Kernel estimation of conditional density with truncated, censored and dependent data

Liang, Han-Ying; Liu, Aiai

doi:10.1016/j.jmva.2013.05.009

Cited by 14 publications

(5 citation statements)

References 25 publications

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“…Bouaziz and Lopez (2010) introduced a semi parametric procedure to estimate the conditional density under censoring response. Liang and Liu (2013) defined a kernel estimator of the conditional density for a left-truncated and right-censored model based on the generalized product-limit estimator of the conditional distributed function.…”

Section: Introductionmentioning

confidence: 99%

Adaptive recursive kernel conditional density estimators under censoring data

Slaoui¹,

Khardani²

2020

ALEA

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Let (T, X) be independent identically distributed pairs of random variables and denote f (t|x) the conditional density of T given X = x, we consider that the random variable T is subject to random censoring by another random variable C. In this paper, we propose and investigate an adaptive recursive kernel conditional density estimation under censored data, which allows us to circumvent the weak performances of Kaplan-Meier estimator (Kaplan and Meier, 1958) in the right-tail of the distribution. The first aim of this paper is to study the properties of the proposed adaptive recursive estimators and compare it with the non-recursive estimator of f (t|x). It turns out that, with an adequate selected bandwidth and a special stepsize, the proposed recursive estimators often provides better results compared to the non-recursive one in terms of estimation error and much better in terms of computational costs. We corroborated these theoretical results through some simulation study.

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Section: Introductionmentioning

confidence: 99%

Adaptive recursive kernel conditional density estimators under censoring data

Slaoui¹,

Khardani²

2020

ALEA

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“…Note that this two types of incomplete data may be occur simultaneously in a study, then the model is known as Left Truncated and Right Censored one (LTRC). Recently, many results have been established for this type of data, we can cite Iglessias-Pérez and Gonzalez-Manteiga (1999), Liang et al (2012) andliang andLiu (2013) for the conditional distribution and conditional probability density estimation. Liang et al (2015) and Guessoum and Tatachak (2020) for conditional quantile and hazard function estimation, respectively.…”

Section: Introductionmentioning

confidence: 99%

Strong uniform consistency rate of an M-estimator of regression function for incomplete data under α-mixing condition

Benseradj

Guessoum

2020

Communications in Statistics - Theory and Methods

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In this paper, we establish weak consistency and asymptotic normality of an M-estimator of the regression function for left truncated and right censored (LTRC) model, where it is assumed that the observations form a stationary α-mixing sequence. The result holds with unbounded objective function, and are applied to derive weak consistency and asymptotic normality of a kernel classical regression curve estimate. We also obtain a uniform weak convergence rate for the product-limit estimator of the lifetime and censored distribution under dependence, which are useful results for our study and other LTRC strong mixing framework. Some simulations are drawn to illustrate the results for finite sample.

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“…The left-truncated data analysis has attracted much attention of many researchers and experts. For example, Woodroofe (1985) derived a method to estimate a distribution function with truncated data; He and Yang (1998) proposed a proper estimation for the truncation probability in the random truncation model; He and Yang (2003) constructed certain weighted least-square estimates of regression parameter in the linear regression model with left-truncated data; Ould-Saïd and Lemdani (2006) obtained asymptotic properties of a nonparametric regression function estimator with randomly truncated data; Liang and Liu (2013) defined a kernel estimator of the conditional density for a left-truncated and right-censored model based on the generalized product-limit estimator of the conditional distributed function; Liang and Baek (2016) constructed the Nadaraya-Watson type and local linear estimators of conditional density function for a left-truncation model. References of truncated data can be found in Stute and Wang (2008), Lemdani et al (2009) and Wang (2013) among others.…”

Section: Introductionmentioning

confidence: 99%

Quantile regression and variable selection for partially linear model with randomly truncated data

Chen

Fan

2017

Stat Papers

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This paper focuses on the problem of estimation and variable selection for quantile regression (QR) of partially linear model (PLM) where the response is subject to random left truncation. We propose a three-stage estimation procedure for parametric and nonparametric parts based on the weights which are random quantities and determined by the product-limit estimates of the distribution function of truncated variable. The estimators obtained in the second and third stages are more efficient than the initial estimators in the first stage. Furthermore, we propose a variable selection procedure for the QR of PLM by combining the estimation method with the smoothly clipped absolute deviation penalty to get sparse estimation of the regression parameter. The oracle properties of the variable selection approach are established. Simulation studies are conducted to examine the performance of our estimators and variable selection method.

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Kernel estimation of conditional density with truncated, censored and dependent data

Cited by 14 publications

References 25 publications

Adaptive recursive kernel conditional density estimators under censoring data

Adaptive recursive kernel conditional density estimators under censoring data

Strong uniform consistency rate of an M-estimator of regression function for incomplete data under α-mixing condition

Quantile regression and variable selection for partially linear model with randomly truncated data

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