Flexible Bivariate Count Data Regression Models

The article develops a semiparametric estimation method for the bivariate count data regression model. We develop a series expansion approach in which dependence between count variables is introduced by means of stochastically related unobserved heterogeneity components, and in which, unlike existing commonly used models, positive as well as negative correlations are allowed. Extensions that accommodate excess zeros, censored data, and multivariate generalizations are also given. Monte Carlo experiments and an empirical application to tobacco use confirms that the model performs well relative to existing bivariate models, in terms of various statistical criteria and in capturing the range of correlation among dependent variables. This article has supplementary materials online.     

Detecting Randomness: A Review of Existing Tests with New Comparisons

In this article we review and compare a number of existing tests for detecting randomness in time series data, with emphasis on stock market index data. By comparing variance ratio tests with traditional statistical tests, we have the most extensive simulation comparison of such procedures. The investigated tests are compared over a diverse group of distributions, models, and stock market applications. In our stock market data analysis, the choice of data transformation can have a noticeable effect on test results. This study provides the reader with a guide as to which test and transformation is most appropriate for their use.     

Using Lasso RCCA for cross-language information retrieval

ABSTRACT

Restricted canonical correlation analysis and the lasso shrinkage method were paired together for canonical correlation analysis with non-negativity restrictions on datasets, where a sample size is much smaller than the number of variables. The method was implemented in an alternating least-squares algorithm and applied to cross-language information retrieval on a dataset with aligned documents in eight languages. A set of experiments was ran to evaluate the method and compare it to other methods in the field.     

Geometry in Canonical Correlations

In this article, a useful proposition relating the canonical correlations in multi-way layout to the singular values of a specific matrix is proved and also a geometrical explanation of canonical correlations as an angle between subspaces is given.     

The Ranges of Limiting Values of Some Partial Correlations under Conditional Independence

Pearson's partial correlation, Kendall's partial tau, and a partial correlation based on Spearman's rho need not be consistent estimators of zero under conditional independence. The ranges of possible limiting values of these correlations are computed under multivariate normality and lognormality. Students should exercise caution when interpreting these partial correlations as a measure of conditional independence.     

An Interesting Property of the Sample Mean under a First-Order Autoregressive Model

The unweighted sample mean is examined as an estimator of the population mean in a first-order autoregressive model. It is demonstrated that the precision of this estimator deteriorates as the number of equally spaced observations taken within a fixed time interval increases.     

Asymptotic Expansion and Conditional Robustness for the Sample Multiple Correlation Coefficient Under Nonnormality

ABSTRACT

Asymptotic distributions of the standardized estimators of the squared and non squared multiple correlation coefficients under nonnormality were obtained using Edgeworth expansion up to O(1/n). Conditions for the normal-theory asymptotic biases and variances to hold under nonnormality were derived with respect to the parameter values and the weighted sum of the cumulants of associated variables. The condition for the cumulants indicates a compensatory effect to yield the robust normal-theory lower-order cumulants. Simulations were performed to see the usefulness of the formulas of the asymptotic expansions using the model with the asymptotic robustness under nonnormality, which showed that the approximations by Edgeworth expansions were satisfactory.     

Tests for random time effects and spatial error correlation in panel regression models

We consider a panel model with spatial autocorrelation and heterogeneity across time. Various Lagrange multiplier and likelihood ratio test statistics are developed for testing time effects and spatial effects, jointly, marginally or conditionally. Limiting null distributions of the tests are derived. Size and power performances of the proposed tests are compared by a Monte-Carlo experiment.     

Testing the Equality of Two Proportions for Combined Unilateral and Bilateral Data

In many medical comparative studies (e.g., comparison of two treatments in an otolaryngological study), subjects may produce either bilateral (e.g., responses from a pair of ears) or unilateral (response from only one ear) data. For bilateral cases, it is meaningful to assume that the information between the two ears from the same subject are generally highly correlated. In this article, we would like to test the equality of the successful cure rates between two treatments with the presence of combined unilateral and bilateral data. Based on the dependence and independence models, we study ten test statistics which utilize both the unilateral and bilateral data. The performance of these statistics will be evaluated with respect to their empirical Type I error rates and powers under different configurations. We find that both Rosner's and Wald-type statistics based on the dependence model and constrained maximum likelihood estimates (under the null hypothesis) perform satisfactorily for small to large samples and are hence recommended. We illustrate our methodologies with a real data set from an otolaryngology study.     

Symbolic correlation integral

This paper aims to introduce the concept of symbolic correlation integral SC that is extensively used in many scientific fields. The new correlation integral SC avoids the noisy parameter 𝜀 of the classical correlation integral, defined by Grassberger and Procaccia (1983 Grassberger, P., Procaccia, I. (1983). Measuring the strangeness of strange attractors. Physica D: Nonlinear Phenomena 9(1–2):189–208.[Crossref], [Web of Science ®] , [Google Scholar]) and extensively used for constructing correlation-integral-based statistics, as in the BDS test. Once the free parameter 𝜀 disappears, it is possible to construct a nonparametric powerful test for independence that can also be used as a diagnostic tool for model selection. The symbolic correlation integral is also extended to deal with multivariate models, and a test for causality is proposed as an example of the theoretical power of the new concept. With extensive Monte Carlo simulations, the paper shows the good size and power performance of symbolic correlation-integral-based tests.