Remarks on Some Nonparametric Estimates of a Density Function

By M. Rosenblatt. 1956

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Citations in the corpus

Bayesian Learning of Kernel Embeddings (2016, methodology): “…integrated squared error is a popular choice (Bowman, 1985), and there is even a formula giving the optimal smoothing parameter asymptotically, see Rosenblatt (1956); Parzen (1962)) but we are not aware of work linking this literature to methods based on positive deﬁnite/RKHS kernels we study…”
Bias Correction of Learned Generative Models using Likelihood-Free Importance Weighting (2019, background): “In spite of the recent successes of deep generative models, existing theoretical results show that learning distributions in an unbiased manner is either impossible or has prohibitive sample complexity [4, 5].”
Bias and Generalization in Deep Generative Models: An Empirical Study (2018, background): “However, estimating p(x) is difficult [1].”
Kernel estimation of density level sets (2005, background): “Indeed, su h an assumption does not permit to onsider the important ase where the density under study is multimodal with a nite number of modes, and hen e the results an not be applied to luster analysis in parti ular.”
PRECOG: PREdiction Conditioned on Goals in Visual Multi-Agent Settings (2019, methodology): “KDE [27, 32] serves as a useful performance bound on all methods; it can compute both m̂ and ê.”
Applied Multivariate Statistical Analysis (2003, background): “Rosenblatt (1956), Whittle (1958), and Parzen (1962) developed an approach which avoids the last three difficulties.”
Kernel density estimation on Riemannian manifolds (2005, background): “(9) The kernels involved in kernel density estimators in the Euclidean case are centered on the observations (Akaike, 1954; Parzen, 1962; Rosenblatt, 1956).”
An updated review of Goodness-of-Fit tests for regression models (2013, background): “…for a density can be written as Tn = T (fnh, f̂θ ), or more exactly as Tn = T ( fnh,Êθ (fnh) ) ≡ T (α̃n) (2) where fnh(x) = n−1 ∑ni=1 Kh(x −Xi) is the kernel density estimator (see Rosenblatt 1956 and Parzen 1962), with K a kernel density function and h the smoothing parameter or bandwidth.”
A Family of Nonparametric Density Estimation Algorithms (2013, background): “A good choice is that of localized radial expansions, which depend on a single parameter: all the complexity of arbitrary, possibly convoluted probability densities can be built through the composition of such simple maps.”
On Memorization in Probabilistic Deep Generative Models (2021, background): “By contrast, a kernel density estimate (KDE) [13, 14] of the probability density may be more sensitive to the presence or absence of a particular observation.”