@article{Stochastic Complexity, Histograms and Hypothesis Testing of Homogeneity_2009, place={Maryland, USA}, volume={3}, url={https://www.ejpam.com/index.php/ejpam/article/view/521}, abstractNote={Information contained in a sample of quantitative data may be summarized or described by a nonparametric histogram density function. An interesting question is how to construct such a histogram density to express the data information with minimum stochastic complexity.The stochastic complexity is a pseudonym of Rissanen's minimum description lengthÂ (MDL) which gives the length of a sequence of decipherable binary code resulted from optimally encoding the data information using a probability distribution based code-book. Here we have derived an optimal generalized histogram density estimator to provide both predictive and non-predictive coding description of a data sample. We have also obtained uniform and almost sure asymptotic approximations for the lengths of both descriptions. As an application of this result to statistical inference a new procedure for hypothesis testing of distribution homogeneityÂ is proposed and is proved to have an asymptotic power of 1.}, number={1}, journal={European Journal of Pure and Applied Mathematics}, year={2009}, month={Dec.}, pages={51–80} }