Remarks on Some Nonparametric Estimates of a Density Function

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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…”
Non‐parametric Estimation of Extreme Risk Measures from Conditional Heavy‐tailed Distributions (2014, methodology): “We propose to use a classical kernel estimator (Parzen, 1962; Rosenblatt, 1956) given by O'a;n.yjx/ D nX iD1 Kh.x Xi /Y ai I¹Yi > yº , nX iD1 Kh.x Xi /; (2) where I¹:º is the indicator function and h D hn is a non-random sequence such that h !”
Asymptotic theory for stationary processes (2011, background): “Rosenblatt (1956) introduced strong mixing processes, while Gänssler and Häeusler (1979) and Hall and Heyde (1980) considered martingales.”
A distributional interpretation of robust optimization (2010, neutral): “function f : R m → R {−∞}, and a non-empty Borel set Z ⊆ R m , the following holds: inf x ′ ∈Z f (x ′ ) = inf µ∈P|µ(Z)=1 R m f (x)dµ(x).”