A New Method for Local Dependence Map and Its Applications

Objective: This work introduces a new method to construct local dependence map based on the estimate for the linear local dependence function H(x,y), which is generalization of Pearson correlation coefficient. The new local dependence map demonstrates a practical tool for local dependence structure between two random variables. The analysis of theoretical concepts is verified by an application based on real datasets in endocrinology. Material and Methods: The method, local dependence map, requires the estimation new local dependence function which is based on regression concepts. After this local dependence function must be converted with local permutation tests in local dependence map which make the local dependence function more interpretable by identifying the regions of positive, negative and zero local dependence. Results: Based on the proposed method and we give two examples based on the real data C-peptide, insulin and TSH, FT3, FT4 from endocrinology in order to show the advantageous of the current dependence maps. They show interesting local dependence features on the other hand overall correlation coefficient is not much informative. Conclusion: Scalar dependence measures such as correlation coefficient are often used as a measure of dependence for data in medical and biological science. However, they cannot reflect the complex dependence structure of two variables. Hence we are now concerned exclusively with the statistical aspects of the dependence structure in dependence maps that will be constructed for the dataset. In this work a new method to construct local dependence map based on the regression concept for the linear local dependence function H(x,y), which is generalization of Pearson correlation coefficient, is established. The proposed new local dependence map is devoted to two examples based on the real data C-peptide, insulin and TSH, FT3, FT4 from endocrinology in order to illustrate the usefulness of the current dependence maps. They show interesting local dependence features on the other hand overall correlation coefficient is not much informative.