Estimation of the truncation probability in the random truncation model

For censored response variable against projected co-variable, a generalized linear model with an unknown link function can cover almost all existing models under censorship. Its special cases include the accelerated failure time model with censored data. Such a model in the uncensored case is called the single-index model in econometrics. In this paper, we systematically study the asymptotic properties. We derive the central limit theorem and the law of the iterated logarithm for an estimator of the direction parameter. We also obtain the optimal convergence rate of an estimator of the unknown link function in the model.

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“…5. Proof of Lemma D. 3 The proof of the lemma is similar to that of Theorem 2.1 of He and Wang [13].…”

Section: Lemma C7 Under Conditions (L5)-(l6) In L We Havementioning

confidence: 87%

Asymptotics for a censored generalized linear model with unknown link function

Wang

Zhu

et al. 2006

Probab. Theory Relat. Fields

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“…In addition, He and Yang (1998) have shown that α n is strongly consistent for α. According to (2.5) and (2.7), we are now in a place to present the plug-in version of f n (·) which we refer to it byf n (·)…”

Section: So the Marginal Distribution Function Of Y Ismentioning

confidence: 89%

“…In application, α is unknown. Among several estimators for α, in this paper we use the more familiar one that is proposed by He and Yang (1998).…”

Section: Introductionmentioning

confidence: 99%

A Berry-Esseen Type Bound in Kernel Density Estimation for a Random Left-Truncation Model

Asghari¹,

Fakoor²,

Sarmad³

2014

Communications for Statistical Applications and Methods

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In this paper we derive a Berry-Esseen type bound for the kernel density estimator of a random left truncated model, in which each datum (Y) is randomly left truncated and is sampled if Y ≥ T , where T is the truncation random variable with an unknown distribution. This unknown distribution is estimated with the Lynden-Bell estimator. In particular the normal approximation rate, by choice of the bandwidth, is shown to be close to n −1/6 modulo logarithmic term. We have also investigated this normal approximation rate via a simulation study.

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“…The first ratio is the same for each i and converges to 1, see He and Yang (1998). The ratio C/C n is also bounded in probability, see Stute and Wang (2008).…”

Section: Accepted M Manuscriptmentioning

confidence: 94%