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1. INFORMATION CRITERION FOR NONPARAMETRIC MODEL-ASSISTED SURVEY ESTIMATORS

   Addison, James ; Xue, Lan ; Lesser, Virginia ( January 2019 , Journal of survey statistics and methodology)

   Nonparametric model-assisted estimators have been proposed to improve estimates of finite population parameters. Flexible nonparametric models provide more reliable estimators when a parametric model is misspecified. In this article, we propose an information criterion to select appropriate auxiliary variables to use in an additive model-assisted method. We approximate the additive nonparametric components using polynomial splines and extend the Bayesian Information Criterion (BIC) for finite populations. By removing irrelevant auxiliary variables, our method reduces model complexity and decreases estimator variance. We establish that the proposed BIC is asymptotically consistent in selecting the important explanatory variables when the true model is additive without interactions, a result supported by our numerical study. Our proposed method is easier to implement and better justified theoretically than the existing method proposed in the literature. 

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2. Robust best linear estimator for Cox regression with instrumental variables in whole cohort and surrogates with additive measurement error in calibration sample

   https://doi.org/10.1002/bimj.201500238  

   Wang, Ching‐Yun ; Song, Xiao ( August 2016 , Biometrical Journal)

   Biomedical researchers are often interested in estimating the effect of an environmental exposure in relation to a chronic disease endpoint. However, the exposure variable of interest may be measured with errors. In a subset of the whole cohort, a surrogate variable is available for the true unobserved exposure variable. The surrogate variable satisfies an additive measurement error model, but it may not have repeated measurements. The subset in which the surrogate variables are available is called acalibration sample. In addition to the surrogate variables that are available among the subjects in the calibration sample, we consider the situation when there is an instrumental variable available for all study subjects. An instrumental variable is correlated with the unobserved true exposure variable, and hence can be useful in the estimation of the regression coefficients. In this paper, we propose a nonparametric method for Cox regression using the observed data from the whole cohort. The nonparametric estimator is the best linear combination of a nonparametric correction estimator from the calibration sample and the difference of the naive estimators from the calibration sample and the whole cohort. The asymptotic distribution is derived, and the finite sample performance of the proposed estimator is examined via intensive simulation studies. The methods are applied to the Nutritional Biomarkers Study of the Women's Health Initiative.

    

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3. Additive partially linear models for ultra‐high‐dimensional regression

   https://doi.org/10.1002/sta4.223  

   Li, Xinyi ; Wang, Li ; Nettleton, Dan ( March 2019 , Stat)

   We consider a semiparametric additive partially linear regression model (APLM) for analysing ultra‐high‐dimensional data where both the number of linear components and the number of non‐linear components can be much larger than the sample size. We propose a two‐step approach for estimation, selection, and simultaneous inference of the components in the APLM. In the first step, the non‐linear additive components are approximated using polynomial spline basis functions, and a doubly penalized procedure is proposed to select nonzero linear and non‐linear components based on adaptive lasso. In the second step, local linear smoothing is then applied to the data with the selected variables to obtain the asymptotic distribution of the estimators of the nonparametric functions of interest. The proposed method selects the correct model with probability approaching one under regularity conditions. The estimators of both the linear part and the non‐linear part are consistent and asymptotically normal, which enables us to construct confidence intervals and make inferences about the regression coefficients and the component functions. The performance of the method is evaluated by simulation studies. The proposed method is also applied to a dataset on the shoot apical meristem of maize genotypes.

    

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4. A test of homogeneity of distributions when observations are subject to measurement errors

   https://doi.org/10.1111/biom.13207  

   Lee, DongHyuk ; Lahiri, Soumendra N. ; Sinha, Samiran ( January 2020 , Biometrics)

   When the observed data are contaminated with errors, the standard two‐sample testing approaches that ignore measurement errors may produce misleading results, including a higher type‐I error rate than the nominal level. To tackle this inconsistency, a nonparametric test is proposed for testing equality of two distributions when the observed contaminated data follow the classical additive measurement error model. The proposed test takes into account the presence of errors in the observed data, and the test statistic is defined in terms of the (deconvoluted) characteristic functions of the latent variables. Proposed method is applicable to a wide range of scenarios as no parametric restrictions are imposed either on the distribution of the underlying latent variables or on the distribution of the measurement errors. Asymptotic null distribution of the test statistic is derived, which is given by an integral of a squared Gaussian process with a complicated covariance structure. For data‐based calibration of the test, a new nonparametric Bootstrap method is developed under the two‐sample measurement error framework and its validity is established. Finite sample performance of the proposed test is investigated through simulation studies, and the results show superior performance of the proposed method than the standard tests that exhibit inconsistent behavior. Finally, the proposed method was applied to real data sets from the National Health and Nutrition Examination Survey. AnRpackageMEtestis available through CRAN.

    

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5. OPTIMAL AUXILIARY PRIORS AND REVERSIBLE JUMP PROPOSALS FOR A CLASS OF VARIABLE DIMENSION MODELS

   https://doi.org/10.1017/S0266466620000018  

   Norets, Andriy ( February 2021 , Econometric Theory)

   This article develops a Markov chain Monte Carlo (MCMC) method for a class of models that encompasses finite and countable mixtures of densities and mixtures of experts with a variable number of mixture components. The method is shown to maximize the expected probability of acceptance for cross-dimensional moves and to minimize the asymptotic variance of sample average estimators under certain restrictions. The method can be represented as a retrospective sampling algorithm with an optimal choice of auxiliary priors and as a reversible jump algorithm with optimal proposal distributions. The method is primarily motivated by and applied to a Bayesian nonparametric model for conditional densities based on mixtures of a variable number of experts. The mixture of experts model outperforms standard parametric and nonparametric alternatives in out of sample performance comparisons in an application to Engel curve estimation. The proposed MCMC algorithm makes estimation of this model practical. 

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