Bootstrapping sample quantiles of discrete data

Jentsch, Carsten; Leucht, Anne

doi:10.1007/s10463-015-0503-3

Cited by 15 publications

(16 citation statements)

References 35 publications

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“…Bootstrap distribution of median for the Poisson sample suffers from the same problem as sampling distribution does. Central Limit Theorem does not hold true for median and bootstrap distribution does not consistently mimic distribution of the sample quantiles [23]. To overcome this problem, Jentsch and Leucht [23] propose two different strategies.…”

Section: Sampling and Bootstrap Distributionsmentioning

confidence: 99%

“…Sampling distribution of the median for Poisson distribution is rather discrete and far from being normal. This stems from the fact that, median of a sample is very much dependent on the limited number of middle values of the sample and sample quantiles for discrete populations are not consistent for the population quantiles, in general [23].…”

Section: Sampling and Bootstrap Distributionsmentioning

confidence: 99%

“…Central Limit Theorem does not hold true for median and bootstrap distribution does not consistently mimic distribution of the sample quantiles [23]. To overcome this problem, Jentsch and Leucht [23] propose two different strategies. On the other hand, bootstrap distributions of means are similar to sampling distributions in terms of shape and spread.…”

Section: Sampling and Bootstrap Distributionsmentioning

confidence: 99%

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An Empirical Look at the Variation Associated with Bootstrap Estimates of Location Parameters

Erişkin¹

2020

Pamukkale J Eng Sci

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ÖzBootstrap is a technique for estimating standard error and bias of the statistic of interest. The idea behind the bootstrap technique is that bootstrap distribution generated by resampling from the sample at hand mimics the sampling distribution of the statistic. Nevertheless, the effect of sample size and number of bootstrap replications on the accuracy of bootstrap predictions is rarely considered and ignored while applying bootstrap. Although there exist limited studies on this matter in the literature, results obtained in these studies are expressed based on the population distribution. In this paper, we provide results of an empirical study that examines the relationship between sample size and number of bootstrap replications and standard errors of bootstrap estimates of location parameters for different population distributions. To that end, we focus on the representativeness of bootstrap distribution to sampling distribution for different continuous and discrete population distributions and different sample sizes, firstly. According to application results, we observe that sample size has more impact on accuracies of bootstrap estimates as regards to number of bootstrap replications. Additionally, we confirm that bootstrap distributions of median based on small sample sizes are inadequate for representing sampling distribution. Lastly, in order to model relationship between standard errors of bootstrap estimates and sample size and number of bootstrap estimations independently of population distribution, we propose a methodology based on jackknifeafter-bootstrap technique and regression modeling.

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Section: Sampling and Bootstrap Distributionsmentioning

confidence: 99%

Section: Sampling and Bootstrap Distributionsmentioning

confidence: 99%

Section: Sampling and Bootstrap Distributionsmentioning

confidence: 99%

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An Empirical Look at the Variation Associated with Bootstrap Estimates of Location Parameters

Erişkin¹

2020

Pamukkale J Eng Sci

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“…However, other statistics as e.g. sample quantiles are not included in this generalized class of functions g; see also Jentsch and Leucht (2016).…”

Section: Bootstrap Consistencymentioning

confidence: 99%

“…For prediction in INAR models, block bootstrap techniques have been used, e.g., by Jung and Tremayne (2006) to estimate the standard errors. Potential further issues of (block) bootstrapping for discrete-valued time series are discussed in Jentsch and Leucht (2016).…”

Section: Introductionmentioning

confidence: 99%

Bootstrapping INAR models

Jentsch¹,

Weiß²

2019

Bernoulli

Self Cite

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Integer-valued autoregressive (INAR) models form a very useful class of processes to deal with time series of counts. Statistical inference in these models is commonly based on asymptotic theory, which is available only under additional parametric conditions and further restrictions on the model order. For general INAR models, such results are not available and might be cumbersome to derive. Hence, we investigate how the INAR model structure and, in particular, its similarity to classical autoregressive (AR) processes can be exploited to develop an asymptotically valid bootstrap procedure for INAR models. Although, in a common formulation, INAR models share the autocorrelation structure with AR models, it turns out that (a) consistent estimation of the INAR coefficients is not sufficient to compute proper 'INAR residuals' to formulate a valid model-based bootstrap scheme, and (b) a naïve application of an AR bootstrap will generally fail. Instead, we propose a general INAR-type bootstrap procedure and discuss parametric as well as semi-parametric implementations. The latter approach is based on a joint semi-parametric estimator of the INAR coefficients and the innovations' distribution. Under mild regularity conditions, we prove bootstrap consistency of our procedure for statistics belonging to the class of functions of generalized means. In an extensive simulation study, we provide numerical evidence of our theoretical findings and illustrate the superiority of the proposed INAR bootstrap over some obvious competitors. We illustrate our method by an application to a real data set about iceberg orders for the Lufthansa stock.

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m‐Out‐of‐n Bootstrap

Lee

2017

Wiley StatsRef: Statistics Reference Online

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Treated as a generalized version of the standard bootstrap, the m ‐out‐of‐ n bootstrap method is reviewed under three broad scenarios: (i) when the standard bootstrap works successfully, (ii) when the standard bootstrap is asymptotically correct but works poorly, and (iii) when the standard bootstrap fails. The last scenario, where the m ‐out‐of‐ n bootstrap provides an appealing remedy for the standard bootstrap, is covered in detail and illustrated with numerical examples. We also address briefly the issues of selection of m and uniform consistency.

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Bootstrapping sample quantiles of discrete data

Cited by 15 publications

References 35 publications

An Empirical Look at the Variation Associated with Bootstrap Estimates of Location Parameters

An Empirical Look at the Variation Associated with Bootstrap Estimates of Location Parameters

Bootstrapping INAR models

m‐Out‐of‐n Bootstrap

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