Non- and semi-parametric estimation in models with unknown smoothness

Kotlyarova, Yulia; Zinde‐Walsh, Victoria

doi:10.1016/j.econlet.2006.06.014

Cited by 14 publications

(10 citation statements)

References 2 publications

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“…Finally, Koenker (2005) points out that the (rather arbitrary) selection of smoothing parameters highly influences whether smoothing actually improves inference in applications. Kotlyarova and Zinde-Walsh (2006), however, provide a method for selecting the optimal bandwidth that shows good performance on large datasets.…”

Section: Binary Quantile Regression: Frequentist Approachesmentioning

confidence: 99%

Binary quantile regression: a Bayesian approach based on the asymmetric Laplace distribution

Benoit

Poel

2010

J of Applied Econometrics

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SUMMARY This paper develops a Bayesian method for quantile regression for dichotomous response data. The frequentist approach to this type of regression has proven problematic in both optimizing the objective function and making inferences on the parameters. By accepting additional distributional assumptions on the error terms, the Bayesian method proposed sets the problem in a parametric framework in which these problems are avoided. To test the applicability of the method, we ran two Monte Carlo experiments and applied it to Horowitz's (1993) often studied work‐trip mode choice dataset. Compared to previous estimates for the latter dataset, the method proposed leads to a different economic interpretation. Copyright © 2010 John Wiley & Sons, Ltd.

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Section: Binary Quantile Regression: Frequentist Approachesmentioning

confidence: 99%

Binary quantile regression: a Bayesian approach based on the asymmetric Laplace distribution

Benoit

Poel

2010

J of Applied Econometrics

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“…Suppose now that several conditional expectations are informative about θ. It may be the case that the different regression functions of interest display different degrees of smoothness, and then lead to choosing heterogeneous rates of convergence for corresponding optimal bandwidths (see Kotlyarova and Zinde-Walsh (2006)). Then, we end up with vectorial functions φ T (θ) and ρ(θ) such that, for each component i:…”

Section: Example 21 (Kernel Smoothing)mentioning

confidence: 99%

Efficient minimum distance estimation with multiple rates of convergence

Antoine

Renault

2012

Journal of Econometrics

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Abstract:This paper extends the asymptotic theory of GMM inference to allow sample counterparts of the estimating equations to converge at (multiple) rates, different from the usual square-root of the sample size. In this setting, we provide consistent estimation of the structural parameters. In addition, we define a convenient rotation in the parameter space (or reparametrization) which permits to disentangle the different rates of convergence. More precisely, we identify special linear combinations of the structural parameters associated with a specific rate of convergence. Finally, we demonstrate the validity of usual inference procedures, like the overidentification test and Wald test, with standard formulas. It is important to stress that both estimation and testing work without requiring the knowledge of the various rates. However, the assessment of these rates is crucial for (asymptotic) power considerations. Possible applications include econometric problems with two dimensions of asymptotics, due to trimming, tail estimation, infill asymptotic, social interactions, kernel smoothing or any kind of regularization. JEL classification: C32; C12; C13; C51.

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“…Combining estimators was recently investigated in the statistical literature, where for the most part convex combinations are used as a means to achieve adaptiveness (Juditsky and Nemirovski, 2000; Yang, 2000). Kotlyarova and Zinde‐Walsh (2006, hereafter KZW) propose non‐convex combinations for estimators with possibly non‐parametric rates. They develop the so‐called combined estimator with weights that minimize the trace of its estimated AMSE.…”

Section: Introductionmentioning

confidence: 99%

Smoothness adaptive average derivative estimation

Schafgans

Zinde‐Walsh

2010

The Econometrics Journal

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Many important models utilize estimation of average derivatives of the conditional mean function. Asymptotic results in the literature on density weighted average derivative estimators (ADE) focus on convergence at parametric rates; this requires making stringent assumptions on smoothness of the underlying density; here we derive asymptotic properties under relaxed smoothness assumptions. We adapt to the unknown smoothness in the model by consistently estimating the optimal bandwidth rate and using linear combinations of ADE estimators for different kernels and bandwidths. Linear combinations of estimators (i) can have smaller asymptotic mean squared error (AMSE) than an estimator with an optimal bandwidth and (ii) when based on estimated optimal rate bandwidth can adapt to unknown smoothness and achieve rate optimality. Our combined estimator minimizes the trace of estimated MSE of linear combinations. Monte Carlo results for ADE confirm good performance of the combined estimator. Copyright (C) The Author(s). Journal compilation (C) Royal Economic Society 2010.

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Non- and semi-parametric estimation in models with unknown smoothness

Cited by 14 publications

References 2 publications

Binary quantile regression: a Bayesian approach based on the asymmetric Laplace distribution

Binary quantile regression: a Bayesian approach based on the asymmetric Laplace distribution

Efficient minimum distance estimation with multiple rates of convergence

Smoothness adaptive average derivative estimation

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