Nonparametric Function Estimation for Clustered Data When the Predictor is Measured without/with Error

By Xihong Lin, Raymond J. Carroll. 2000

347 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/398ac2c044f5411c1fe2250f02168f4518afb06e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Jane-ling Wang
2. H. Muller
3. Fang Yao
4. Yehua Li
5. Raymond J. Carroll
6. Wenyang Zhang
7. Xihong Lin
8. Peter Hall

In Statistics and Probability

1. H. Muller
2. Jane-ling Wang
3. Jianqing Fan
4. Fang Yao
5. Yehua Li
6. Raymond J. Carroll
7. Wenyang Zhang
8. Hua Liang

Citations in the corpus

• Local Polynomial Mixed-Effects Models for Longitudinal Data (2002, methodology): “Also note that the “working independence” estimators (Hoover et al. 1998; Lin and Carroll 2000) favor the cases with smaller ni and larger n, whereas our LLME estimator favors the cases with a larger ratio of ni to n.”
• A nonparametric random effects estimator (2005, background): “Local Linear Weighted Least Squares (LLWLS), by minimizing (y − Xδ(x))0W(x)(y − Xδ(x)) ( 7 )”
• Semiparametric and Nonparametric Regression Analysis of Longitudinal Data (2001, background): “If, say, we have n = 11000 persons and each person has Ni = 2 observations at random time points, then, with appropriate bandwidths, smoothed estimates likely will contain only one observation per person, and even current GAMI approaches may be adequate (cf. Lin and Carroll 2000).”
• Semiparametric Regression for Clustered Data Using Generalized Estimating Equations (2001, methodology): “, Tij D Ti), then, in contrast to the results reported in this paper, Lin and Carroll (2001) showed that the proŽ lekernel method works as usual and yields a p n consistent and semiparametric efŽ cient estimate of ‚ if the true covariance is assumed and regular smoothing is used.”
• Low order approximations in deconvolution and regression with errors in variables (2004, background): “See, for example, the problems discussed by Wang et al. (1996), Gould et al. (1997), Luo et al. (1998), Holcomb (1999), Lin and Carroll (1999, 2000), Kim and Gleser (2000), Chen and Cowling (2001) and Novick and Stefanski (2002).”
• Penalized spline models for functional principal component analysis (2006, background): “…best of our knowledge, no asymptotic consistency results of penalized spline models for functional data are available so far, whereas kernel and smoothing spline approaches for clustered data have been investigated by Lin and Carroll (2000), Wang (2003), Lin et al. (2004) and Wang et al. (2005).”
• Estimation of the covariance matrix of random effects in longitudinal studies (2007, methodology): “Lin and Carroll [19] recommend that we ignore the within cluster correlation when kernel smoothing is employed.”
• MULTILEVEL FUNCTIONAL PRINCIPAL COMPONENT ANALYSIS (2009, methodology): “This model is the “hierarchical functional model” introduced by Morris et al. (2003) and also used by Bigelow and Dunson (2007) and Baladandayuthapani et al.”
• More Efficient Local Polynomial Estimation in Nonparametric Regression With Autocorrelated Errors (2003, background): “¢/ is nonparametric, which has been analyzed by, for example, Robinson (1983) and Masry (1996a,b). In this case, standard kernel regression smoothers do not take into account the correlation structure in Xt or ut and estimate the regression function in the same way as if these processes were indepen”
• Polynomial Spline Estimation and Inference for Varying Coefficient Models with Longitudinal Data (2003, methodology): “timation of this model using the local polynomial method and smoothing splines has been studied in Hoover, Rice, Wu and Yang (1998), Fan and Zhang (2000), Wu and Chiang (2000), Wu, Yu and Chiang (2000), Chiang, Rice and Wu (2001) and others.”
• SIMEX estimation for single-index model with covariate measurement error (2016, background): “(III) Extrapolation step For the extrapolant function, we consider the widely used quadratic function G(λ, ) = Γ1 + Γ2λ + Γ3λ2 with = (Γ1, Γ2, Γ3)T (Lin and Carroll 2000; Liang and Ren 2005).”
• Grouped effects estimators in fixed effects models (2016, background): “Nonparametric random effects estimators are proposed by Lin and Carroll (2000) and Ullah and Roy (1998), with general properties of such estimators established in Henderson and Ullah (2005).”
• Time-Varying Additive Models for Longitudinal Data (2013, background): “However, it was shown by Lin and Carroll (2000) in a closely related setting that the best strategy to handle longitudinal data with a local smoother is to ignore the within-subject correlation and use a working independent correlation instead, that is, pretend that the observations within each…”
• Asymptotic optimality and efficient computation of the leave-subject-out cross-validation (2012, methodology): “…Zeger and Diggle (1994), Zhang et al. (1998), Lin and Ying (2001), Wang, Carroll and Lin (2005)] and nonparametric [e.g., Fan and Zhang (2000), Lin and Carroll (2000), Rice and Silverman (1991), Wang (1998, 2003), Welsh, Lin and Carroll (2002), Zhu, Fung and He (2008)] models have been…”
• Backfitting Random Varying‐Coefficient Models with Time‐Dependent Smoothing Covariates (2004, background): “Lin & Carroll (2000) have shown that the ‘working-independence’ estimator is asymptotically most efficient among a class of kernel GEE estimators in non-parametric kernel regression for clustered data.”
• Nonparametric Regression Analysis of Longitudinal Data (2005, background): “They are usually referred to as ”longitudinal data” in biomedical applications, where a small number of repeated measurements, ni, over time per subject is common, and as ”functional data” in engineering and biological applications, where ni is often large.”