Global Bahadur representation for nonparametric censored regression quantiles and its applications

Kong, Eric Siu-Wai; Linton, Oliver; Xia, Yingcun

doi:10.1920/wp.cem.2011.3311

Cited by 5 publications

(11 citation statements)

References 37 publications

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“…ii under random censoring. Fortunately, such a result has been established by Theorem 4.3 of Kong et al (2013). To formally restate their result, let us introduce the following notations.…”

Section: Resultsmentioning

confidence: 98%

“…On the other hand, in practice, a simple truncation can always be applied to ensure 0 ≤ S n (·|x, z) ≤ 1. See Spierdijk (2008) and Kong et al (2013) for a similar discussion.…”

Section: Random Censoringmentioning

confidence: 94%

“…The second is to apply the redistribution-of-mass idea of Efron (1967); see also Portnoy (2003), Peng and Huang (2008) and Wang and Wang (2009). The third strategy that we consider in this paper is based on the observation that E[D/S(Y |X, Z)] = 1; see Bang and Tsiatis (2003) and Kong et al (2013). Adopting the same notation as in Section 3.1.1, this leads to the minimization problem of…”

Section: Random Censoringmentioning

confidence: 99%

“…Third, to correct for the bias induced by random censoring, Honore et al (2002) replaced the check-shape objective function of quantile regression by its conditional expectation given the regressors and the censoring indicator (D). By contrast, this paper adopts a reweighting method following Bang and Tsiatis (2003) and Kong et al (2013).…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Identification and estimation of partially linear censored regression models with unknown heteroscedasticity

Zhang

Liu

2015

The Econometrics Journal

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In this paper, we introduce a new identification and estimation strategy for partially linear regression models with a general form of unknown heteroscedasticity, that is, Y = X β 0 + m(Z) + U and U = σ (X, Z) , where is independent of (X, Z) and the functional forms of both m(·) and σ (·) are left unspecified. We show that in such a model, β 0 and m(·) can be exactly identified while σ (·) can be identified up to scale as long as σ (X, Z) permits sufficient nonlinearity in X. A two-stage estimation procedure motivated by the identification strategy is described and its large sample properties are formally established. Moreover, our strategy is flexible enough to allow for both fixed and random censoring in the dependent variable. Simulation results show that the proposed estimator performs reasonably well in finite samples.

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“…ii under random censoring. Fortunately, such a result has been established by Theorem 4.3 of Kong et al (2013). To formally restate their result, let us introduce the following notations.…”

Section: Resultsmentioning

confidence: 98%

“…On the other hand, in practice, a simple truncation can always be applied to ensure 0 ≤ S n (·|x, z) ≤ 1. See Spierdijk (2008) and Kong et al (2013) for a similar discussion.…”

Section: Random Censoringmentioning

confidence: 94%

Section: Random Censoringmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Identification and estimation of partially linear censored regression models with unknown heteroscedasticity

Zhang

Liu

2015

The Econometrics Journal

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“…In the future, we would also like to further explore this idea to other QR problems under memory constraints or in a distributed setup, e.g., 1penalized high-dimensional quantile regression (see, e.g., ; Wang, Wu and Li (2012) ;Fan, Xue and Zou (2016)) and censored quantile regression (see, e.g., Wang and Wang (2009) ;Kong, Linton and Xia (2013);Volgushev et al (2014); Leng and Tong (2014); Zheng et al (2018)).…”

Section: Bias and Variance Analysismentioning

confidence: 99%

Quantile regression under memory constraint

Chen¹,

Liu²,

Zhang³

2019

Ann. Statist.

112

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This paper studies the inference problem in quantile regression (QR) for a large sample size n but under a limited memory constraint, where the memory can only store a small batch of data of size m. A natural method is the naïve divide-and-conquer approach, which splits data into batches of size m, computes the local QR estimator for each batch, and then aggregates the estimators via averaging. However, this method only works when n = o(m 2 ) and is computationally expensive. This paper proposes a computationally efficient method, which only requires an initial QR estimator on a small batch of data and then successively refines the estimator via multiple rounds of aggregations. Theoretically, as long as n grows polynomially in m, we establish the asymptotic normality for the obtained estimator and show that our estimator with only a few rounds of aggregations achieves the same efficiency as the QR estimator computed on all the data. Moreover, our result allows the case that the dimensionality p goes to infinity. The proposed method can also be applied to address the QR problem under distributed computing environment (e.g., in a large-scale sensor network) or for real-time streaming data.

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Local Partitioned Quantile Regression

Zhang

2016

Econom. Theory

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In this paper, we consider the nonparametric estimation of a broad class of quantile regression models, in which the partially linear, additive, and varying coefficient models are nested. We propose for the model a two-stage kernel-weighted least squares estimator by generalizing the idea of local partitioned mean regression (Christopeit and Hoderlein, 2006,Econometrica74, 787–817) to a quantile regression framework. The proposed estimator is shown to have desirable asymptotic properties under standard regularity conditions. The new estimator has three advantages relative to existing methods. First, it is structurally simple and widely applicable to the general model as well as its submodels. Second, both the functional coefficients and their derivatives up to any given order can be estimated. Third, the procedure readily extends to censored data, including fixed or random censoring. A Monte Carlo experiment indicates that the proposed estimator performs well in finite samples. An empirical application is also provided.

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Global Bahadur representation for nonparametric censored regression quantiles and its applications

Cited by 5 publications

References 37 publications

Identification and estimation of partially linear censored regression models with unknown heteroscedasticity

Identification and estimation of partially linear censored regression models with unknown heteroscedasticity

Quantile regression under memory constraint

Local Partitioned Quantile Regression

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