Smooth regression analysis

By G. Watson. 1964

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Citations in the corpus

Deep Weighted Averaging Classifiers (2018, background): “where K(x,xi ) is a kernel, such as a Gaussian [35, 57].”
Does data interpolation contradict statistical optimality? (2018, methodology): “In particular, the Nadaraya-Watson estimator [9, 13] is defined as”
Relative Positional Encoding for Transformers with Linear Complexity (2021, unknown): “Following classical non-parametric regression principles (Nadaraya, 1964; Watson, 1964), it consists in a simple weighted sum: where each attention coefﬁcient a mn ∈ R + – gathered in the M × N matrix A – indicates how important the value v n is in the computation of the output y m .”
Power Curve Estimation With Multivariate Environmental Factors for Inland and Offshore Wind Farms (2015, unknown): “…on the kernelbased approach, namely, using a conditional kernel density estimation (CKD) (Rosenblatt 1969; Hyndman, Bashtannyk, and Grunwald 1996) for estimating the conditional density, p(y|x), or a kernel regression (Nadaraya 1964; Watson 1964) for estimating the conditional expectation, E(y|x).”
An Empirical Comparison of Machine Learning Models for Time Series Forecasting (2010, background): “Nadaraya and Watson developed this model (Nadaraya [43] and Watson [52]).”
Determinants of the link between financial and economic development: Evidence from a functional coefficient model (2014, methodology): “Estimation We apply a semiparametric estimator of β(ω) similar to the Nadaraya–Watson estimator (Nadaraya, 1964; Watson, 1964) which is given by β ωð Þ ¼ X−1 ωð ÞY ωð Þ; ð5Þ whereX ωð Þ ¼ ∑Ni¼1∑Tt¼1exit ex ′itKh ωit−ωð Þ andY ωð Þ ¼ ∑Ni¼1 ∑Tt¼1 exiteyitKh ωit−ωð Þ, Kh(⋅) = K(⋅/h)/h, with K(·) being…”
Nonparametric Kernel Regression with Multiple Predictors and Multiple Shape Constraints (2012, methodology): “This class of kernel smoothers includes the Nadaraya-Watson estimator (Nadaraya (1965),Watson (1964)), the Priestley-Chao estimator (Priestley and Chao (1972)), the Gasser-Müller estimator (Gasser and Müller (1979)) and the local polynomial estimator (Fan (1992)), among others.”
Design of Experiments in Nonlinear Models: Asymptotic Normality, Optimality Criteria and Small-Sample Properties (2013, methodology): “This corresponds to the method suggested by Wolfe (1970) in a more general context.”
Nonparametric analysis of covariance (2001, background): “…space of r-times continuously diierentiable functions on the interval 0; 1]: Let ^ g i (t) = P n i j=1 K t?t ij h i Y ij P n i j=1 K t?t ij h i (2.4) denote the Nadaraya-Watson estimator of the ith regression function g i and h i the corresponding bandwidth see Nadaraya (1964) and Watson (1964)].”
Semiparametric Analysis to Estimate the Deal Effect Curve (2001, background): “For the Nadaraya (1964) and Watson (1964) estimator the choice of w i in O m. (cid:1) / is where K. (cid:1) / is a “Kernel function”, and h the “bandwidth parameter”.”
The dynamics of regional inequalities (2009, unknown): “11 See Nadaraya (1964) and Watson (1964).”
Genomic-Assisted Prediction of Genetic Value With Semiparametric Procedures (2006, background): “This is the reason why this type of estimator is called ‘‘local,’’ in the sense that observations with x i coordinates closer to the focal point x are weighted more strongly in the computation of the ﬁtted value ^ E ð y j x Þ .”
INFINITE ORDER CROSS-VALIDATED LOCAL POLYNOMIAL REGRESSION (2015, background): “The seminal work of Nadaraya (1965) and Watson (1964) examined the ‘local constant’ variant (which is a limiting case of the local polynomial estimator with polynomial order p = 0), while the local linear variant (p = 1) is dominant in applied settings as it possesses one of the best boundary…”