Nonparametric regression with infinite order flat-top kernels

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Banded and tapered estimates for autocovariance matrices and the linear process bootstrap (2010, methodology): “We also use three different weight functions: rectangular, defined by j(x) 1⁄4 1f|x| < 1g; trapezoidal as defined in eqn (4); and infinitely differentiable, as defined in McMurry and Politis (2004) and shown in Figure 1. Simulations were performed in R (R Development Core Team, 2009). Results are ba”
√n-consistent parameter estimation for systems of ordinary differential equations : bypassing numerical integration via smoothing (2010, unknown): “that arose in a different context in [31], see formula (3) on page 552 there, so that it could have the required properties in our context.”
HIGHER-ORDER ACCURATE, POSITIVE SEMIDEFINITE ESTIMATION OF LARGE-SAMPLE COVARIANCE AND SPECTRAL DENSITY MATRICES (2005, unknown): “For example, McMurry and Politis (2004) constructed a member of the flat-top family that is infinitely differentiable; it is defined as λID,b,c(x) = ⎧⎪⎪⎪⎨ ⎪⎪⎩ 1 if |x| ≤ c exp (−b exp(−b/(|x| − c)2)/(|x| − 1)2) if c < |x| < 1 0 if |x| ≥ 1 (24) where c ∈ (0, 1], and b > 0 is a shape parameter.”