‎Before analyzing a time series data‎, ‎it is better to verify the dependency of the data‎, ‎because if the data be independent‎, ‎the fitting of the time series model is not efficient‎. ‎In recent years‎, ‎the power divergence statistics used for the goodness of fit test‎. ‎In this paper‎, ‎we introduce an independence test of time series via power divergence which depends on the parameter λ‎. ‎We obtain asymptotic distribution of the test statistic‎. ‎Also using a simulation study‎, ‎we estimate the error type I and test power for some λ and n‎. ‎Our simulation study shows that for extremely large sample sizes‎, ‎the estimated error type I converges to the nominal α‎, ‎for any λ‎. ‎Furthermore‎, ‎the modified chi-square‎, ‎modified likelihood ratio‎, ‎and Freeman-Tukey test have the most power‎.

‎Testing the Hypothesis of independence of a p-variate vector subvectors‎, ‎as a pretest for many others related tests‎, ‎is always as a matter of interest‎. ‎When the sample size n is much larger than the dimension p‎, ‎the likelihood ratio test (LRT) with chisquare approximation‎, ‎has an acceptable performance‎. ‎However‎, ‎for moderately high-dimensional data by which n is not much larger than p‎, ‎the chisquare approximation for null distribution of the LRT statistic is no more usable‎. ‎As a general case‎, ‎here‎, ‎a simultaneous subvectors independence testing procedure in all k p-variate normal distributions is considered‎. ‎To test this hypothesis‎, ‎a normal approximation for the null distribution of the LRT statistic was proposed‎. ‎A simulation study was performed to show that the proposed normal approximation outperforms the chisquare approximation‎. ‎Finally‎, ‎the proposed testing procedure was applied on prostate cancer data‎.

‎T‎oday, with the increasing access to administrative databases and the high volume of data registered in organizations, the traditional methods of data collection and analysis are not effective due to the response burden. Accordingly, the transition from traditional ‎survey methods to modern methods of data collection and analysis with the register-based statistics approach has received more and more attention from statistical data analysts. In register-based methods, it is especially important to create an integrated database by linking database records of different organizations. ‎Many record linkage algorithms have been developed using the Fellegi and Sunter ‎‎‎model‎. ‎The Fellegi-Sunter model does not leverage information contained in field values and does not care about specific possible values of a string variable (more common and less common values)‎. ‎In this ‎‏‎article‎, ‎a method that can be able to infuse these differences in specific possible values of a string variable in the Fellegi-Sunter model is presented‎.‎ ‎‎‎On the ‎other, ‎‎the ‎‎model proposed by Fellegi-Sunter‎, ‎as well as the method for adjusting the matching weights in the frequency-based record linkage‎, ‎binding in this paper, ‎are based on the assumption of conditional independence‎. ‎In some applications of record linkage‎, ‎this assumption is not met in agreement or disagreement of common variables which are used for matching‎. ‎One solution used in such a case is to use log-linear model which allows interactions between matching variables in the model‎.‎‎

In this ‎‏‎article‎, ‎we deal with two generalizations of Fellegi-Sunter ‎‎‎‎‎model, ‎one with the correction of the matching weights and the other with using a log-linear model with interactions in absence of conditional independence‎. ‎The proposed methods are implemented on labour force data set of Statistical Centre of Iran using R‎.

This paper proposes a different attitude for analyzing three-way contingency tables using conditional independence. We show that different  types of independence explored in log-linear models can be achieved without using these models and only by using conditional independence. Some numerical examples are presented to illustrate the proposed methods.