scholarly journals Maximum pseudo‐likelihood estimation based on estimated residuals in copula semiparametric models

2020 ◽  
Author(s):  
Marek Omelka ◽  
Šárka Hudecová ◽  
Natalie Neumeyer
Keyword(s):  
Likelihood Estimation ◽  
Semiparametric Models ◽  
Pseudo Likelihood ◽  
Pseudo Likelihood Estimation

scholarly journals Augmented pseudo-likelihood estimation for two-phase studies

2019 ◽  
Vol 29 (2) ◽  
pp. 344-358
Author(s):  
Claudia Rivera-Rodriguez ◽  
Sebastien Haneuse ◽  
Molin Wang ◽  
Donna Spiegelman
Keyword(s):  
Phase I ◽  
Phase Ii ◽  
Likelihood Estimation ◽  
Weighted Likelihood ◽  
Finite Sample ◽  
Cross Sectional Survey ◽  
Two Phase ◽  
Cross Sectional ◽  
Pseudo Likelihood ◽  
Pseudo Likelihood Estimation

In many public health and medical research settings, information on key covariates may not be readily available or too expensive to gather for all individuals in the study. In such settings, the two-phase design provides a way forward by first stratifying an initial (large) phase I sample on the basis of covariates readily available (including, possibly, the outcome), and sub-sampling participants at phase II to collect the expensive measure(s). When the outcome of interest is binary, several methods have been proposed for estimation and inference for the parameters of a logistic regression model, including weighted likelihood, pseudo-likelihood and maximum likelihood. Although these methods yield consistent estimation and valid inference, they do so solely on the basis of the phase I stratification and the detailed covariate information obtained at phase II. Moreover, they ignore any additional information that is readily available at phase I but was not used as part of the stratified sampling design. Motivated by the potential for efficiency gains, especially concerning parameters corresponding to the additional phase I covariates, we propose a novel augmented pseudo-likelihood estimator for two-phase studies that makes use of all available information. In contrast to recently-proposed weighted likelihood-based methods that calibrate to the influence function of the model of interest, the methods we propose do not require the development of additional models and, therefore, enjoy a degree of robustness. In addition, we expand the broader framework for pseudo-likelihood based estimation and inference to permit link functions for binary regression other than the logit link. Comprehensive simulations, based on a one-time cross sectional survey of 82,887 patients undergoing anti-retroviral therapy in Malawi between 2005 and 2007, illustrate finite sample properties of the proposed methods and compare their performance competing approaches. The proposed method yields the lowest standard errors when the model is correctly specified. Finally, the methods are applied to a large implementation science project examining the effect of an enhanced community health worker program to improve adherence to WHO guidelines for at least four antenatal visits, in Dar es Salaam, Tanzania.

A Block Successive Lower-Bound Maximization Algorithm for the Maximum Pseudo-Likelihood Estimation of Fully Visible Boltzmann Machines

2016 ◽  
Vol 28 (3) ◽  
pp. 485-492 ◽  
Author(s):  
Hien D. Nguyen ◽  
Ian A. Wood
Keyword(s):  
Lower Bound ◽  
Likelihood Function ◽  
Likelihood Estimation ◽  
Convergence Criterion ◽  
Boltzmann Machines ◽  
Pseudo Likelihood ◽  
Global Maximizer ◽  
Ga Algorithm ◽  
Pseudo Likelihood Estimation ◽  
The Relationship

Maximum pseudo-likelihood estimation (MPLE) is an attractive method for training fully visible Boltzmann machines (FVBMs) due to its computational scalability and the desirable statistical properties of the MPLE. No published algorithms for MPLE have been proven to be convergent or monotonic. In this note, we present an algorithm for the MPLE of FVBMs based on the block successive lower-bound maximization (BSLM) principle. We show that the BSLM algorithm monotonically increases the pseudo-likelihood values and that the sequence of BSLM estimates converges to the unique global maximizer of the pseudo-likelihood function. The relationship between the BSLM algorithm and the gradient ascent (GA) algorithm for MPLE of FVBMs is also discussed, and a convergence criterion for the GA algorithm is given.

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