A note on expressing wilks’ a as the product of independent beta variables

The purpose of this note is to show that the null distribution of Wilks’ A can be expressed as the product of p independent beta variables regardless of the relationship of p and q, where p is the number of variables and q is the degrees of freedom associated with the hypothesis.     

A note on Morris’ bound for search designs

A lower bound is given for the number of experimental runs required in search designs for two-level orthogonal array of strength one.     

A note on the posterior inference for the Yule–Simon distribution

The Yule–Simon distribution has been out of the radar of the Bayesian community, so far. In this note, we propose an explicit Gibbs sampling scheme when a Gamma prior is chosen for the shape parameter. The performance of the algorithm is illustrated with simulation studies, including count data regression, and a real data application to text analysis. We compare our proposal to the frequentist counterparts showing better performance of our algorithm when a small sample size is considered.     

A note on the equality of the OLSE and the BLUE of the parametric function in the general Gauss–Markov model

In this note we consider the equality of the ordinary least squares estimator (OLSE) and the best linear unbiased estimator (BLUE) of the estimable parametric function in the general Gauss–Markov model. Especially we consider the structures of the covariance matrix V for which the OLSE equals the BLUE. Our results are based on the properties of a particular reparametrized version of the original Gauss–Markov model.      

A note on “Data depths satisfying the projection property”

This note is on two theorems in a paper by Rainer Dyckerhoff (Allg. Stat. Arch. 88:163–190, 2004). We state a missing condition in Theorem 3. On the other hand, Theorem 2 can be weakened.     

A simplified proof of a theorem on the difference of the moore–penrose inverses of two positive semi–difinte matrices

Simplified proofs are given of a standard result that establishes positive semi–definiteness of the difference of the inverses of two non–singular matrices, and of the extension of this result by Milliken and Akdeniz (1977) to the difference of the Moore–Penrose inverse of two singular matrices.     

A note on the Jarque–Bera normality test for GARCH innovations

In this paper, we consider the validity of the Jarque–Bera normality test whose construction is based on the residuals, for the innovations of GARCH (generalized autoregressive conditional heteroscedastic) models. It is shown that the asymptotic behavior of the original form of the JB test adopted in this paper is identical to that of the test statistic based on true errors. The simulation study also confirms the validity of the original form since it outperforms other available normality tests.     

A Note on Application of Nesterov’s Method in Solving Lasso-Type Problems

Many different algorithms have been proposed to solve penalized variable selection problems, in particular lasso and its variants, including group lasso and fused lasso. Loss functions other than quadratic loss also pose significant challenges for finding efficient solvers. Here, we note that Nesterov’s method can be used to transform an optimization problem with general smooth convex loss to quadratic loss with identity covariate matrix in each iteration. After such reduction, the problem becomes much easier to solve or even can be solved in closed form in some cases. We perform some simulations and apply our implementation to phoneme discrimination.     

A note on consistent estimation of Kullback–Leibler discrepancy in Poisson regression

A recent theorem by Hannig and Lee on consistency of their estimator of Kullback–Leibler discrepancy is re-proved under assumptions suitably modified to correct a fault in the original proof.     

EEG in the diagnostics of Alzheimer’s disease

Dementia caused by Alzheimer’s disease (AD) is worldwide one of the main medical and social challenges for the next years and decades. An automated analysis of changes in the electroencephalogram (EEG) of patients with AD may contribute to improving the quality of medical diagnoses. In this paper, measures based on uni- and multi-variate spectral densities are studied in order to measure slowing and, in greater detail, reduced synchrony in the EEG signals. Hereby, an EEG segment is interpreted as sample of a (weakly) stationary stochastic process. The spectral density was computed using an indirect estimator. Slowing was considered by calculating the spectral power in predefined frequency bands. As measures for synchrony between single EEG signals, we analyzed coherences, partial coherences, bivariate and conditional Granger causality; for measuring synchrony between groups of EEG signals, we considered coherences, partial coherences, bivariate and conditional Granger causality between the respective first principal components of each group, and dynamic canonic correlations. As measure for local synchrony within a group, the amount of variance explained by the respective first principal component of static and dynamic principal component analysis was investigated. These measures were exemplarily computed for resting state EEG recordings from 83 subjects diagnosed with probable AD. Here, the severity of AD is quantified by the Mini Mental State Examination score.     

Tukey’s M-estimator of the Poisson parameter with a special focus on small means

We treat robust M-estimators for independent and identically distributed Poisson data. We introduce modified Tukey M-estimators with bias correction and compare them to M-estimators based on the Huber function as well as to weighted likelihood and other estimators by simulation in case of clean data and data with outliers. In particular, we investigate the problem of combining robustness and high efficiencies at small Poisson means caused by the strong asymmetry of such Poisson distributions and propose a further estimator based on adaptive trimming. The advantages of the constructed estimators are illustrated by an application to smoothing count data with a time varying mean and level shifts.     

A note on bootstrap and other empirical procedures for testing linear hypotheses ’without normality

For testing linear hypotheses without the assumption of normal distributions besides the asymptotically optimal test there exists a lot of possibilities to construct em¬pirical procedures by approximating the unknown distribution of the test statistic or some of its parameters from the sample itself. This note contains comparisons of some of such procedures for small samples. In the easiest case of an unknown, mean in a small simulation study there the actual significance level is compared with the nominal level a. Two empiri¬cal procedures seem to be as good as the asymptotical procedure while the others, including a bootstrap procedure, seem to be unreliable     

Extended tables of the distribution of friedman’ s s-statistic in the two-way layout

Friedman’s (1937, 1940) S-statistic is designed to test the hypothesis that there is no treatment effect in a randomized-block design with k treatments and n blocks. In this paper we give tables of the null distribution of S for k = 5, n = 6(1)8, and for k = 6, n = 2(1)6. Computational details are discussed.     

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.     

On the asymptotic bias of grenander’s mode estimator

Grenander introduced a direct estimator of the mode for a large class of densities. This note considers a large subclass of these densities for which Grenander’s estimator is asymptotically biased. Some of the distributions from this subclass include the F, gamma, and beta for which asymptotic expressions for the bias are given. To reduce the bias, it is recommended to choose larger values for one of the parameters of the estimator when the underlying distribution is nonsymmetric.     

A note on scheffé's method of deriving confidence sets for directions and ratios of normals

Scheffé (1970) introduced a method for deriving confidence sets for directions and ratios of normals. The procedure requires use of an approximation and Scheffé provided evidence that the method performs well for cases in which the variances of the random deviates are known. This paper extends Scheffé's numerical integrations to the case of unknown variances. Our results indicate that Scheffé's method works well when variances are unknown     

A generalization of Turnbull’s estimator for nonparametric estimation of the conditional survival function with interval-censored data

Simple nonparametric estimates of the conditional distribution of a response variable given a covariate are often useful for data exploration purposes or to help with the specification or validation of a parametric or semi-parametric regression model. In this paper we propose such an estimator in the case where the response variable is interval-censored and the covariate is continuous. Our approach consists in adding weights that depend on the covariate value in the self-consistency equation proposed by Turnbull (J R Stat Soc Ser B 38:290–295, 1976), which results in an estimator that is no more difficult to implement than Turnbull’s estimator itself. We show the convergence of our algorithm and that our estimator reduces to the generalized Kaplan–Meier estimator (Beran, Nonparametric regression with randomly censored survival data, 1981) when the data are either complete or right-censored. We demonstrate by simulation that the estimator, bootstrap variance estimation and bandwidth selection (by rule of thumb or cross-validation) all perform well in finite samples. We illustrate the method by applying it to a dataset from a study on the incidence of HIV in a group of female sex workers from Kinshasa.