On Estimating Regression

By E. Nadaraya. 1964

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Statistics and Probability

Citations in the corpus

Time-series forecasting with deep learning: a survey (2020, background): “Indeed, a rich body of literature exists for automated approaches to time-series forecasting—including automatic parametric model selection [18], and traditional machine learning methods such as kernel regression [19] and support vector regression [20].”
Learning Optimal and Fair Decision Trees for Non-Discriminative Decision-Making (2019, methodology): “The idea of using a locally weighted average to estimate the conditional expectation is a well known technique in statistics referred to as Kernel Regression, see e.g., (Nadaraya 1964).”
Meta-Learning: A Survey (2018, neutral): “The weights of the μj ’s are computed using the Nadaraya-Watson kernel-weighted average, where each task is represented as a vector of relative landmarks, and the Epanechnikov quadratic kernel [104] is used to measure the similarity between the relative landmark vectors of tj and tnew.”
Making AI Forget You: Data Deletion in Machine Learning (2019, methodology): “They include linear models [55, 27, 83, 81, 18, 74], certain types of lazy learning [88, 6, 11] techniques such as non-parametric Nadaraya-Watson kernel regressions [61] or nearest-neighbors methods [22, 74], recursive support vector machines [19, 81], and co-occurrence based collaborative filtering”
Does data interpolation contradict statistical optimality? (2018, methodology): “In particular, the Nadaraya-Watson estimator (Nadaraya, 1964; Watson, 1964) is deﬁned as where K : R d → R is a kernel function and h > 0 is a bandwidth and we assume that the denominator does not vanish.”
ROBUST LOCAL POLYNOMIAL REGRESSION FOR DEPENDENT DATA (2001, methodology): “When the sequence is i.i.d., the nonparametric estimation of m(x) was first introduced independently by Nadaraya (1964) and Watson (1964): for a sample of size n, m̂(x) = n∑ j=1 wn(x,Xj)Yj , (1.1) where wn(x,Xj) = K( Xj − x hn )/ n∑ i=1 K( Xi − x hn ).”
Sparsity Invariant CNNs (2017, methodology): “Second, we apply the Nadaraya-Watson regres-sor [47,64] using a Gaussian kernel on the sparse depth input.”
Zipf's Law for Cities in the Regions and the Country (2011, unknown): “The estimation was performed using the NadarayaWatson technique (see Nadaraya 1964; Watson 1964; Härdle 1992) which estimates the expectation of growth conditional on size.”
Kernel bandwidth optimization in spike rate estimation (2009, methodology): “overlap, we adopt the Nadaraya-Watson kernel regression (Nadaraya 1964; Watson 1964) of w̄ t as a local bandwidth at time t:”
Estimating Semiparametric Panel Data Models by Marginal Integration (2012, unknown): “We will prove asymptotic properties only for the local linear method, which includes Nadaraya-Watson as a special case.”
Contour regression: A general approach to dimension reduction (2005, background): “However, they can be easily paralleled for thresholding based on a ﬁxed proportion: Modulo the fact that c need not go to 0 as n → ∞ , the comparison of these two thresholding options is analogous to that between a kernel and a nearest-neighbor estimator [18, 21, 22].”
Clustering by Scale-Space Filtering (2000, unknown): “Such an iteration can be interpreted as an iterative local centroid estimation [13], [33], [ 34 ], [35], [36].”
Transformers learn in-context by gradient descent (2022, unknown): “Interestingly, when choosing W0 = 0, we furthermore see that a single self-attention layer or Transformer block can be regarded as doing nonparametric kernel smoothing ŷ = ∑N i=1 yik(xi, xtest) based on the data given in-context (Nadaraya, 1964; Watson, 1964).”
An updated review of Goodness-of-Fit tests for regression models (2013, methodology): “…there exist a large variety of smoothing methods for regression models, this review will mainly consider kernel type estimators such as the Nadaraya–Watson estimator (Nadaraya 1964; Watson 1964), given by mnh(x) = n ∑ i=1 Wni(x)Yi, with Wni(x) = Kh(x − Xi)∑n j=1 Kh(x − Xj) , i = 1, . . . , n.”