Nonparametric regression under qualitative smoothness assumptions

By Enno Mammen. 1991

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Citations in the corpus

Additive models with trend filtering (2017, background): “, Mammen (1991)), where A > 0 is a constant that depends only on R.”
VAR for VaR: Measuring Tail Dependence Using Multivariate Regression Quantiles (2015, unknown): “(2010) or the isotonization method suggested by Mammen (1991).5In passing, we note that in the subsequent empirical study later, we exclusively focus on estimating the MVMQ-CAViaR model at the 1% level only (i.”
Estimation of a convex function: characterizations and asymptotic theory. (2001, unknown): “For some work on computation of the estimators studied here, see Mammen (1991), Jongbloed (1998) and Meyer (1997).”
Forecasting and Stress Testing with Quantile Vector Autoregression (2019, methodology): “The asymptotic variance-covariance matrix can be consistently estimated as suggested in theorems 3 and 4 of White et al. (2015), or using bootstrap based methods in the spirit of Buchinsky (1995).”
A Nonparametric Approach to Measuring and Testing Curvature (2005, background): “The second category includes tests based on nonparametric estimation of functions subject to convex/concave restriction (e.g., Hildreth 1954; Mammen 1991; Wang 1992; Yatchew 1992).”
Estimation of a k-monotone density: limit distribution theory and the Spline connection (2005, unknown): “Such a result was already proved by Mammen [29] (see Lemma 8) in the context of nonparametric regression, where the true regression curve, m, is piecewise concave/convex or convex/concave such that m is twice continuously differentiable in the neighborhood of x0, and m′′(x0) = 0.”
Inequality constrained quantile regression (2005, background): “Mammen (1991) , for example, considers kernel smoothing followed by a pooled-adjacent-violators (PAV) step as well as a procedure that reverses the order of these operations.”
Nonparametric Shape-Restricted Regression (2017, background): “sub-Gaussian with mean zero and f ′′(t) 6= 0, the rate of convergence of f̂n(t) is known to be n −2/5 (see [92]).”
Doubly penalized estimation in additive regression with high-dimensional data (2019, methodology): “For the space W11 or V1, the entropy H(u,G∗j (1),‖ · ‖n) can be obtained from Mammen (1991), still of order u−1/m = u−1, as described in the Supplementary Material, Section S2.”
Semi-nonparametric estimation of the call-option price surface under strike and time-to-expiry no-arbitrage constraints☆ (2015, unknown): “Necessary calendar arbitrage constraints for European options, similar to those known for American-style options, were first obtained by Reiner (2000) and Gatheral (2004).”
Shape restricted regression with random Bernstein polynomials (2007, methodology): “Major approaches to this problem include the projection methods for constrained smoothing, which are discussed in Mammen et al. [24] and contain smoothing splines methods and kernel and local polynomial methods and others as special cases, the isotonic regression approach studied by Mukerjee [25], M”
QUANTILE AND PROBABILITY CURVES WITHOUT CROSSING (2007, methodology): “3 by isotonization in the second.2 Similarly to Mammen (1991), we can employ quantile estimation in the first step followed by isotonization in the second, obtaining an interesting method whose properties have yet to be studied.”
Estimating a Convex Function in Nonparametric Regression (2007, background): “Mammen (1991) derived the rate of convergence of a least squares estimator of a convex or concave regression function and its derivative at a fixed point, while recently Groeneboom et al. (2001) proved consistency and derived the asymptotic distribution of the estimator at a fixed point of positive…”
Nonparametric Least Squares Estimation of a Multivariate Convex Regression Function (2010, background): “Proof: Property (i ) follows from Moreau’s decomposition theorem, which can be stated as: Consider a closed convex set C on a Hilbert space H with inner product 〈·, ·〉 and norm ‖ · ‖. Then, for any x ∈ H there is only one vector xC ∈ C satisfying ‖x − xC ‖ = argminξ∈C {‖x − ξ‖}. The vector xC is cha”