A new weighted rank coefficient of concordance

There are many situations where n objects are ranked by b>2 independent sources or observers and in which the interest is focused on agreement on the top rankings. Kendall's coefficient of concordance [10 M. Kendall and B. Smith, The problem of m rankings, Ann. Math. Stat. 10 (1939), pp. 275–287. doi: 10.1214/aoms/1177732186[Crossref] , [Google Scholar]] assigns equal weights to all rankings. In this paper, a new coefficient of concordance is introduced which is more sensitive to agreement on the top rankings. The limiting distribution of the new concordance coefficient under the null hypothesis of no association among the rankings is presented, and a summary of the exact and approximate quantiles for this coefficient is provided. A simulation study is carried out to compare the performance of Kendall's, the top-down and the new concordance coefficients in detecting the agreement on the top rankings. Finally, examples are given for illustration purposes, including a real data set from financial market indices.     

A robust test for testing the correlation coefficient

A test based on Tiku's MML (modified maximum likelihood) estimators is developed for testing that the population correlation coefficient is zero. The test is compared with various other tests and shown to have good Type I error robustness and power for numerous symmetric and skew bivariate populations.     

The effect of fat-tailed error terms on the properties of systemwise RESET test

The small sample properties of the systemwise RESET (Regression Specification Error Test) test for functional misspecification are investigated using normal and non-normal error terms. When using normally distributed or less heavy tailed error terms, we find the Rao's multivariate F-test to be best among all other alternative test methods (i.e. Wald, Lagrange Multiplier and Likelihood Ratio). Using the bootstrap critical values, however, all test methods perform satisfactorily in almost all situations. However, the test methods perform extremely badly (even the RAO test) when the error terms are very heavy tailed.     

A Bayesian estimate of the concordance correlation coefficient with skewed data

Concordance correlation coefficient (CCC) is one of the most popular scaled indices used to evaluate agreement. Most commonly, it is used under the assumption that data is normally distributed. This assumption, however, does not apply to skewed data sets. While methods for the estimation of the CCC of skewed data sets have been introduced and studied, the Bayesian approach and its comparison with the previous methods has been lacking. In this study, we propose a Bayesian method for the estimation of the CCC of skewed data sets and compare it with the best method previously investigated. The proposed method has certain advantages. It tends to outperform the best method studied before when the variation of the data is mainly from the random subject effect instead of error. Furthermore, it allows for greater flexibility in application by enabling incorporation of missing data, confounding covariates, and replications, which was not considered previously. The superiority of this new approach is demonstrated using simulation as well as real‐life biomarker data sets used in an electroencephalography clinical study. The implementation of the Bayesian method is accessible through the Comprehensive R Archive Network. Copyright © 2015 John Wiley & Sons, Ltd.     

On the sample correlation coefficient in the truncated bivariate normal population

The truncated bivariate normal distribution (TBVND) with truncation in both variables on the left is studied here. The behaviour of the sample correlation coefficient is assessed through its moments when the sample is from such a population. Some inequalities established by Rao et al. (1968) are extended     

A robust procedure for testing an assumed value of the population correlation coefficient

For testing that the population correlations coefficientp Q, Tiku and Balakrishnan1986) developed a robust test. This test is extended here to situcitions where one wants to test that p p , p being a specified non-zero value of p. o o     

Bootstrap power of the generalized correlation coefficient

We present a bootstrap Monte Carlo algorithm for computing the power function of the generalized correlation coefficient. The proposed method makes no assumptions about the form of the underlying probability distribution and may be used with observed data to approximate the power function and pilot data for sample size determination. In particular, the bootstrap power functions of the Pearson product moment correlation and the Spearman rank correlation are examined. Monte Carlo experiments indicate that the proposed algorithm is reliable and compares well with the asymptotic values. An example which demonstrates how this method can be used for sample size determination and power calculations is provided.     

A comment on mckay's approximation for the coefficient of variation

Some clarification of statistics based on McKay's x² approximation for the distribution of the sample coefficient of variation is presented. The conclusions of Warren (1982) are shown to result from the confusion of two definitions for the sample coefficient of variation.     

A robust estimate of the correlation coefficient for bivariate normal distribution using ranked set sampling

A robust estimate of the correlation coefficient for a bivariate normal distribution using balanced ranked set sampling is studied. We show that this estimate is at least as efficient as the corresponding estimate based on simple random sampling and highly efficient compared to the maximum likelihood estimate using balanced ranked set sampling. The estimate is robust to common ranking errors. Small sample performance of the estimate is studied by simulation under imperfect and perfect ranking. A variance stabilizing transformation for the confidence interval of the correlation coefficient is obtained.     

A new jackknife test for homogeneity of variances

A new jackknife test is proposed to test the equality of variances in several populations. The new test is based on jackknifing one group of observations at a time, instead of one observation in each group as recommended by Miller for a two sample case, and by Layard for several samples. The proposed test is examined, and compared with other tests, in terms of power and robustness with respect to a wide variety of non-normal distributions. It is found that the new test is robust and has reasonably high power for normal as well as for non-normal observations, irrespective of the sample size. Furthermore, the proposed test is certainly superior to all other tests considered here in small to moderate size samples, and is as good as or better than the other tests in large samples, irrespective of the distribution of sampling observations.     

A robust test for the homogeneity of scales

Many robust tests for the equality of variances have been proposed recently. Brown and Forsythe (1974) and Layard (1973) review some of the well-known procedures and compare them by simulation methods. Brown and Forsythe’s alternative formulation of Levene’s test statistic is found to be quite robust under certain nonnormal distributions. The performance of the methods, however, suffers in the presence of heavy tailed distributions such as the Cauchy distribution.

In this paper, we propose and study a simple robust test. The results obtained from the Monte Carlo study compare favorably with those of the existing procedures.     

A robust coefficient of determination for regression

To assess the quality of the fit in a multiple linear regression, the coefficient of determination or R² is a very simple tool, yet the most used by practitioners. Indeed, it is reported in most statistical analyzes, and although it is not recommended as a final model selection tool, it provides an indication of the suitability of the chosen explanatory variables in predicting the response. In the classical setting, it is well known that the least-squares fit and coefficient of determination can be arbitrary and/or misleading in the presence of a single outlier. In many applied settings, the assumption of normality of the errors and the absence of outliers are difficult to establish. In these cases, robust procedures for estimation and inference in linear regression are available and provide a suitable alternative.     

A new random permutation test in ANOVA models

This paper developed an exact method of random permutations when testing both interaction and main effects in the two-way ANOVA model. The method of this paper can be regarded as a much improved model when compared with those of the previous studies such as Still and White (1981) and ter Braak (1992). We further conducted a simulation experiment in order to check the statistical performance of the proposed method. The proposed method works relatively well for small sample sizes compare with the existing methods. This work was supported by Korea Science and Engineering Foundation Grant (R14-2003-002-0100)     

The exact unconditional z-pooled test for equality of two binomial probabilities: optimal choice of the Berger and Boos confidence coefficient

Exact unconditional tests for comparing two binomial probabilities are generally more powerful than conditional tests like Fisher's exact test. Their power can be further increased by the Berger and Boos confidence interval method, where a p-value is found by restricting the common binomial probability under H ₀ to a 1?γ confidence interval. We studied the average test power for the exact unconditional z-pooled test for a wide range of cases with balanced and unbalanced sample sizes, and significance levels 0.05 and 0.01. The detailed results are available online on the web. Among the values 10^?3, 10^?4, …, 10^?10, the value γ=10^?4 gave the highest power, or close to the highest power, in all the cases we looked at, and can be given as a general recommendation as an optimal γ.     

Additional approximations to the distribution of a structural coefficient estimator for the case of two included endogenous variables

Four new approximations t o the exact distribution of the two-stage l e a s t squares estimator of astructuralcoefficient for

the case of two included endogeneous variables are introduced and compared with the others in the literatur e . Two of the new approximations are based on the Pearson distribution and are found to be adequate throughout the parameter space. A normal approximation using exact moments and an approximation based on the saddlepoint method (Holly and Phillips,1979) are found to be

poor for a wide range of parameter values.     

A direct procedure for monitoring the coefficient of variation using a variable sample size scheme

A variable sample size (VSS) scheme directly monitoring the coefficient of variation (CV), instead of monitoring the transformed statistics, is proposed. Optimal chart parameters are computed based on two criteria: (i) minimizing the out-of-control ARL (ARL₁) and (ii) minimizing the out-of-control ASS (ASS₁). Then the performances are compared between these two criteria. The advantages of the proposed chart over the VSS chart based on the transformed statistics in the existing literature are: the former (i) provides an easier alternative as no transformation is involved and (ii) requires less number of observations to detect a shift when ASS₁ is minimized.     

New weighted rank correlation coefficients sensitive to agreement on top and bottom rankings

Three new weighted rank correlation coefficients are proposed which are sensitive to both agreement on top and bottom rankings. The first one is based on the weighted rank correlation coefficient proposed by Maturi and Abdelfattah [13 T.A. Maturi and E.H. Abdelfattah, A new weighted rank correlation, J. Math. Stat. 4 (2008), pp. 226–230. doi: 10.3844/jmssp.2008.226.230[Crossref] , [Google Scholar]], the second and the third are based on the order statistics and the quantiles of the Laplace distribution, respectively. The limiting distributions of the new correlation coefficients under the null hypothesis of no association between the rankings are presented, and a summary of the exact and approximate quantiles for these coefficients is provided. A simulation study is performed to compare the performance of Kendall's tau, Spearman's rho, and the new weighted rank correlation coefficients in detecting the agreement on the top and the bottom rankings simultaneously. Finally, examples are given for illustration purposes, including a real data set from financial market indices.     

A permutation test for the spread of three-dimensional rotation data

The permutation test is a nonparametric test that can be used to compare measures of spread for two data sets, but is yet to be explored in the context of three-dimensional rotation data. A permutation test for such data is developed and the statistical power of this test is considered under various conditions. The test is then used in a brief application comparing movement around the calcaneocuboid joint for a human, chimpanzee, and baboon.     

A permutation test for multivariate data with grouped components

In this paper, we consider a nonparametric test procedure for multivariate data with grouped components under the two sample problem setting. For the construction of the test statistic, we use linear rank statistics which were derived by applying the likelihood ratio principle for each component. For the null distribution of the test statistic, we apply the permutation principle for small or moderate sample sizes and derive the limiting distribution for the large sample case. Also we illustrate our test procedure with an example and compare with other procedures through simulation study. Finally, we discuss some additional interesting features as concluding remarks.     

A permutation test approach to the choice of size k for the nearest neighbors classifier

The k nearest neighbors (k-NN) classifier is one of the most popular methods for statistical pattern recognition and machine learning. In practice, the size k, the number of neighbors used for classification, is usually arbitrarily set to one or some other small numbers, or based on the cross-validation procedure. In this study, we propose a novel alternative approach to decide the size k. Based on a k-NN-based multivariate multi-sample test, we assign each k a permutation test based Z-score. The number of NN is set to the k with the highest Z-score. This approach is computationally efficient since we have derived the formulas for the mean and variance of the test statistic under permutation distribution for multiple sample groups. Several simulation and real-world data sets are analyzed to investigate the performance of our approach. The usefulness of our approach is demonstrated through the evaluation of prediction accuracies using Z-score as a criterion to select the size k. We also compare our approach to the widely used cross-validation approaches. The results show that the size k selected by our approach yields high prediction accuracies when informative features are used for classification, whereas the cross-validation approach may fail in some cases.