H‐likelihood Predictive Intervals for Unobservables

Journal of Statistical Planning and Inference

2017

Self Cite

Gaussian process regression (GPR) model has been widely used to fit data when the regression function is unknown and its nice properties have been well established. In this article, we introduce an extended t-process regression (eTPR) model, which gives a robust best linear unbiased predictor (BLUP). Owing to its succinct construction, it inherits many attractive properties from the GPR model, such as having closed forms of marginal and predictive distributions to give an explicit form for robust BLUP procedures, and easy to cope with large dimensional covariates with an efficient implementation by slightly modifying existing BLUP procedures. Properties of the robust BLUP are studied. Simulation studies and real data applications show that the eTPR model gives a robust fit in the presence of outliers in both input and output spaces and has a good performance in prediction, compared with the GPR and locally weighted scatterplot smoothing (LOESS) methods.

Section: Predictive Distributionmentioning

confidence: 99%

Extendedt-process regression models

Wang

Shi

Journal of Statistical Planning and Inference

2017

Self Cite

“…The bootstrap method can also be used to calculate other quantities, such as the subject-specific random-effects. It can be considered as an extension of PIs 15 for random-effects to curve predictions.…”

Section: Inference Methodsmentioning

confidence: 99%

“…Existing PIs for subject-specific inferences often give liberal intervals as we shall show later. Lee and Kim 15 studied PIs for random-effect models and we extend them to HPFR models. The numerical studies show that the nominal confidence level (NCL) is well maintained using the approach.…”

Section: Introductionmentioning

confidence: 99%

Robust functional regression model for marginal mean and subject-specific inferences

Cao

Shi

2017

Stat Methods Med Res

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We introduce flexible robust functional regression models, using various heavy-tailed processes, including a Student t-process. We propose efficient algorithms in estimating parameters for the marginal mean inferences and in predicting conditional means as well interpolation and extrapolation for the subject-specific inferences. We develop bootstrap prediction intervals for conditional mean curves. Numerical studies show that the proposed model provides robust analysis against data contamination or distribution misspecification, and the proposed prediction intervals maintain the nominal confidence levels. A real data application is presented as an illustrative example.

“…In practice, the validity of joint maximization needs to be investigated on a model‐by‐model basis (Lee et al, 2006). When canonical scale is not certain, Lee and Kim (2016) suggested to use the predictive likelihood in Section 2.6.…”

Section: What Is H‐likelihood?mentioning

confidence: 99%

“…Lee and Kim (2016) further considered the confidence distribution (Xie & Singh, 2013) approach to construct interval estimators for unobservables. They showed that the interval estimator based on the plug‐in method is inconsistent unless θ and v are orthogonal.…”

Section: What Is H‐likelihood?mentioning

confidence: 99%

A review of h‐likelihood and hierarchical generalized linear model

Jin

WIREs Computational Stats

2020

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Fisher's classical likelihood has become the standard procedure to make inference for fixed unknown parameters. Recently, inferences of unobservable random variables, such as random effects, factors, missing values, etc., have become important in statistical analysis. Because Fisher's likelihood cannot have such unobservable random variables, the full Bayesian method is only available for inference. An alternative likelihood approach is proposed by Lee and Nelder. In the context of Fisher likelihood, the likelihood principle means that the likelihood function carries all relevant information regarding the fixed unknown parameters. Bjørnstad extended the likelihood principle to extended likelihood principle; all information in the observed data for fixed unknown parameters and unobservables are in the extended likelihood, such as the h‐likelihood. However, it turns out that the use of extended likelihood for inferences is not as straightforward as the Fisher likelihood. In this paper, we describe how to extract information of the data from the h‐likelihood. This provides a new way of statistical inferences in entire fields of statistical science. This article is categorized under: Statistical Models > Generalized Linear Models Algorithms and Computational Methods > Maximum Likelihood Methods