The practice of non‐parametric estimation by solving inverse problems: the example of transformation models

Fève, Frédérique; Florens, Jean‐Pierre

doi:10.1111/j.1368-423x.2010.00314.x

Cited by 29 publications

(31 citation statements)

References 44 publications

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“…Feve and Florens (2010) and Darolles, Fan, Florens, and Renault (2011) extend the discrepancy rule proposed by Morozov (1993) and Engl, Hanke, and Neubauer (1996) and suggest a data driven selection method. As explained in Engl, Hanke, and Neubauer (1996), the discrepancy principle is based on the comparison between the residual of the functional equation and the assumed bound for the noise level.…”

Section: Selection Of Regularization Parameter(s)mentioning

confidence: 64%

“…In order to get estimates of H and ϕ, conditional expectations can be replaced by their empirical counterparts, i.e., by kernel estimators. In fact, the implementation of this method has already been discussed in detail in papers such as Darolles, Fan, Florens, and Renault (2011);Feve and Florens (2010);Sokullu (2016b).…”

Section: The Modelmentioning

confidence: 99%

“…Selection of regularization parameter in NPIV problems has already been studied by Feve and Florens (2010); Darolles, Fan, Florens, and Renault (2011);Centorinno (2015) among others. Feve and Florens (2010) and Darolles, Fan, Florens, and Renault (2011) extend the discrepancy rule proposed by Morozov (1993) and Engl, Hanke, and Neubauer (1996) and suggest a data driven selection method.…”

Section: Selection Of Regularization Parameter(s)mentioning

confidence: 99%

“…Moreover, the regularization parameter defined by this rule is shown to be convergent and of optimal order. Both Feve and Florens (2010) and Darolles, Fan, Florens, and Renault (2011) use the idea of minimizing a function of squared norm of residuals. The squared norm of residuals cannot be used directly and a function of it is needed as it reaches its minimum at α = 0.…”

Section: Selection Of Regularization Parameter(s)mentioning

confidence: 99%

“…It is of crucial importance since it balances the fitting and smoothing of the estimated functional parameters. Various selection methods have been considered in the literature, such as the discrepancy rule (Feve and Florens, 2010;Florens and Sokullu, 2016), truncation (Horowitz, 2011), and cross-validation (Centorinno, 2015). Except for Florens and Sokullu (2016), none of these papers consider a semiparametric transformation model, which is characterized by the need for selecting two different regularization parameters: one for the transformation of the outcome, and one for the structural function.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Cross-Validation Selection of Regularisation Parameter(s) for Semiparametric Transformation Models

Sokullu¹,

Stouli²

2017

Annals of Economics and Statistics

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We propose cross-validation criteria for the selection of regularization parameter(s) in the semiparametric instrumental variable transformation model proposed in Florens and Sokullu (2016). In the presence of an endogenous regressor, this model is characterized by the need to choose two regularization parameters, one for the structural function and one for the transformation of the outcome. We consider two-step and simultaneous criteria, and analyze the finite-sample performance of the estimator using the corresponding regularization parameters by means of several Monte-Carlo simulations. Our numerical experiments show that simultaneous selection of regularization parameters provides significant improvements in the performance of the estimator. We also apply our methods to the choice of regularization parameters in the estimation of two-sided network effects in the German magazine industry.

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Section: Selection Of Regularization Parameter(s)mentioning

confidence: 64%

Section: The Modelmentioning

confidence: 99%

Section: Selection Of Regularization Parameter(s)mentioning

confidence: 99%

Section: Selection Of Regularization Parameter(s)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Cross-Validation Selection of Regularisation Parameter(s) for Semiparametric Transformation Models

Sokullu¹,

Stouli²

2017

Annals of Economics and Statistics

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A Semi‐Parametric Analysis of Two‐Sided Markets: An Application to the Local Daily Newspapers in the USA

Sokullu

2015

J of Applied Econometrics

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This paper considers an empirical semiparametric model for two-sided markets. Contrary to existing empirical literature on two-sided markets, we specify network effects and probability distribution functions of net benefits of the two sides nonparametrically. We then estimate the model by nonparametric IV regression for local daily newspapers from the US. We show that semiparametric specification is supported by the data and the network effects are neither linear nor monotonic. With a numerical illustration we demonstrate that the mark-up of the newspaper on each side changes drastically with the nonlinearly specified network effects from the case with linear network effects.

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Non-parametric Models with Instrumental Variables

Florens

2011

Inverse Problems and High-Dimensional Estimation

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This paper gives a survey of econometric models characterized by a relation between observable and unobservable random elements where these unobservable terms are assumed to be independent of another set of observable variables called instrumental variables. This kind of specification is usefull to address the question of endogeneity or of selection bias for example. These models are treated non parametrically and in all the example we consider the functional parameter of interest is defined as the solution of a linear or non linear integral equation. The estimation procedure then requires to solve a (generally ill-posed) inverse problem. We illustrate the main questions (construction of the equation, identification, numerical solution, asymptotic properties, selection of the regularization parameter) by the different models we present.

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The practice of non‐parametric estimation by solving inverse problems: the example of transformation models

Cited by 29 publications

References 44 publications

Cross-Validation Selection of Regularisation Parameter(s) for Semiparametric Transformation Models

Cross-Validation Selection of Regularisation Parameter(s) for Semiparametric Transformation Models

A Semi‐Parametric Analysis of Two‐Sided Markets: An Application to the Local Daily Newspapers in the USA

Non-parametric Models with Instrumental Variables

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