Kernel Smoothing

By Matt P. Wand, M. Chris Jones. 1995

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Citations in the corpus

Interpreting Models via Single Tree Approximation (2016, methodology): “Some methods focus on estimating the underlying distribution by smoothers [Wand and Jones, 1994], while the others, for instance, bootstrapping or residual permutation, attempt to directly manipulate and reorganize the samples to generate more samples.”
MoverScore: Text Generation Evaluating with Contextualized Embeddings and Earth Mover Distance (2019, background): “) (Wand and Jones, 1994) can be illustrated as: One typical solution for KDE clustering to minimize f ( z ) is taking Mean Shift (Comaniciu and Meer, 2002), deﬁned as: γ ij k (cid:48) ( d ( v j , z i,j )) ∂d ( v j , z i,j ) ∂ v Firstly, v τ +1 j can be updated while c τ +1 ij is ﬁxed: )) z i,j i,j…”
Discovering regions of different functions in a city using human mobility and POIs (2012, methodology): “and the bandwidth r is determined according to MISE criterion [17].”
Wavelet Estimators in Nonparametric Regression: A Comparative Simulation Study (2001, methodology): “We refer, for example, to the monographs of Härdle (1990), Green & Silverman (1994), Wand & Jones (1995), Fan & Gijbels (1996) and Eubank (1999) for extensive bibliographies.”
Variable kernel density estimation (2003, background): “For an overview of fixed bandwidth kernel density estimation see Wand & Jones (1995) or Simonoff (1996).”
Kernel density estimation for heavy-tailed distributions using the champernowne transformation (2005, methodology): “In a simulation study, the proposed method shows a good performance.”
Fully Bayesian spline smoothing and intrinsic autoregressive priors (2003, unknown): “( Eubank, 1988; Wand & Jones, 1995; Fan & Gijbels, 1996).”
Improved kernel estimation of copulas: Weak convergence and goodness-of-fit testing (2009, unknown): “For background information on multivariate kernels see for example Wand and Jones (1995) and Fan and Gijbels (1996).”
Estimation of integrated squared density derivatives from a contaminated sample (2002, methodology): “See for example Wand and Jones (1995). Hence, a simple estimator for the quantity θr+lk=2 is then obtained by replacing σ2 X in equation (3.”
Testing for the equality of k regression curves (2007, methodology): “By properties of the kernel estimator (see for example Wand and Jones (1995)) and assumption (A2-ii), we have that f̂mix(x) − fmix(x) = OP ((nhn) −1/2) and f̂mix(x)f −1 mix(x) − 1 = OP ((nhn) −1/2).”
Density Estimation (2004, unknown): “Assuming that the underlying density is sufficiently smooth and that the kernel has finite fourth moment, it can be shown using Taylor series that Bias{f̂h(x)} = h2 2 µ2(K)f ′′(x) + o(h2), Var{f̂h(x)} = 1 nh R(K)f (x) + o ( 1 nh ) , where R(K) = ∫ K2(y) dy (e.g., Wand and Jones, 1995, pages 20–21).”
Bandwidth Selection in Kernel Density Estimation (2010, methodology): “see chapter 2 in Wand and Jones (1995), [26].”
On difference‐based variance estimation in nonparametric regression when the covariate is high dimensional (2005, methodology): “In addition to the kernel estimator (15), a local linear estimator with the same kernel was investigated (Wand and Jones, 1995).”