Semiparametric smoothing of sparse contingency tables

In the paper simple resampling technique based on semiparametric smoothing is introduced. Although the method is very flexible and in principle can be applied to any sparse data and ill-posed statistical problem, its efficient or even reasonable implementation requires special investigation. In the paper a problem of fitting local dependence structure of finite-state random sequences is addressed. This problem is relevant, for example, in genetics, bioinformatics, computer linguistics, etc., and usually leads to analysis of sparse contingency tables of dependent categorical data. Thus, the classical assumptions of log-linear model, a standard technique for analysis of contingency tables, do not hold. A framework convenient for implementation of semiparametric smoothing and resampling is proposed. It is based on a special representation form of data under consideration and generalized logit model. A computer experiment is carried out to gain better insight on practical performance of the procedure.