Consistent Nonparametric Regression

By C. Stone. 1977

Subfields: Statistics and Probability, Statistical Learning Theory

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Citations in the corpus

A Retrieve-and-Edit Framework for Predicting Structured Outputs (2018, methodology): “Our model is related to nonparametric regression techniques [32], where in our case, proximity learned by the encoder corresponds to a neighborhood,”
Local Linear Forests (2018, methodology): “Random forests were first introduced by Breiman (2001), building on the work of Breiman et al. (1984) on recursive partitioning (CART), Breiman (1996) on bagging, and Amit and Geman (1997) on randomized trees.”
Filtering with State-Observation Examples via Kernel Monte Carlo Filter (2013, methodology): “s nonparametrically, and then use it to run a particle ﬁlter with a transition model. Vlassis et al. (2002) proposed to apply conditional density estimation based on the k-nearest neighbors approach (Stone, 1977) for learning the observation model. A problem here is that conditional density estimati”
Consistency of Random Forests (2014, methodology): “Additive regression models, which extend linear models, were popularized by Stone (1985) and Hastie and Tibshirani (1986). These models, which decompose the regression function as a sum of univariate functions, are flexible and easy to interpret.”
Flexible Simulated Moment Estimation of Nonlinear Errors-in-Variables Models (2001, unknown): “ForK-nearest-neighbor estimators with K3 `, K/n3 0, (ii) follows by lemma 8 of Robinson (1987) and proposition 1 of Stone (1977), while (iii)(a) holds by construction.”
Towards optimal doubly robust estimation of heterogeneous causal effects (2020, background): “For many linear smoothers i | w i ( x ; X n ) | ≤ C with probability one, so that c n = 1 (e.g., this is a condition in the celebrated theorem of Stone [1977] guaranteeing weak universal consistency of linear smoothers).”
A fully automatic and robust brain MRI tissue classification method (2003, background): “distributions. It was shown (Devroye, 1981; Stone, 1977 ) that if k satises both of the conditions:”
On the Rate of Convergence of the Bagged Nearest Neighbor Estimate (2010, unknown): “n → ∞ (Stone [ 27 ], Devroye [9], and Problems 11.7, 11.8 of Devroye, Gy¨orfi and Lugosi [10]).”
Estimating Semiparametric Panel Data Models by Marginal Integration (2012, unknown): “The popular estimators are Nadaraya-Watson (Nadaraya (1964); Watson (1964)), Gasser-M¨uller (Gasser and M¨uller (1984)), and local linear (Stone (1977); Cleveland (1979); Fan (1992); Ruppert and Wand (1994)), among others.”
Estimation of the Conditional Variance in Paired Experiments (2008, methodology): “We would like to thank John Lindsey and two anonymous referees for helpful suggestions. sample-size-dependent smoothing parameter choices (see, e.g., Stone, 1977).”
Sharp Sensitivity Analysis for Inverse Propensity Weighting via Quantile Balancing (2021, unknown): “Let ˆ Q τ ( x , z ) be an estimate of the conditional quantile function of Y obtained by some kind of quantile regression (e.g., Stone 1977; Koenker and Bassett 1978; Meinshausen 2006; Athey, Tibshirani, and Wager 2019).”