Asymptotic Results for Multinomial Models

In this work, we derived new asymptotic results for multinomial models. To obtain these results, we started by studying limit distributions in models with a compact parameter space. This restriction holds since the key parameter whose components are the probabilities of the possible outcomes have non-negative components that add up to 1. Based on these results, we obtained confidence ellipsoids and simultaneous confidence intervals for models with normal limit distributions. We then studied the covariance matrices of the limit normal distributions for the multinomial models. This was a transition between the previous general results and on the inference for multinomial models in which we considered the chi-square tests, confidence regions and non-linear statistics—namely log-linear models with two numerical applications to those models. Namely, our approach overcame the hierarchical restrictions assumed to analyse the multidimensional contingency table.

Generalized Fréchet Bounds for Cell Entries in Multidimensional Contingency Tables

We consider the lattice, $\mathcal{L}$, of all subsets of a multidimensional contingency table and establish the properties of monotonicity and supermodularity for the marginalization function, $n(\cdot)$, on $\mathcal{L}$. We derive from the supermodularity of $n(\cdot)$ some generalized Fr\'echet inequalities complementing and extending inequalities of Dobra and Fienberg. Further, we construct new monotonic and supermodular functions from $n(\cdot)$, and we remark on the connection between supermodularity and some correlation inequalities for probability distributions on lattices. We also apply an inequality of Ky Fan to derive a new approach to Fr\'echet inequalities for multidimensional contingency tables.

A Novel Coding and Discrimination (CODIS) ‎Algorithm to Extract Features from Arabic Texts to ‎Discriminate Arabic Poems

This article proposes a new algorithm to ‎discriminate Arabic poems by inserting Arabic poems ‎texts and coding Arabic letters, extracting letters features ‎depending on letter shapes to construct a multidimensional ‎contingency table, and analyses the frequencies of letters in ‎the inserted texts statistically. The proposed coding and ‎discrimination (CODIS) algorithm could be applied for ‎different Arabic texts in any media. A sample of five poems ‎for six poets was examined to implement a CODIS algorithm. ‎A Chi-Square statistic is used to determine the relation between ‎the features and discriminate poems.‎

استعمال معامل الاقتران المتعدد لتمييز القصائد العربية لعينة من الشعراء

المستخلص يهدف البحث إلى التمييز بين القصائد لكل شاعر من خلال خصائص وصفات الحروف العربية حيث إستعملت أربع تصنيفات للحروف العربية على أساسها تم إدراج تكرارات الحروف في جدول إقتران متعدد الإتجاهات (Multidimensional contingency table) ولكل إتجاه (تصنيف) مستويين أو أكثر ومنه أيجاد قيمة معامل الإقتران لكل قصيدة ضمن عينة البحث والتي تتألف من ستة شعراء من عصور مختلفة ولكل شاعر خمس قصائد. تمت برمجة الطريقة بإستخدام برنامج الماتلاب (MATLAB) وقد أثبتت الطريقة كفائتها بنسبة 53% بالنسبة لعينة البحث المقترحة ككل وبنسبة تتراوح بين 90% إلى 95% بالنسبة للقصائد لكل شاعر.

Modeling Changes in the In-Migration Patterns of Northern Saskatchewan Communities : a Log-Linear Approach

This paper examines changes in the historical pattern of in-migration to small frontier communities in northern Saskatchewan in three time periods: 1927-1960, 1961-1970 and 1971-1976. The problems associated with spatial interaction modeling in a developing or frontier region are noted, particularly the low volume of in-migration and the inappropriateness of mass terms as surrogate measures of nodal attractiveness and propulsiveness. As an alternative, a log-linear approach is adopted, whereby multidimensional contingency-table analysis of categorical data reveals structural components in the spatial-interaction process. Initial results indicate that the gender of the migrant has no effect on the propensity to migrate and that spatial patterns of in-migration have not changed over time.