Nonparametric regression with nonparametrically generated covariates

Mammen, Enno; Rothe, Christoph; Schienle, Melanie

doi:10.1214/12-aos995

Cited by 87 publications

(84 citation statements)

References 31 publications

(33 reference statements)

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“…The estimation problem is similar to the one of kernel estimation with errorsin-variables. The implications of this for kernel regression have been analyzed in Mammen et al (2012) and Sperlich (2009) in a cross-sectional framework. We follow a similar strategy: We split up the total estimation error into two components: One component due to the estimation of σ 2 t in the first step, and a second component due to the sampling error of the estimator based on the actual terms of use, available at https://www.cambridge.org/core/terms.…”

Section: Nonparametric Estimation Of the Sv Modelmentioning

confidence: 99%

“…In the nonparametric case, our two-stage estimation problem is similar to the one considered in Sperlich (2009) where kernel regression with generated regressors is considered; see also Newey, Powell, and Vella (1999), Xiao, Linton, Carroll, and Mammen (2003), and Mammen, Rothe, and Schienle (2012). The parametric estimators can be seen as a two-step semiparametric estimation procedure, where a parametric estimator relies on a preliminary nonparametric estimator; see e.g., Kristensen (2010b) and Mammen, Rothe, and Schienle (2013).…”

Section: Introductionmentioning

confidence: 99%

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Estimation of Stochastic Volatility Models by Nonparametric Filtering

Kanaya

Kristensen²

2015

Econom. Theory

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A two-step estimation method of stochastic volatility models is proposed: In the first step, we nonparametrically estimate the (unobserved) instantaneous volatility process. In the second step, standard estimation methods for fully observed diffusion processes are employed, but with the filtered/estimated volatility process replacing the latent process. Our estimation strategy is applicable to both parametric and nonparametric stochastic volatility models, and can handle both jumps and market microstructure noise. The resulting estimators of the stochastic volatility model will carry additional biases and variances due to the first-step estimation, but under regularity conditions we show that these vanish asymptotically and our estimators inherit the asymptotic properties of the infeasible estimators based on observations of the volatility process. A simulation study examines the finite-sample properties of the proposed estimators.

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Section: Nonparametric Estimation Of the Sv Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Estimation of Stochastic Volatility Models by Nonparametric Filtering

Kanaya

Kristensen²

2015

Econom. Theory

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“…For both cases, we use the standardized Epanechnikov kernel and undersmoothing ROT bandwidths by specifying h = [s Z n −1/5 s U c n −1/5 ] in both DGPs 1 and 2 andλ 1 =λ 2 = n −2/5 in DGP 2 when we regress either X i or ε 2 i on V i . The use of undersmoothing bandwidths helps to eliminate the effect of early stage estimates' bias on the final estimate; see Mammen, Rothe and Schienle (2010). To obtain the CDXW estimate, we need first to obtain the local linear estimate of E (X i |V i ) by specifying a similar undersmoothing bandwidth.…”

Section: Evaluation Of the Local Linear Gmm Estimatesmentioning

confidence: 99%

Local Linear GMM Estimation of Functional Coefficient IV Models With an Application to Estimating the Rate of Return to Schooling

Murtazashvili

Ullah

2013

Journal of Business & Economic Statistics

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We consider the local linear GMM estimation of functional coefficient models with a mix of discrete and continuous data and in the presence of endogenous regressors. We establish the asymptotic normality of the estimator and derive the optimal instrumental variable that minimizes the asymptotic variance-covariance matrix among the class of all local linear GMM estimators. Data-dependent bandwidth sequences are also allowed for. We propose a nonparametric test for the constancy of the functional coefficients, study its asymptotic properties under the null hypothesis as well as a sequence of local alternatives and global alternatives, and propose a bootstrap version for it. Simulations are conducted to evaluate both the estimator and test. Applications to the 1985 Australian Longitudinal Survey data indicate a clear rejection of the null hypothesis of the constant rate of return to education, and that the returns to education obtained in earlier studies tend to be overestimated for all the work experience.JEL Classifications: C12, C13, C14

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“…If this is the case, the estimation error in the generated covariateŴ would affect the rates of convergence off C|Ŵ Z (see Mammen, Rothe, & Schienle (2012)) and then of our estimator. This can be seen from Theorem 3.…”

Section: If φ(T) = (− Log(t))mentioning

confidence: 99%

Semiparametric estimation of random coefficients in structural economic models

Hoderlein¹,

Nesheim²,

Simoni³

2012

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This paper discusses nonparametric estimation of the distribution of random coefficients in a structural model that is nonlinear in the random coefficients. We establish that the problem of recovering the probability density function (pdf ) of random parameters falls into the class of convexly-constrained inverse problems. The framework offers an estimation method that separates computational solution of the structural model from estimation. We first discuss nonparametric identification. Then, we propose two alternative estimation procedures to estimate the density and derive their asymptotic properties. Our general framework allows us to deal with unobservable nuisance variables, e.g., measurement error, but also covers the case when there are no such nuisance variables. Finally, Monte Carlo experiments for several structural models are provided which illustrate the performance of our estimation procedure.

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Nonparametric regression with nonparametrically generated covariates

Cited by 87 publications

References 31 publications

Estimation of Stochastic Volatility Models by Nonparametric Filtering

Estimation of Stochastic Volatility Models by Nonparametric Filtering

Local Linear GMM Estimation of Functional Coefficient IV Models With an Application to Estimating the Rate of Return to Schooling

Semiparametric estimation of random coefficients in structural economic models

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