Maximum likelihood estimation for a special exponential family under random double-truncation

• Published in: Computational statistics Vol. 30; no. 4; pp. 1199 - 1229
• Main Authors: Hu, Ya-Hsuan, Emura, Takeshi
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2015; Springer Nature B.V
• Subjects: Algorithms; Computation; Data processing; Density; Economic Theory/Quantitative Economics/Mathematical Methods; Mathematics and Statistics; Nonparametric statistics; Normal distribution; Original Paper; Probability and Statistics in Computer Science; Probability Theory and Stochastic Processes; Samples; Statistical analysis; Statistical methods; Statistics; Survival analysis; Newton–Raphson algorithm; Survival analysis; Truncated data; Fixed point iteration
• ISSN: 0943-4062; 1613-9658
• DOI: 10.1007/s00180-015-0564-z

Doubly-truncated data often appear in lifetime data analysis, where samples are collected under certain time constraints. Nonparametric methods for doubly-truncated data have been studied well in the literature. Alternatively, this paper considers parametric inference when samples are subject to double-truncation. Efron and Petrosian (J Am Stat Assoc 94:824–834, 1999 ) proposed to fit a parametric family, called the special exponential family, with doubly-truncated data. However, non-trivial technical aspects, such as parameter space, support of the density, and computational algorithms, have not been discussed in the literature. This paper fills this gap by providing the technical aspects, including adequate choices of parameter space as well as support, and reliable computational algorithms. Simulations are conducted to verify the suggested techniques, and real data are used for illustration.