Simultaneous Confidence Bands and Hypothesis Testing in Varying‐coefficient Models

By Jianqing Fan, Wenyang Zhang. 2000

239 citations recorded by the source corpus.

Subfields: Analytical Chemistry, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/0b278688daa0053805cd1d58fab6fba3467fc234

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In Analytical Chemistry

In Statistics and Probability

Citations in the corpus

On the Cox Model With Time-Varying Regression Coefficients (2005, methodology): “Models with varying regression coefficients other than the Cox model have been studied by, for example, Hastie and Tibshirani (1993), Cai, Fan, and Li (2000), Fan and Zhang (2000), and Huang, Wu, and Zhou (2002).”
Flexible generalized varying coefficient regression models (2012, methodology): “This model was proposed and studied by Chen and Tsay (1993), Kauermann and Tutz (1999), Fan and Zhang (1999, 2000), Cai, Fan and Li (2000), Cai, Fan and Yao (2000) and Fan, Yao and Cai (2003).”
A Confidence Corridor for Sparse Longitudinal Data Curves (2011, background): “See Proof of Theorem 6.5, page 268 of Fan and Yao (2005).”
Optimal Confidence Bands for Shape-Restricted Curves (2003, background): “Under such restrictions, (1.1) can be achieved approximately for large sample sizes; see, for example, Bickel and Rosenblatt (1973), Knafl et al. (1985), Hall and Titterington (1988), Härdle and Marron (1991), Eubank and Speckman (1993), Fan and Zhang (2000), and the references cited therein.”
Statistical Methods with Varying Coefficient Models. (2008, methodology): “Fan and Zhang (2000) established the following theorem: Theorem 2. d v,n = (−2 log h) 1/2 + 1 (−2 log h) 1/2 log 1 4ν 0 π (K (t)) 2 dt , ν 0 = K 2 (t)dt.”
Inference of time-varying regression models (2012, methodology): “Varying coefficient models have been extensively studied in the literature, and they are useful for characterizing nonconstancy relationship between predictors and responses in regression models; see, for example, [19, 20, 28, 29, 33, 44, 52, 55].”
Local and global asymptotic inference in smoothing spline models (2012, methodology): “The approach of [2] was originally developed in the context of density estimation, and it was then extended to M-estimation by [17] and local polynomial estimation by [5, 11, 44].”
Functional Varying Coefficient Models for Longitudinal Data (2010, methodology): “These methods include polynomial spline (Huang, Wu and Zhou 2004) and smoothing spline (Chiang, Rice and Wu 2001) approaches, as well as local polynomial smoothing (Fan and Zhang 2000; Wu and Chiang 2000).”
A semiparametric spatial dynamic model (2014, background): “By the standard argument in Fan and Gijbels [3] and Lemma 1 in Fan and Zhang [4], we have T = (2K2(0)− ν2∗)h−2 + o(h−2), when h= o(n−1/6) and nh2 →∞, where ν∗ = ∫ K2(t)dt.”
Simultaneous inference of linear models with time varying coefficients (2010, methodology): “Following Fan and Zhang (2000), we first centre each of the three pollutants by their averages so that the intercept β1.”
ADAPTIVE SEMI-VARYING COEFFICIENT MODEL SELECTION (2012, methodology): “The proof of the Lemma can be found in Mack and Silverman (1982), or Fan and Zhang (2000a).”
Robust and efficient variable selection for semiparametric partially linear varying coefficient model based on modal regression (2013, methodology): “Semiparametric partially linear varying coefficient model (SPLVCM) is an extension of partially linear model and varying coefficient model (Hastie and Tibshirani 1993; Cai et al. 2000; Fan and Zhang 1999; Fan and Zhang 2000).”
A Smooth Simultaneous Confidence Corridor for the Mean of Sparse Functional Data (2014, methodology): “…SCC via concentration inequalities, while another strand of literature including Bickel and Rosenblatt (1973), Johnston (1982), Xia (1998), and Fan and Zhang (2000) constructed the SCC by Gaussian strong approximation and extreme value theory, which though did not assume that for family of…”
Semiparametric Time‐Varying Coefficients Regression Model for Longitudinal Data (2005, methodology): “Many tests have been developed for testing covariate effects in non-parametric regression models, varying-coefficient regression models and additive models, see e.g. Fan & Zhang (2000), Dette & Neumeyer (2001) and the references therein.”
Bootstrap confidence bands for regression curves and their derivatives (2003, methodology): “(1998), following earlier results of Hall (1991a, 1992) where it is shown that undersmoothing is more efficient than explicit bias correction, when the goal is to minimize the coverage error of the confidence band. Other approaches to construct confidence bands are investigated by Knafl, Sacks and Y”
Varying Coefficient Regression Models: A Review and New Developments (2015, background): “Fan & Zhang (2000) considered the construction of simultaneous confidence bands for fj in model (1.1) as well as testing problems whether some coefficient functions fj belong to a parametric family.”
Adaptive varying‐coefficient linear models (2003, background): “…Hastie and Tibshirani (1993), Carroll et al. (1998), Kauermann and Tutz (1999), Xia and Li (1999a), Zhang and Lee (1999, 2000) and Fan and W. Zhang (1999, 2000) on local multidimensional regression, Ramsay and Silverman (1997) on functional data analysis, Hoover et al. (1998), Wu et al.…”