A Nonparametric Test for Deviation from Randomness with Applications to Stock Market Index Data

The proposed test detects deviations from randomness, without a priori distributional assumption, when observations are not independent and identically distributed (i.i.d.), which is suitable for our motivating stock market index data. Departures from i.i.d. are tested by subdividing data into subintervals and then using a conditional probability measure within intervals as a binomial test. This nonparametric test is designed to detect deviations of neighboring observations from randomness when the dataset consists of time series observations. Simulation results and a comparison with Lo and MacKinlay's (1988 Lo, A. W. and MacKinlay, A. C. 1988. Stock market prices do not follow random walks: Evidence from a simple specification test. The Review of Financial Studies, 1: 41–66. [Crossref], [Web of Science ®] , [Google Scholar]) variance ratio test showed that our proposed test is a competitive alternative.     

Further Results on Order Statistics Generated by Two Simulation Methods

Uniform order statistics generated by two simulation methods are compared by means of Pitman’s measure of closeness. This measure, as a probability, is shown to be asymptotically 1/2. Some results are also established for fixed points of the cumulative distribution function (CDF) for a uniform order statistic. These fixed points are important for calculations involving the joint distribution of these order statistics.     

A Comparative Study of Different Methodologies for Fault Diagnosis in Multivariate Quality Control

Different methodologies for fault diagnosis in multivariate quality control have been proposed in recent years. These methods work in the space of the original measured variables and have performed reasonably well when there is a reduced number of mildly correlated quality and/or process variables with a well-conditioned covariance matrix. These approaches have been introduced by emphasizing their positive or negative virtues, generally on an individual basis, so it is not clear for the practitioner the best method to be used. This article provides a comprehensive study of the performance of diverse methodological approaches when tested on a large number of distinct simulated scenarios. Our primary aim is to highlight key weaknesses and strengths in these methods as well as clarifying their relationships and the requirements for their implementation in practice.     

McDonald's ωt,Cronbach's α, and Generalized θ for Composite Reliability of Common Factors Structures

In the common factor model for subtest scores, several reliability coefficients, including Cronbach's α, have been found to be biased. In this article, we introduce a new coefficient, θ_G, or Generalized θ, which is a generalized version of Armor's θ coefficient and is equal to the true reliability when the dimensions are orthogonal and the measures are parallel. We assessed the McDonald's ω_t, α, and θ_G in terms of mean bias, efficiency, and precision using a Monte Carlo simulation. θ_G outperformed ω_t when the factors were orthogonal or nearly orthogonal with low correlations between them.     

Clustering the mixed panel dataset using Gower's distance and k-prototypes algorithms

ABSTRACT

Panel datasets have been increasingly used in economics to analyze complex economic phenomena. Panel data is a two-dimensional array that combines cross-sectional and time series data. Through constructing a panel data matrix, the clustering method is applied to panel data analysis. This method solves the heterogeneity question of the dependent variable, which belongs to panel data, before the analysis. Clustering is a widely used statistical tool in determining subsets in a given dataset. In this article, we present that the mixed panel dataset is clustered by agglomerative hierarchical algorithms based on Gower's distance and by k-prototypes. The performance of these algorithms has been studied on panel data with mixed numerical and categorical features. The effectiveness of these algorithms is compared by using cluster accuracy. An experimental analysis is illustrated on a real dataset using Stata and R package software.     

A network algorithm for the exact treatment of the 2×k contingency table

A common statistical problem encountered in biomedical research is to test the hypothesis that the parameters of k binomial populations are all equal. An exact test of significance of this hypothesis is possible in principle, the appropriate null distribution being a normalized product of k binomial coefficients. However, the problem of computing the tail area of this distribution can be formidable since it requires the enumeration of all sets of k binomial coefficients whose product is less than a given constant. Existing algorithms, all of which rely on explicit enumeration to generate feasible binomial coefficients     

Estimators for the Finite Mixture of Rayleigh Model Based on Progressively Censored Data

In this article, based on progressively Type-II censored samples from a heterogeneous population that can be represented by a finite mixture of two-component Rayleigh lifetime model, the problem of estimating the parameters and some lifetime parameters (reliability and hazard functions) are considered. Both Bayesian and maximum likelihood estimators are of interest. A class of natural conjugate prior densities is considered in the Bayesian setting. The Bayes estimators are obtained using both the symmetric (squared error) loss function, and the asymmetric (LINEX and General Entropy) loss functions. It has been seen that the estimators obtained can be easily evaluated for this type of censoring by using suitable numerical methods. Finally, the performance of the estimates have been compared on the basis of their simulated maximum square error via a Monte Carlo simulation study.     

A Discussion of Permutation Tests Conditional to Observed Responses in Unreplicated 2 M Full Factorial Designs

ABSTRACT

In this article we present a new solution to test for effects in unreplicated two-level factorial designs. The proposed test statistic, in case the error components are normally distributed, follows an F random variable, though our attention is on its nonparametric permutation version. The proposed procedure does not require any transformation of data such as residualization and it is exact for each effect and distribution-free. Our main aim is to discuss a permutation solution conditional to the original vector of responses. We give two versions of the same nonparametric testing procedure in order to control both the individual error rate and the experiment-wise error rate. A power comparison with Loughin and Noble's test is provided in the case of a unreplicated 2⁴ full factorial design.     

Locally optimal invariant tests for change in level

The classical change point problem is considered, from the invariance point of view. Locally optimal invariant tests are derived for the change in level, when the initial level and the common variance are assumed to be unknown. The tests derived by Chernoff and Zacks (1964) and Gardner (1969), for the change in level, when variance is known, are shown to be locally optimal invariant tests.