002     

A maxmin linear test of normal means and its application to lachin’s data

For stochastic ordering tests for normal distributions there exist two well known types of tests. One of them is based on the maximum likelihood ratio principle, the other is the most stringent somewhere most powerful test of Schaafsma and Smid(for a comprehensive treatment see Robertson, Wright and Dykstra(1988), for the latter test also Shi and Kudo(1987)). All these tests are in general numerically tedious. Wei, Lachin(1984)and particularly Lachin(1992)formulate a simple and easily computable test. However, it is not known so far for which sort of ordered alternatives his test is optimal

In this paper it is shown that his procedure is a maxmin test for reasonable subalternatives, provided the covariance matrix has nonnegative row sums. If this property is violated then his procedure can be altered in such a manner that the resul ting test again is a maxmin test. An example is glven where the modified procedure even in the least favourable case leads to a nontrifling increase in power. The fact that Lachins test resp. the modified version are maxmin tests on appropriate subalternatives amounts to the property that they are maxmin tests on subhypotheses which are relevant in practical applications.