Penalized Spline Estimation for Partially Linear Single-Index Models

By Yan Yu, David Ruppert. 2002

569 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/8ee3dea9c1d354fe9ab7f6820a7c64de78c707dc

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In Statistics and Probability

Citations in the corpus

The EFM approach for single-index models (2011, methodology): “In addition, Yu and Ruppert (2002) fitted the partially linear single-index models using a penalized spline method.”
A Multiple-Index Model and Dimension Reduction (2008, background): “An important special case of model (B) is when dB = 1, that is, Y = γ 0 X + g(β 1 X) + ε, where g(·) is a univariate unknown function, which again includes the partially linear single-index model (Carroll et al. 1997; Yu and Ruppert 2002) as its special case.”
Twenty years of P-splines (2015, methodology): “P-splines have been implemented in other types of single-index models, e.g. see Yu and Ruppert (2002) and Lu et al. (2006).”
Empirical likelihood confidence regions in a partially linear single‐index model (2006, background): “As we know, estimating efficiently, in particular, β is challenging and the asymptotic variance of the existing estimators is of very complicated structure; see Carroll et al. (1997) and relevant work such as Härdle et al. (1993) and Yu and Ruppert (2002, 2004).”
A SINGLE-INDEX QUANTILE REGRESSION MODEL AND ITS ESTIMATION (2012, background): “See Ichimura (1993) and Yu and Ruppert (2002) for detailed discussion.”
Determination of linear components in additive models (2011, methodology): “…linear model in a more general setting has also been investigated lately, such as the single-index component estimation in additive models in Yu and Ruppert (2002), generalised additive models in Aerts, Claeskens, and Wand (2002), small area estimation in Opsomer, Claeskens, Ranalli,…”
Estimation for a partial-linear single-index model (2009, methodology): “e true parameter β(r) 0 must satisfy the constraint kβ (r) 0 k < 1, and β is inﬁnitely diﬀerentiable in a neighborhood of β(r) 0 . This “remove-one-component” method for β has also been applied in Yu and Ruppert (2002). To obtain the estimator, consider a Jacobian matrix of β with respect to β(r)”
Profile‐kernel versus backfitting in the partially linear models for longitudinal/clustered data (2004, methodology): “We conjecture that the method of penalised low-order basis splines of Yu & Ruppert (2002) is also semiparametric efficient if the number of knots grows at an appropriate rate and if the smoothing parameter is appropriately selected, but deriving these two items in generality may well prove to be…”
A Gaussian process regression approach to a single-index model (2011, methodology): “Hastie, Tibshirani, and Friedman 2001 ; Yu and Ruppert, 2002 ).”
BAYESIAN ESTIMATION IN SINGLE-INDEX MODELS (2004, methodology): “For typical applications, q =2 ,m =15−20, and δ =0 .001 work well, cf. the number of knots used in Yu and Ruppert (2002) .”
Varying Index Coefficient Models (2015, background): “In the research of obesity or nutritional health science, age has been repeatedly reported as an important factor with a positive effect on body fat percentage (see Zamboni et al. (1997) and Jackson et al.”
On the asymptotics of penalized splines (2008, unknown): “Exceptions are papers such as Yu & Ruppert (2002) and Wand (1999), where the number of knots is held fixed as the sample size increases.”
Partial linear single index models with distortion measurement errors (2013, background): “2004), partial linear single index models (Liang et al. 2010; Carroll et al. 1997; Yu and Ruppert 2002; Xia and Härdle 2006), and varying-coefficient models (Hastie and Tibshirani 1993; Fan and Zhang 1999).”