Csiszar’s ϕ-divergences for testing the order in a Markov chain

x ₁, ..., x _n+r can be treated as the sample values of a Markov chain of order r or less (chain in which the dependence extends over r+1 consecutive variables only), and consider the problem of testing the hypothesis H ₀ that a chain of order r− 1 will be sufficient on the basis of the tools given by the Statistical Information Theory: _ϕ-Divergences. More precisely, if p _{a 1 ....., a r}: _{a r +1} denotes the transition probability for a r ^th order Markov chain, the hypothesis to be tested is H ₀:p _{a 1 ....., a r}: _{a r +1} = p _{a 2 ....., a r}: _{a r +1}, a _i ∈{1, ..., s}, i = 1, ..., r + 1 The tests given in this paper, for the first time, will have as a particular case the likelihood ratio test and the test based on the chi-squared statistic. Received: August 3, 1998; revised version: November 25, 1999     

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.     

Non-nested model selection based on the quantiles and it’s application in time series

We consider the problem of model selection based on quantile analysis and with unknown parameters estimated using quantile leasts squares. We propose a model selection test for the null hypothesis that the competing models are equivalent against the alternative hypothesis that one model is closer to the true model. We follow with two applications of the proposed model selection test. The first application is in model selection for time series with non-normal innovations. The second application is in model selection in the NoVas method, short for normalizing and variance stabilizing transformation, forecast. A set of simulation results also lends strong support to the results presented in the paper.     

A note on the generalisation of cochran’s theorem

Khatri (1968) has extended Cochran’s theorem (1934) to matrices which are not necessarily symmetric. An alternative proof of the theorem is furnished here with some generalization with respect to one of Khatri’s conditions.     

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.     

Overview of Friedman’s Test and Post-hoc Analysis

When the null hypothesis of Friedman’s test is rejected, there is a wide variety of multiple comparisons that can be used to determine which treatments differ from each other. We will discuss the contexts where different multiple comparisons should be applied, when the population follows some discrete distributions commonly used to model count data in biological and ecological fields. Our simulation study shows that sign test is very conservative. Fisher’s LSD and Tukey’s HSD tests computed with ranks are the most liberal. Theoretical considerations are illustrated with data of the Azores Buzzard (Buteo buteo rothschildi) population from Azores, Portugal.     

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.     

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.     

Estimators based on trimmed Kendall’s tau in multivariate copula models

A common method of estimating the parameters of dependency in multivariate copula models is by maximum likelihood principle, termed as Inference From Marginals (IFM); see Joe (1997)  [13]. To avoid possible misspecification of the marginal distributions, some authors suggest rank-based procedures for estimating the parameters of dependency in a multivariate copula model. A standard approach for this problem is through maximization of the pseudolikelihood, as discussed in Genest et al. (1995)  [9] and Shih and Louis (1995)  [23]. Alternative estimators based on the inversion of two multivariate extensions of Kendall’s tau, due to Kendall and Babington Smith (1940)  [14] and Joe (1990)  [12], were used in Genest et al. (2011)  [10]. In the literature, dependency of data was considered in the whole data space. However, it may be better to divide the data set into two distinct sets, lower and higher than a threshold, and then evaluate the dependency parameters in these sets. In this way, we may have different dependency parameters in these sets which may shed additional light. For example, in drought analysis, precipitation and minimum temperature may be modeled using copulas in which case we can infer that dependency between precipitation and minimum temperature are severe when they are less than a certain threshold. In this paper, after introducing trimmed Kendall’s tau when such a threshold is imposed, we consider modeling dependency using it as a measure. Asymptotic distribution of trimmed Kendall’s tau is also investigated, and a test for the null hypothesis of equality between Kendall’s tau and trimmed Kendall’s tau is constructed. We can use this hypothesis testing procedure for testing the hypothesis that data are dependent before a threshold value and are independent after the threshold. An explicit form of the asymptotic distribution of trimmed Kendall’s tau and of the mentioned test statistic are also derived for some special families of copulas. Finally, the results of a simulation study and an illustrative example are provided.     

The Consumer’s Risk and Costs in Zero-Acceptance Number Sampling

The primary purpose of sampling inspection is the protection of consumer’s interests. Although under simple cost models, sampling inspection never serves the producer’s interest, some form of sampling inspection can be beneficial to the consumer under the same assumptions. We consider the case of isolated lot inspection and examine the consumer risk, economic sample design, and errors in the inspection process. Acceptance sampling is shown to be cost-effective to the consumer whenever the lot quality is less than perfect, and even for perfect lot quality in the presence of inspection errors.     

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.     

Authors’ response: on the role of data,statistics and decisions in a pandemic

AStA Advances in Statistical Analysis -     

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.     

A Note on Estimation of a Distribution Function in a Nonparametric Set-up Using Stein’s Shrinkage Estimation Technique

Based on Stein’s famous shrinkage estimation of a multivariate normal distribution, we propose a new type of estimators of the distribution function of a random variable in a nonparametric setup. The proposed estimators are then compared with the empirical distribution function, which is the best equivariant estimator under a well-known loss function. Our extensive simulation study shows that our proposed estimators can perform better for moderate to large sample sizes.