Statistical inference for a general class of distributions with time-varying parameters

In this article we are interested in a general class of distributions for independent not necessarily identically distributed random variables, closed under minima, that includes a number of discrete and continuous distributions like the Geometric, Exponential, Weibull or Pareto. The main parameter involved in this class of distributions is assumed to be time varying with several possible modeling options. This is of particular interest in reliability and survival analysis for describing the time to event or failure. The maximum likelihood estimation of the parameters is addressed and the asymptotic properties of the estimators are discussed. We provide real and simulated examples and we explore the accuracy of the estimating procedure as well as the performance of classical model selection criteria in choosing the correct model among a number of competing models for the time-varying parameters of interest.

[1]  J. Cavanaugh,et al.  A regression model selection criterion based on bootstrap bumping for use with resistant fitting , 2000 .

[2]  Ralph A. Bradley,et al.  The asymptotic properties of ML estimators when sampling from associated populations , 1962 .

[3]  Milan Stehlík,et al.  Small Sample Robust Testing for Normality against Pareto Tails , 2012, Commun. Stat. Simul. Comput..

[4]  Jan Bulla,et al.  Stylized facts of financial time series and hidden semi-Markov models , 2006, Comput. Stat. Data Anal..

[5]  Gianpaolo Pulcini,et al.  Inference and test in modeling the failure/repair process of repairable mechanical equipments , 2000, Reliab. Eng. Syst. Saf..

[6]  A Method for Multivariate Probability Distributions Construction via Parameter Dependence , 2013 .

[7]  Milan Stehlík,et al.  On Small Samples Testing for Frailty Through Homogeneity Test , 2015, Commun. Stat. Simul. Comput..

[8]  Clifford M. Hurvich,et al.  Regression and time series model selection in small samples , 1989 .

[9]  G. M. Clark,et al.  ESTIMATING PARAMETERS OF THE POWER LAW PROCESS WITH TWO MEASURES OF FAILURE TIME , 1998 .

[10]  Jan Bulla,et al.  hsmm - An R package for analyzing hidden semi-Markov models , 2010, Comput. Stat. Data Anal..

[12]  Junfeng Shang.  A Multiple Comparison Procedure Based on a Variant of the Schwarz Information Criterion in a Mixed Model , 2010 .

[13]  Narayanaswamy Balakrishnan,et al.  Likelihood Testing With Censored and Missing Duration Data , 2015 .

[14]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[15]  Sangyeol Lee,et al.  On entropy-based goodness-of-fit test for asymmetric Student-t and exponential power distributions , 2017 .

[17]  Vicente Núñez-Antón,et al.  Alternative approaches to study lifetime data under different scenarios: from the PH to the modified semiparametric AFT model , 2006, Comput. Stat. Data Anal..

[18]  Abhik Ghosh,et al.  Robust estimation for non-homogeneous data and the selection of the optimal tuning parameter: the density power divergence approach , 2015 .

[19]  Sangyeol Lee,et al.  On first-order integer-valued autoregressive process with Katz family innovations , 2017 .

[20]  V. Núñez-Antón,et al.  Bayesian modelling of the mean and covariance matrix in normal nonlinear models , 2009 .

[21]  J. Filus.  On a type of dependency between Weibull lifetimes of system components , 1991 .

[22]  Joseph E. Cavanaugh,et al.  An improved Akaike information criterion for state-space model selection , 2006, Comput. Stat. Data Anal..