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An objective non-local prior for skew-symmetric models

F. J. Rubio

Abstract

We propose an objective non-local prior for testing symmetry against skew-symmetric alternatives. The prior is derived through a formal construction rule by assigning a uniform distribution to a discrepancy-based measure of the shape parameter's effect. This approach avoids the need for user-specified hyperparameters and produces a weakly informative prior tailored to the skew-symmetric family. We illustrate the use of the proposed prior in the context of testing normality against skew-normal alternatives through both a simulation study and a real-data application.

An objective non-local prior for skew-symmetric models

Abstract

We propose an objective non-local prior for testing symmetry against skew-symmetric alternatives. The prior is derived through a formal construction rule by assigning a uniform distribution to a discrepancy-based measure of the shape parameter's effect. This approach avoids the need for user-specified hyperparameters and produces a weakly informative prior tailored to the skew-symmetric family. We illustrate the use of the proposed prior in the context of testing normality against skew-normal alternatives through both a simulation study and a real-data application.
Paper Structure (10 sections, 2 theorems, 13 equations, 10 figures, 1 table)

This paper contains 10 sections, 2 theorems, 13 equations, 10 figures, 1 table.

Table of Contents

  1. Introduction
  2. Objective priors based on a discrepancy measure
  3. The discrepancy measure
  4. Moment-Objective Minimum-Discrepancy (MOOMIN) Prior
  5. Discrepancy-Informed Moment (DIMOM) Prior
  6. Hypothesis testing
  7. Bayes factor rates
  8. Simulation Study
  9. Real data application
  10. Discussion

Key Result

Proposition 1

Consider the skew-symmetric model eq:skewsymmetric, and suppose that $\int_{-\infty}^{\infty} \vert \omega(x)\vert f(x) dx < \infty$, $f(0) < \infty$, $\int_{-\infty}^{\infty} \vert \omega(x) \vert g(x) dx < \infty$, and $g$ is continuously differentiable. Then, Consider now the case $\omega(x) = x$. Then,

Figures (10)

  • Figure 1: Skew-normal distribution: (a) Discrepancy measure, (b) signed discrepancy measure, and (c) MOOMIN prior and its approximation \ref{['eq:moomin_app']}. The vertical red lines in (a) and (b) are shown at $\lambda = \pm 1$.
  • Figure 2: Simulation results for $n=100$ based on the Jeffreys prior, the approximate MOOMIN prior, and the DIMOM prior: (a) $\lambda = 0$, (b) $\lambda = 1$, and (c) $\lambda = 2.5$.
  • Figure 3: Simulation results for $n=50$: (a) $\lambda = 0$, (b) $\lambda = 1$, and (c) $\lambda = 2.5$.
  • Figure 4: Simulation results for $n=200$: (a) $\lambda = 0$, (b) $\lambda = 1$, and (c) $\lambda = 2.5$.
  • Figure 5: Simulation results for $n=500$: (a) $\lambda = 0$, (b) $\lambda = 1$, and (c) $\lambda = 2.5$.
  • ...and 5 more figures

Theorems & Definitions (2)

  • Proposition 1
  • Proposition 2