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Register a new userA robust estimation for the extended t-process regression model
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Added by
Kai Li
Publication date
2018
fields
Mathematical Statistics
and research's language is
English
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Robust estimation and variable selection procedure are developed for the extended t-process regression model with functional data. Statistical properties such as consistency of estimators and predictions are obtained. Numerical studies show that the proposed method performs well.
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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.
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In recent years, much of the focus in monitoring child mortality has been on assessing changes in the under-five mortality rate (U5MR). However, as the U5MR decreases, the share of neonatal deaths (within the first month) tends to increase, warranting increased efforts in monitoring this indicator in addition to the U5MR. A Bayesian splines regression model is presented for estimating neonatal mortality rates (NMR) for all countries. In the model, the relationship between NMR and U5MR is assessed and used to inform estimates, and spline regression models are used to capture country-specific trends. As such, the resulting NMR estimates incorporate trends in overall child mortality while also capturing data-driven trends. The model is fitted to 195 countries using the database from the United Nations Interagency Group for Child Mortality Estimation, producing estimates from 1990, or earlier if data are available, until 2015. The results suggest that, above a U5MR of 34 deaths per 1000 live births, at the global level, a 1 per cent increase in the U5MR leads to a 0.6 per cent decrease in the ratio of NMR to U5MR. Below a U5MR of 34 deaths per 1000 live births, the proportion of deaths under-five that are neonatal is constant at around 54 per cent. However, the relationship between U5MR and NMR varies across countries. The model has now been adopted by the United Nations Inter-agency Group for Child Mortality Estimation.
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