Youngki Shin

Testing for Threshold Effects in Regression Models

In this article, we develop a general method for testing threshold effects in regression models, using sup-likelihood-ratio (LR)-type statistics. Although the sup-LR-type test statistic has been considered in the literature, our method for establishing the asymptotic null distribution is new and nonstandard. The standard approach in the literature for obtaining the asymptotic null distribution requires that there exist a certain quadratic approximation to the objective function. The article provides an alternative, novel method that can be used to establish the asymptotic null distribution, even when the usual quadratic approximation is intractable. We illustrate the usefulness of our approach in the examples of the maximum score estimation, maximum likelihood estimation, quantile regression, and maximum rank correlation estimation. We establish consistency and local power properties of the test. We provide some simulation results and also an empirical application to tipping in racial segregation. This article has supplementary materials online.

The lasso for high-dimensional regression with a possible change-point

Summary We consider a high dimensional regression model with a possible change point due to a covariate threshold and develop the lasso estimator of regression coefficients as well as the threshold parameter. Our lasso estimator not only selects covariates but also selects a model between linear and threshold regression models. Under a sparsity assumption, we derive non‐asymptotic oracle inequalities for both the prediction risk and the l1‐estimation loss for regression coefficients. Since the lasso estimator selects variables simultaneously, we show that oracle inequalities can be established without pretesting the existence of the threshold effect. Furthermore, we establish conditions under which the estimation error of the unknown threshold parameter can be bounded by a factor that is nearly n−1 even when the number of regressors can be much larger than the sample size n. We illustrate the usefulness of our proposed estimation method via Monte Carlo simulations and an application to real data.

Rank estimation of partially linear index models

We consider a generalized regression model with a partially linear index. The index contains an additive non‐parametric component in addition to the standard linear component, and the model is characterized by an unknown monotone link function. We propose weighted rank estimation procedures for estimating (a) the coefficients for the linear component, (b) the non‐parametric component (and its derivative) and (c) the average derivative for the non‐parametric component. The method is applied to study the non‐linear relationship between household income and children’s cognitive development.

Semiparametric estimation of the Box--Cox transformation model

and Monte Carlo experiments show adequate finite sample performance. Copyright The Author(s). Journal compilation Royal Economic Society 2008

Heteroscedastic Transformation Models With Covariate Dependent Censoring

In this article we propose an inferential procedure for transformation models with conditional heteroscedasticity in the error terms. The proposed method is robust to covariate dependent censoring of arbitrary form. We provide sufficient conditions for point identification. We then propose an estimator and show that it is √n-consistent and asymptotically normal. We conduct a simulation study that reveals adequate finite sample performance. We also use the estimator in an empirical illustration of export duration, where we find advantages of the proposed method over existing ones.

LOCAL RANK ESTIMATION OF TRANSFORMATION MODELS WITH FUNCTIONAL COEFFICIENTS

This paper considers a nonparametric functional coefficient model with an unknown link function. The model gives flexibility to the standard interaction-variable model by allowing an arbitrary functional form of heterogeneous marginal effects. A local rank estimation procedure is proposed for the functional coefficients along with its asymptotic property.

Length-bias Correction in Transformation Models with Supplementary Data

In this article, I propose an inferential procedure of monotone transformation models with random truncation points, which may not be observable. This class includes length-biased samples that are common in duration analysis. The proposed estimator can be applied to more general situations than existing estimators, since it imposes restrictions on neither the transformation function nor the error terms. Furthermore, it does not require observed truncation points either. It is sufficient for point identification to know the cdf of the truncation variable, which can be estimated from supplementary data that are easily found in applications. The estimator converges to a normal distribution at the rate of and Monte Carlo simulations confirm its robustness to error distributions in finite samples. For an empirical illustration, I estimate the effect of unemployment insurance benefits on unemployment duration, using length-biased microdata and supplementary macrodata.

Oracle Estimation of a Change Point in High Dimensional Quantile Regression

ABSTRACT In this article, we consider a high-dimensional quantile regression model where the sparsity structure may differ between two sub-populations. We develop ℓ1-penalized estimators of both regression coefficients and the threshold parameter. Our penalized estimators not only select covariates but also discriminate between a model with homogenous sparsity and a model with a change point. As a result, it is not necessary to know or pretest whether the change point is present, or where it occurs. Our estimator of the change point achieves an oracle property in the sense that its asymptotic distribution is the same as if the unknown active sets of regression coefficients were known. Importantly, we establish this oracle property without a perfect covariate selection, thereby avoiding the need for the minimum level condition on the signals of active covariates. Dealing with high-dimensional quantile regression with an unknown change point calls for a new proof technique since the quantile loss function is nonsmooth and furthermore the corresponding objective function is nonconvex with respect to the change point. The technique developed in this article is applicable to a general M-estimation framework with a change point, which may be of independent interest. The proposed methods are then illustrated via Monte Carlo experiments and an application to tipping in the dynamics of racial segregation. Supplementary materials for this article are available online.