Capturing a Change in the Covariance Structure of a Multivariate Process

This research is inspired from monitoring the process covariance structure of q attributes where samples are independent, having been collected from a multivariate normal distribution with known mean vector and unknown covariance matrix. The focus is on two matrix random variables, constructed from different Wishart ratios, that describe the process for the two consecutive time periods before and immediately after the change in the covariance structure took place. The product moments of these constructed random variables are highlighted and set the scene for a proposed measure to enable the practitioner to calculate the run-length probability to detect a shift immediately after a change in the covariance matrix occurs. Our results open a new approach and provides insight for detecting the change in the parameter structure as soon as possible once the underlying process, described by a multivariate normal process, encounters a permanent/sustained upward or downward shift.

Choosing Imputation Models

Imputing missing values is an important preprocessing step in data analysis, but the literature offers little guidance on how to choose between imputation models. This letter suggests adopting the imputation model that generates a density of imputed values most similar to those of the observed values for an incomplete variable after balancing all other covariates. We recommend stable balancing weights as a practical approach to balance covariates whose distribution is expected to differ if the values are not missing completely at random. After balancing, discrepancy statistics can be used to compare the density of imputed and observed values. We illustrate the application of the suggested approach using simulated and real-world survey data from the American National Election Study, comparing popular imputation approaches including random forests, hot-deck, predictive mean matching, and multivariate normal imputation. An R package implementing the suggested approach accompanies this letter.

Statistical Model of Correlation Difference and Related-Key Linear Cryptanalysis

The goal of this work is to propose a related-key model for linear cryptanalysis. We start by giving the mean and variance of the difference of sampled correlations of two Boolean functions when using the same sample of inputs to compute both correlations. This result is further extended to determine the mean and variance of the difference of correlations of a pair of Boolean functions taken over a random data sample of fixed size and over a random pair of Boolean functions. We use the properties of the multinomial distribution to achieve these results without independence assumptions. Using multivariate normal approximation of the multinomial distribution we obtain that the distribution of the difference of related-key correlations is approximately normal. This result is then applied to existing related-key cryptanalyses. We obtain more accurate right-key and wrong-key distributions and remove artificial assumptions about independence of sampled correlations. We extend this study to using multiple linear approximations and propose a Χ2-type statistic, which is proven to be Χ2 distributed if the linear approximations are independent. We further examine this statistic for multidimensional linear approximation and discuss why removing the assumption about independence of linear approximations does not work in the related-key setting the same way as in the single-key setting.

Concordance rate of a four-quadrant plot for repeated measurements

Background To assure the equivalence between new clinical measurement methods and the standard methods, the four-quadrant plot and the plot’s concordance rate is used in clinical practice, along with Bland-Altman analysis. The conventional concordance rate does not consider the correlation among the data on individual subjects, which may affect its proper evaluation. Methods We propose a new concordance rate for the four-quadrant plot based on multivariate normal distribution to take into account the covariance within each individual subject. The proposed concordance rate is formulated as the conditional probability of the agreement. It contains a parameter to set the minimum concordant number between two measurement methods, which is regarded as agreement. This parameter allows flexibility in the interpretation of the results. Results Through numerical simulations, the AUC value of the proposed method was 0.967, while that of the conventional concordance rate was 0.938. In the application to a real example, the AUC value of the proposed method was 0.999 and that of the conventional concordance rate was 0.964. Conclusion From the results of numerical simulations and a real example, the proposed concordance rate showed better accuracy and higher diagnosability than the conventional approaches.