Computation of finite population parameters and approximate probability values for multi-response randomized block permutation procedures (mrbp)

An algorithm is presented for computing the finite population parameters and the approximate probability values associated with a recently-developed class of statistical inference techniques termed multi-response randomized block permutation procedures (MRBP).     

Inequalities for sums of squares of reranked differences involving ties and missing data

An inequality for the sum of squares of rank differences associated with Spearman’s rank correlation coefficient, when ties and missing data are present in both rankings, was established numerically in Loukas and Papaioannou (1991 Loukas, S., Papaioannou, T. (1991). Rank correlation inequalities with ties and missing data. Stat. Probab. Lett. 11:53–56.[Crossref], [Web of Science ®] , [Google Scholar]). That inequality is improved and generalized.     

Generating Bivariate Uniform Data with a Full Range of Correlations and Connections to Bivariate Binary Data

In this article, random number generation algorithms for generating bivariate uniform data based on a known class of symmetric bivariate uniform distributions that allow the entire correlation range are given, and its previously unrecognized connection with bivariate binary data is established via matching the cumulative distribution functions.     

Average rank correlation statistics in the presence of ties

The problem of n judges ranking r objects is considered in the situation where ties are permitted. Asymtotic distributions under the null hypothesis of complete randomness in the rankings are derived for the test statistics of average rank correlations between all pairs of ranking where the rank correlations are measured either by Spearman rho or Kendall tau. The relative efficeincies of these average rank correlatins are derived using approximate Bahadur slope and limiting pitman efficiency, and in both cases the Kendall statistic is shown to be more efficient. Some interpretatins of these and related results are also given.     

C219. Comment on ”calculating binomial probabilities when the trial probabilities are unequal“

In complex models like hidden Markov chains, the convergence of the MCMC algorithms used to approximate the posterior distribution and the Bayes estimates of the parameters of interest must be controlled in a robust manner. We propose in this paper a series of online controls, which rely on classical non-parametric tests, to evaluate independence from the start-up distribution, stability of the Markov chain, and asymptotic normality. These tests lead to graphical control spreadsheets which arepresentedin the set-up of normalmixture hidden Markov chains to compare the full Gibbs sampler with an aggregated Gibbs sampler based on the forward – backward formulas.     

General scores statistics on ranks in the analysis of unbalanced designs

The authors consider the situation of incomplete rankings in which n judges independently rank k_i ∈ {2, …, t} objects. They wish to test the null hypothesis that each judge picks the ranking at random from the space of k_i! permutations of the integers 1, …, k_i. The statistic considered is a generalization of the Friedman test in which the ranks assigned by each judge are replaced by real‐valued functions a(j, k_i), 1 ≤ j ≤ k_i ≤ t of the ranks. The authors define a measure of pairwise similarity between complete rankings based on such functions, and use averages of such similarities to construct measures of the level of concordance of the judges' rankings. In the complete ranking case, the resulting statistics coincide with those defined by Hájek & ?idák (1967, p. 118), and Sen (1968). These measures of similarity are extended to the situation of incomplete rankings. A statistic is derived in this more general situation and its properties are investigated.     

Rank correlation methods for missing data

The subject of rank correlation has had a rich history. It has been used in numerous applications in tests for trend and for independence. However, little has been said about how to define rank correlation when the data are incomplete. The practice has often been to ignore missing observations and to define rank correlation for the smaller complete record. We propose a new class of measures of rank correlation which are based on a notion of distance between incomplete rankings. There is the potential for a significant increase in efficiency over the approach which ignores missing observations as demonstrated by a specific case.     

Simulating dependent discrete data

This article describes a method for simulating n-dimensional multivariate non-normal data, with emphasis on count-valued data. Dependence is characterized by either Pearson correlations or Spearman correlations. The simulation is accomplished by simulating a vector of correlated standard normal variates. The elements of this vector are then transformed to achieve the target marginal distributions. We prove that the method corresponds to simulating data from a multivariate Gaussian copula. The simulation method does not restrict pairwise dependence beyond the limits imposed by the marginal distributions and can achieve any Pearson or Spearman correlation within those limits. Two examples are included. In the first example, marginal means, variances, Pearson correlations, and Spearman correlations are estimated from the epileptic seizure data set of Diggle et al. [P. Diggle, P. Heagerty, K.Y. Liang, and S. Zeger, Analysis of Longitudinal Data, Oxford University Press, Oxford, 2002]. Data with these means and variances are simulated to first achieve the estimated Pearson correlations and then achieve the estimated Spearman correlations. The second example is of a hypothetical time series of Poisson counts with seasonal mean ranging between 1 and 9 and an autoregressive(1) dependence structure.     

On multivariate Gaussian copulas

Gaussian copulas are handy tool in many applications. However, when dimension of data is large, there are too many parameters to estimate. Use of special variance structure can facilitate the task. In many cases, especially when different data types are used, Pearson correlation is not a suitable measure of dependence. We study the properties of Kendall and Spearman correlation coefficients—which have better properties and are invariant under monotone transformations—used at the place of Pearson coefficients. Spearman correlation coefficient appears to be more suitable for use in such complex applications.