Avoiding the Pitfalls of Testing Sharp Hypotheses: The Nonparametric Case

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  • Presentation type: Oral Presentation (EBEB)
  • Track: EBEB
  • Keywords: Agnostic tests; Pragmatic hypotheses; Bayesian nonparametrics; Density Estimation;
  • 1 Universidade Federal de São Carlos

Avoiding the Pitfalls of Testing Sharp Hypotheses: The Nonparametric Case

Rodrigo Lassance

Universidade Federal de São Carlos

Abstract

Standard statistical tests have at least three major issues that have become more explicit throughout the years: (i) outcomes that do not adhere to what a researcher wants to know, (ii) logical contradictions when applying multiple tests and (iii) rejection of precise hypotheses that are not relevant in a practical perspective. All of these problems are solved through the use of agnostic tests and pragmatic hypotheses. However, no study has yet been made to solve these issues in nonparametric tests. In this paper, we explore pragmatic hypotheses in a nonparametric setting, which reduces the number of presuppositions to the least possible and provides more realistic scenarios. By expanding the theory in Coscrato et al. (2019), we delimit the different types of precise hypotheses of interest and the respective challenges each of them presents. Then, we provide an example of its application, showing how one can proceed to delimit a nonparametric pragmatic hypothesis and derive a Bayesian test that challenges (i)-(iii).

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