Bootstrapping the NPMLE for doubly truncated data

Moreira, Carla; Uña‐Álvarez, Jacobo de

doi:10.1080/10485250903556102

Cited by 50 publications

(42 citation statements)

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“…On the other hand, it is often natural to utilize distributional assumptions of the truncation limits into estimation. In particular, the assumptions that the left-truncation limit u * i is a realization from a uniform distribution, and the right-truncation limit is v * i = u * i +d 0 , where d 0 > 0 is a constant, are often plausible in doubly-truncated data (Stovring and Wang 2007;Moreira and de Uña-Álvarez 2010). A related paper is De Uña-álvarez (2004) who constructed a moment-based estimator which is more efficient than the NPMLE when u * i follows a uniform distribution, and v * i = u * i +d 0 is a right-censoring limit (instead of right-truncation limit).…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…The data have been analyzed previously. Moreira and de Uña-Álvarez (2010) and nonparametrically estimated the distribution function and survival function, respectively, based on the NPMLE. Hu and Emura (2015) performed model selection among the pool of parametric models, and concluded that the cubic SEF gives the best fit.…”

Section: Data Analysis 61 the Childhood Cancer Data (Moreira And De mentioning

confidence: 99%

“…Since the variable of the observed sample is truncated by the lower and upper truncation limits, the sampled data is said to be "doubly truncated" (Efron and Petrosian 1999). For instance, Moreira and de Uña-Álvarez (2010) considered doubly truncated data arising from the epidemiological study of the childhood cancer in North Portugal. Here, the truncation limits correspond to the 5-year recruitment period during which the samples are ascertained.…”

Section: Introductionmentioning

confidence: 99%

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Asymptotic inference for maximum likelihood estimators under the special exponential family with double-truncation

Emura

Konno

2015

Stat Papers

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Biased sampling affects the inference for population parameters of interest if the sampling mechanism is not appropriately handled. This paper considers doublytruncated data arising in lifetime data analysis in which samples are subject to both left-and right-truncations. To correct for the sampling bias with doubly-truncated data, maximum likelihood estimator (MLE) has been proposed under a parametric family called the special exponential family (Efron and Petrosian, in J Am Stat Assoc 94: [824][825][826][827][828][829][830][831][832][833][834] 1999). However, there is still a lack of justifying the fundamental properties for the MLE, including consistency and asymptotic normality. In this paper, we point out that the classical asymptotic theory for the independent and identically distributed data is not suitable for studying the MLE under double-truncation due to the nonidentical truncation intervals. Alternatively, we formalize the asymptotic results under independent but not identically distributed data that suitably takes into account for the between-sample heterogeneity of truncation intervals. We establish the consistency and asymptotic normality of the MLE under a reasonably simple set of regularity conditions. Then, we give asymptotically valid techniques to estimate standard errors and to construct confidence intervals. Simulations are conducted to verify the suggested techniques, and childhood cancer data are used for illustration. B Takeshi Emura

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Section: Conclusion and Discussionmentioning

confidence: 99%

Section: Data Analysis 61 the Childhood Cancer Data (Moreira And De mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Asymptotic inference for maximum likelihood estimators under the special exponential family with double-truncation

Emura

Konno

2015

Stat Papers

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“…Moreira and de Uña-Álvarez [13] demonstrated that the simple bootstrap is a suitable method to estimate the finite sample distribution of the NPMLE. Specifically, we draw a simple random sample n) with replacement from the original doubly truncated data with equal probability 1/n.…”

Section: The Proposed Estimatormentioning

confidence: 99%

Median regression model with doubly truncated data

Shen

2014

Journal of Applied Statistics

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We study the problem of fitting a heteroscedastic median regression model with doubly truncated data. A self-consistency equation is proposed to obtain an estimator. We set up a least absolute deviation estimating function. We establish the consistency and asymptotic normality for the case when covariates are discrete. The finite sample performance of the proposed estimators are investigated through simulation studies. The proposed method is illustrated using the AIDS Blood Transfusion Data.

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“…The available results, Shen (2008), do no provide answers to important practical issues such as the computation of standard errors and the construction of confidence limits. Moreira and de Uña-Álvarez (2010) proposed the simple bootstrap as a suitable method to approximate the finite sample distribution of the NPMLE for doubly truncated data, extending the ideas in Gross and Lai (1996) for the one-sided truncated scenario. Gross and Lai (1996) and Moreira and de Uña-Álvarez (2010) also presented a critical comparison with the obvious bootstrap method.…”

Section: Bootstrap Approximation Of the Npmlementioning

confidence: 99%

DTDA: AnRPackage to Analyze Randomly Truncated Data

Moreira¹,

Álvarez²,

Casais³

2010

J. Stat. Soft.

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In this paper, the R package DTDA for analyzing truncated data is described. This package contains tools for performing three different but related algorithms to compute the nonparametric maximum likelihood estimator of the survival function in the presence of random truncation. More precisely, the package implements the algorithms proposed by Efron and Petrosian (1999) and Shen (2008), for analyzing randomly one-sided and two-sided (i.e., doubly) truncated data. These algorithms and some recent extensions are briefly reviewed. Two real data sets are used to show how DTDA package works in practice.

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Bootstrapping the NPMLE for doubly truncated data

Cited by 50 publications

References 11 publications

Asymptotic inference for maximum likelihood estimators under the special exponential family with double-truncation

Asymptotic inference for maximum likelihood estimators under the special exponential family with double-truncation

Median regression model with doubly truncated data

DTDA: AnRPackage to Analyze Randomly Truncated Data

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