Semiparametric Estimation of Partially Linear Transformation Models Under Conditional Quantile Restriction

Zhang, Zhengyu

doi:10.1017/s0266466614000887

Cited by 5 publications

(6 citation statements)

References 37 publications

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“…The reason for employing the linear part

x_{1} β_{10}

is also applicable for model identification under the maximum score approach. Similar model specification can be found in Krief () and Zhang (). For empirical study, the economic implication behind why Z does not contain X 1 is that X 1 has no influence on endogenous dummy variable D , which is easy to inspect.…”

Section: Identificationmentioning

confidence: 99%

Identification and estimation of heteroscedastic binary choice models with endogenous dummy regressors

Zhang

2018

The Econometrics Journal

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Summary In this paper, we consider the semiparametric identification and estimation of a heteroskedastic binary choice model with endogenous dummy regressors and no parametric restriction on error term distribution. Our approach addresses various drawbacks associated with previous estimators proposed for this model. It allows for (i) general multiplicative heteroskedasticity in both selection and outcome equations, (ii) a nonparametric selection mechanism, and (iii) multiple discrete endogenous regressors. The resulting three-stage estimator is shown to be asymptotically normal, with a convergence rate that can be arbitrarily close to n −1/2 if certain smoothness assumptions are satisfied. Simulation results show that our estimator performs reasonably well in finite samples. Our approach is then used to study the intergenerational transmission of smoking habits in British households.

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“…The reason for employing the linear part

x_{1} β_{10}

Section: Identificationmentioning

confidence: 99%

Identification and estimation of heteroscedastic binary choice models with endogenous dummy regressors

Zhang

2018

The Econometrics Journal

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“…Table 1 reports means and stand deviations (STDs) of the

ξ_{β_{0}}

values for four estimators of

β_{0}

{\hat{β}}_{T_{1}}

(MAVE estimator under

T_{1}

{\hat{β}}_{T_{2}}

(MAVE estimator under

T_{2}

\overset{β}{true}

(estimator selected from

{\hat{β}}_{T_{1}}

and

{\hat{β}}_{T_{2}}

using cross validation method), and

{\hat{β}}_{ZZ}

(Zhang's, 2014 estimator (). It can be seen that in some cases

{\hat{β}}_{T_{1}}

performed better than

{\hat{β}}_{T_{2}}

, and worse in other cases.…”

Section: Simulationsmentioning

confidence: 99%

“…Results of the IILLR and ZZ (Zhang, ) estimators for the nonlinear link function

g false(\cdot false)

are tabulated in Table 3. We can see that the IILLR estimator performs much better than the ZZ estimator in all the cases we considered.…”

Section: Simulationsmentioning

confidence: 99%

“…It is worth noting that Zhang () studied a partially linear transformation model, which is quite similar to model . They assume that the link function

g false(\cdot false)

is completely nonparametric, while

g false(\cdot false)

in model is a single‐index function.…”

Section: Introductionmentioning

confidence: 99%

“…However, it imposes conditional quantile restriction. In the simulation studies, we shall compare our propose procedure with Zhang's () method, and we will see that our propose procedure is better.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A partially linear single‐index transformation model and its nonparametric estimation

2015

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In this paper, we consider the nonparametric estimation of the partially linear single‐index transformation model, where the transformation function, single‐index function and error distribution are all completely unknown. We first use the minimum average variance estimation method to estimate the regression coefficients, and then propose a new incorporated local linear regression estimator for the derivative function of the single‐index function. Accordingly by integration we can obtain the estimator of the single‐index function. Finally we propose a constrained least square estimator for the transformation function, where basis function approximation is employed and cross validation method is proposed to select suitable sets of basis functions. Asymptotical properties of the estimators are established. Simulation studies show that our proposed estimators work well. A real‐world data analysis of total health care charges was used to illustrate the proposed procedure. The Canadian Journal of Statistics 43: 97–117; 2015 © 2015 Statistical Society of Canada

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Identification and Estimation in a Correlated Random Coefficients Transformation Model

Zhang

Jin

Mu³

2021

Econom. Theory

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This study examines identification and estimation in a correlated random coefficients (CRC) model with an unknown transformation of the dependent variable, namely $\lambda \left (Y^{*}\right)=B_{0}+X^{\prime }B$ , where the latent outcome $Y^{*}$ may be subject to a certain kind of censoring mechanism, $\lambda (\cdot)$ is an unknown, one-to-one monotone function, and the random coefficients $\left (B_{0},B\right)$ are allowed to be correlated with one or several components of X. Under a conditional median independence plus a conditional median zero restriction, the mean of B is shown to be identified up to scale. Moreover, we show the derivative of the median structural function (MSF) is point identified. This derivative of MSF resembles the marginal treatment effect introduced by Heckman and Vytlacil (2005, Econometrica 73, 669–738). It generalizes the usual average treatment effect in a linear CRC model and coincides with $E(B)$ when $\lambda $ is equal to the identity function; it is invariant to both location and scale normalization on the coefficients. We develop estimators for the identified parameters and derive asymptotic properties for the derivative of MSF. An empirical example using the U.K. Family Expenditure Survey is provided.

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Semiparametric Estimation of Partially Linear Transformation Models Under Conditional Quantile Restriction

Cited by 5 publications

References 37 publications

Identification and estimation of heteroscedastic binary choice models with endogenous dummy regressors

Identification and estimation of heteroscedastic binary choice models with endogenous dummy regressors

A partially linear single‐index transformation model and its nonparametric estimation

Identification and Estimation in a Correlated Random Coefficients Transformation Model

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