Non-parametric kernel density estimation- based permutation test: Implementation and comparisons.

TL;DR: The procedure followed in this work reproduces similar pattern comparing with already published works, giving some rightfulness to the implemented tools, and is the one based on mutual information very useful, user friendly, and powerful.

Abstract: Background:A classical problem in statistical inference is testing the equality of two or more distributions from independent random samples. To solve this problem, kernel density estimation based tests are very promising but still relatively unexplored. In this work, design, implementation and characterization of permutation-based tests, all built on kernel density estimation is constructed, aimed to achieve a comparative study with eight different measures used as test statistics, and introducing the measure of mutual information as a new plausible method. Three simulated samples from a combination of six models were used in the evaluation. Appropriate functions have been written in programming language for statistical computing R, following requirements, as tools to achieve our goals. Conclusion: The result shows that the procedure followed in this work reproduces similar pattern comparing with already published works, giving some rightfulness to the implemented tools. As a main conclusion and among the compared methods, is the one based on mutual information very useful, user friendly, and powerful. Its use does not need assumptions about the distribution of the samples. It presents good results for the case with small samples, and is easy applicable for very large samples, when also increase its performance. Sammandrag Backgrund: Ett klassiskt problem in statistisk inferens ar att testa likheten mellan tva eller flera fordelningar fran oberoende stickprov. For att losa detta problem, tester baserade pa karnskattning ar mycket lovande men fortfarande relativt mindre undersokta. I detta arbete, utformning, genomforande och karakterisering av permutation -baserade tester, alla byggda pa karnskattning ar konstruerade, i syfte att uppna en jamforande studie med atta olika storlekar som anvants som test statistik, och infora omsesidig information som en ny trovardig metod. Tre simulerade stickprov fran en kombination av sex modellerna anvandes i utvarderingen. Lampliga funktioner har skrivits i programsprak for statistisk, R, efter krav, for att anvandas som verktyg for att na vara mal. Slutsats: Resultatet visar att det tillvagagangssatt som foljts i detta arbete aterger liknande monster jamfor med redan publicerat arbeten, vilket ger en viss trovardighet till det anvanda verktyget. De mest centrala slutsatsen ar att bland de jamforda metoderna, ar den som bygger pa omsesidig information mycket anvandbar, anvandarvanlig och kraftfull. Dess tillampning behover inte antaganden om fordelningen av stickproven. Det ger goda resultat for fallet med sma prov, och ar anvandbar for mycket omfattande prov, da ocksa oka i sin styrka.