Methods to Deal with Unknown Populational Minima during Parameter Inference

by   Matheus Henrique Junqueira Saldanha, et al.

There is a myriad of phenomena that are better modelled with semi-infinite distribution families, many of which are studied in survival analysis. When performing inference, lack of knowledge of the populational minimum becomes a problem, which can be dealt with by making a good guess thereof, or by handcrafting a grid of initial parameters that will be useful for that particular problem. These solutions are fine when analyzing a single set of samples, but it becomes unfeasible when there are multiple datasets and a case-by-case analysis would be too time consuming. In this paper we propose methods to deal with the populational minimum in algorithmic, efficient and/or simple ways. Six methods are presented and analyzed, two of which have full theoretical support, but lack simplicity. The other four are simple and have some theoretical grounds in non-parametric results such as the law of iterated logarithm, and they exhibited very good results when it comes to maximizing likelihood and being able to recycle the grid of initial parameters among the datasets. With our results, we hope to ease the inference process for practitioners, and expect that these methods will eventually be included in software packages themselves.



page 9


A general Bayesian bootstrap for censored data based on the beta-Stacy process

We introduce a novel procedure to perform Bayesian non-parametric infere...

Robust and Efficient Parameter Estimation for Discretely Observed Stochastic Processes

In various practical situations, we encounter data from stochastic proce...

Bayesian Survival Analysis Using Gamma Processes with Adaptive Time Partition

In Bayesian semi-parametric analyses of time-to-event data, non-parametr...

Efficient drift parameter estimation for ergodic solutions of backward SDEs

We derive consistency and asymptotic normality results for quasi-maximum...

Tuning Multigrid Methods with Robust Optimization

Local Fourier analysis is a useful tool for predicting and analyzing the...

Estimation of Semi-Markov Multi-state Models: A Comparison of the Sojourn Times and Transition Intensities Approaches

Semi-Markov models are widely used for survival analysis and reliability...

A Non-Iterative Transformation Method for Boundary-Layer with Power-Law Viscosity for Newtonian Fluids

In this paper, we have defined and applied a non-ITM to an extended Blas...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.