Direct estimation of the index coefficient in a single-index model

By M. Hristache, Anatoli B. Juditsky, Vladimir Spokoiny. 2001

363 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/810d5968aade30dc148c1160d0fbcabfb27cc9f6

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. Xiangrong Yin
2. Bing Li
3. Lijian Yang
4. Wolfgang Karl Härdle
5. Lixing Zhu
6. Liugen Xue
7. Yingcun Xia
8. Li Wang

In Statistics and Probability

1. Yingcun Xia
2. Lixing Zhu
3. Xiangrong Yin
4. Bing Li
5. Liugen Xue
6. Wolfgang Karl Härdle
7. R. Dennis Cook
8. Jane-ling Wang

Citations in the corpus

• SMALL BANDWIDTH ASYMPTOTICS FOR DENSITY-WEIGHTED AVERAGE DERIVATIVES (2013, neutral): “…imposed by the bias and asymptotic linearity requirements can be eased by increasing the order of the kernel, estimators employing higher-order kernels are commonly believed to have poor small-sample properties (e.g., Robinson, 1988, p. 938; Hristache, Juditsky, and Spokoiny, 2001, p. 597).”
• Penalized Spline Estimation for Partially Linear Single-Index Models (2002, methodology): “We propose P-spline estimation for partially linear singleindex models, which may be classie ed as an M-estimation approach of Hristache et al. (2001) .”
• Nonparametric checks for single-index models (2005, methodology): “was studied by among others, Li and Duan [25], Härdle, Hall and Ichimura [16], Ichimura [23] and Hristache, Juditsky and Spokoiny [22].”
• BAYESIAN ESTIMATION IN SINGLE-INDEX MODELS (2004, methodology): “Recently, a sophisticated method of iterative improvement was introduced by Hristache, Juditsky and Spokoiny (2001a) ; this method extends to multiple-index models, see Hristache, Juditsky, Polzehl and Spokoiny (2001b).”
• Optimal rates and adaptation in the single-index model using aggregation (2007, neutral): “For the estimation of the index, see for instance Hristache et al. (2001); for testing the parametric versus the nonparametric single-index assumption, see Stute and Zhu (2005).”
• Least squares estimation in the monotone single index model (2016, methodology): “Standard methods for estimating α0 and Ψ0 rely on smoothness assumptions on Ψ0, and hence involve a smoothing parameter which has to be carefully chosen, see e.g. Härdle et al. (1993), Chiou and Müller (2004), Hristache et al. (2001) and references therein.”
• Model-based mean square error estimators for k-nearest neighbour predictions and applications using remotely sensed data for forest inventories (2009, background): “When the relationship between the attribute and the ancillary variables is locally linear the SIMmodel should be near optimal (Carroll et al., 2007; Hristache et al., 2001).”
• Successive direction extraction for estimating the central subspace in a multiple-index regression (2008, methodology): “Furthermore, our method uses a two-dimensional kernel, whereas MAVE and SAE employ higher dimensional kernels, thus increasing the extent of local sparsity in kernel smoothing.”