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336,271
ASYMPTOTIC EQUIVALENCE OF ESTIMATORS OF AVERAGE DERIVATIVES
"... This paper establishes the asymptotic equivalence among four semiparametric sample analog estimators of average derivatives of a regression function and their corresponding slope or ratioofmoments estimators. Keywords: Average derivative estimators, Semiparametric, Asymptotic equivalance. ..."
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This paper establishes the asymptotic equivalence among four semiparametric sample analog estimators of average derivatives of a regression function and their corresponding slope or ratioofmoments estimators. Keywords: Average derivative estimators, Semiparametric, Asymptotic equivalance.
Asymptotic equivalence for nonparametric regression
 Math. Methods Statist
"... Abstract. We consider a nonparametric model En, generated by independent observations Xi, i = 1,..., n, with densities p(x, θi), i = 1,..., n, the parameters of which θi = f(i/n) ∈ Θ are driven by the values of an unknown function f: [0, 1] → Θ in a smoothness class. The main result of the paper i ..."
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Abstract. We consider a nonparametric model En, generated by independent observations Xi, i = 1,..., n, with densities p(x, θi), i = 1,..., n, the parameters of which θi = f(i/n) ∈ Θ are driven by the values of an unknown function f: [0, 1] → Θ in a smoothness class. The main result of the paper is that, under regularity assumptions, this model can be approximated, in the sense of the Le Cam deficiency pseudodistance, by a nonparametric Gaussian shift model Yi = Γ(f(i/n)) + εi, where ε1,..., εn are i.i.d. standard normal r.v.’s, the function Γ(θ) : Θ → R satisfies Γ′(θ) = √I(θ) and I(θ) is the Fisher information corresponding to the density p(x, θ). 1.
On Sequences That Are Asymptotically Equivalent to . . .
"... . We present a characterization of the sequences in a Banach space that have a sequence of blocks cofinally equivalent to the standard basis of #p (1 # p < #) or c 0 . 1. Introduction A central question in Banach space theory has been to identify the class of Banach spaces that contain almo ..."
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. We present a characterization of the sequences in a Banach space that have a sequence of blocks cofinally equivalent to the standard basis of #p (1 # p < #) or c 0 . 1. Introduction A central question in Banach space theory has been to identify the class of Banach spaces that contain
Asymptotic equivalence of density estimation and Gaussian white noise
 Ann. Statist
, 1996
"... Signal recovery in Gaussian white noise with variance tending to zero has served for some time as a representative model for nonparametric curve estimation, having all the essential traits in a pure form. The equivalence has mostly been stated informally, but an approximation in the sense of Le Cam’ ..."
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Cited by 123 (5 self)
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’s deficiency distance ∆ would make it precise. The models are then asymptotically equivalent for all purposes of statistical decision with bounded loss. In nonparametrics, a first result of this kind has recently been established for Gaussian regression (Brown and Low, 1993). We consider
Asymptotic equivalence of nonparametric autoregression and nonparametric
, 2006
"... It is proved that nonparametric autoregression is asymptotically equivalent in the sense of Le Cam’s deficiency distance to nonparametric regression with random design as well as with regular nonrandom design. 1. Introduction. We assume that observations X0,...,Xn from a stationary autoregressive pr ..."
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Cited by 7 (0 self)
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It is proved that nonparametric autoregression is asymptotically equivalent in the sense of Le Cam’s deficiency distance to nonparametric regression with random design as well as with regular nonrandom design. 1. Introduction. We assume that observations X0,...,Xn from a stationary autoregressive
Asymptotic equivalence theory for nonparametric regression with random design
 Ann. Statist
, 2002
"... This paper establishes the global asymptotic equivalence between the nonparametric regression with random design and the white noise under sharp smoothness conditions on an unknown regression or drift function. The asymptotic equivalence is established by constructing explicit equivalence mappings b ..."
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Cited by 39 (6 self)
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This paper establishes the global asymptotic equivalence between the nonparametric regression with random design and the white noise under sharp smoothness conditions on an unknown regression or drift function. The asymptotic equivalence is established by constructing explicit equivalence mappings
Asymptotic equivalence for nonparametric regression with multivariate and random design
, 2008
"... We show that nonparametric regression is asymptotically equivalent in Le Cam’s sense with a sequence of Gaussian white noise experiments as the number of observations tends to infinity. We propose a general constructive framework based on approximation spaces, which permits to achieve asymptotic equ ..."
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Cited by 20 (2 self)
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We show that nonparametric regression is asymptotically equivalent in Le Cam’s sense with a sequence of Gaussian white noise experiments as the number of observations tends to infinity. We propose a general constructive framework based on approximation spaces, which permits to achieve asymptotic
ASYMPTOTIC EQUIVALENCE OF VOLTERRA DIFFERENCE SYSTEMS
"... lo The purpose of this paper is to give some results on the asymptotic relationship between the solutions of a linear difference equation and its perturbed nonlinear equation. 1. ..."
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lo The purpose of this paper is to give some results on the asymptotic relationship between the solutions of a linear difference equation and its perturbed nonlinear equation. 1.
THE ASYMPTOTIC EQUIVALENCE OF THE DIFFERENTIAL EQUATIONS WITH MODIFIED ARGUMENT
"... Abstract. This paper treats the asymptotic equivalence of the equations x ′ (t) = A(t)x(t) and x ′ (t) = A(t)x(t) + f(t, x(g(t))) using the notion of ϕcontraction. 2000 Mathematics Subject Classification: 34K05, 47H10. 1. ..."
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Abstract. This paper treats the asymptotic equivalence of the equations x ′ (t) = A(t)x(t) and x ′ (t) = A(t)x(t) + f(t, x(g(t))) using the notion of ϕcontraction. 2000 Mathematics Subject Classification: 34K05, 47H10. 1.
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