Moments of doubly truncated multivariate distributions

• Grant number: 18/11580-1
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• Effective date (Start): October 31, 2018
• Effective date (End): October 30, 2019
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Statistics
• Principal Investigator: Larissa Avila Matos
• Grantee: Christian Eduardo Galarza Morales
• Supervisor: Victor Hugo Lachos Davila
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Research place: University of Connecticut (UCONN), United States
• Associated to the scholarship: 15/17110-9 - Robust Estimation in Spatial Models for Censored Data, BP.DR

Abstract

Computation of the product moments of the truncated multivariate Student-t (TMVT) distribution under the double truncation have been presented by Lachos et al. (2017) (see also, Ho et al. (2012)). Following Lachos et al. (2017), this paper develops recurrence relations for integrals that involve the density of multivariate scale mixtures of skew-normal (SMSN) distributions. These recursions offer fast computation of arbitrary order product moments of truncated multivariate SMSN (TMVSMSN) and folded multivariate SMSN (FMVSMSN) distributions with the first two moments of the TMVSMSN and FMVSMSN as a byproduct. With these results, application to data containing bounded and missing responses is possible. The proposed methods will be implemented to a new R package (integrating C++ and Fortran), providing practitioners a convenient tool for further applications in several fields. (AU)

Scientific publications

(6)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

GALARZA, CHRISTIAN E.; LIN, TSUNG-, I; WANG, WAN-LUN; LACHOS, VICTOR H.. On moments of folded and truncated multivariate Student-t distributions based on recurrence relations. METRIKA, v. 84, n. 6, p. 26-pg., 2021-01-19. (18/11580-1, 15/17110-9)

GALARZA MORALES, CHRISTIAN E.; MATOS, LARISSA A.; DEY, DIPAK K.; LACHOS, VICTOR H.. On Moments of Folded and Doubly Truncated Multivariate Extended Skew-Normal Distributions. JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS, JAN 2022. (18/11580-1, 15/17110-9)

GALARZA, CHRISTIAN E.; MATOS, LARISSA A.; CASTRO, LUIS M.; LACHOS, VICTOR H.. Moments of the doubly truncated selection elliptical distributions with emphasis on the unified multivariate skew-t distribution. JOURNAL OF MULTIVARIATE ANALYSIS, v. 189, p. 15-pg., 2022-01-03. (18/11580-1, 15/17110-9, 20/16713-0)

GALARZA MORALES, CHRISTIAN E.; LACHOS, VICTOR H.; BOURGUIGNON, MARCELO. A skew-t quantile regression for censored and missing data. STAT, v. 10, n. 1, DEC 2021. (15/17110-9, 18/11580-1)

GALARZA, CHRISTIAN E.; LIN, I, TSUNG-; WANG, WAN-LUN; LACHOS, VICTOR H.. On moments of folded and truncated multivariate Student-t distributions based on recurrence relations. METRIKA, JAN 2021. (15/17110-9, 18/11580-1)

GALARZA MORALES, CHRISTIAN E.; LACHOS, VICTOR H.; BOURGUIGNON, MARCELO. A skew-t quantile regression for censored and missing data. STAT, v. 10, n. 1, p. 15-pg., 2021-12-01. (18/11580-1, 15/17110-9)