75,858 research outputs found
ON THE RESAMPLING METHOD IN SAMPLE MEDIAN ESTIMATION
Bootstrap is one of the resampling statistical methods. This method was proposed by B. Efron. The main idea of bootstrap is to treat the original sample of values as a stand-in for the population and to resample with replacement from it repeatedly. Bootstrap allows estimation of the sampling distribution of almost any statistics using only very simple methods. This paper presents a modification of a resampling procedure based on bootstrap sampling. The proposal leads to sampling from population with density function f(x), where f(x) is estimated based on the kernel estimation. The properties of the method were analyzed in the median estimation in Monte Carlo study.The proposal could be useful for the parameters estimation in the case of a small sample. This method could be used in quality control procedures such as control charts or in the acceptance sampling
A comparison of block and semi-parametric bootstrap methods for variance estimation in spatial statistics
Efron (1979) introduced the bootstrap method for independent data but it cannot be easily applied to spatial data because of their dependency. For spatial data that are correlated in terms of their locations in the underlying space the moving block bootstrap method is usually used to estimate the precision measures of the estimators. The precision of the moving block bootstrap estimators is related to the block size which is difficult to select. In the moving block bootstrap method also the variance estimator is underestimated. In this paper, first the semi-parametric bootstrap is used to estimate the precision measures of estimators in spatial data analysis. In the semi-parametric bootstrap method, we use the estimation of the spatial correlation structure. Then, we compare the semi-parametric bootstrap with a moving block bootstrap for variance estimation of estimators in a simulation study. Finally, we use the semi-parametric bootstrap to analyze the coal-ash data
Bootstrap consistency for general semiparametric -estimation
Consider -estimation in a semiparametric model that is characterized by a
Euclidean parameter of interest and an infinite-dimensional nuisance parameter.
As a general purpose approach to statistical inferences, the bootstrap has
found wide applications in semiparametric -estimation and, because of its
simplicity, provides an attractive alternative to the inference approach based
on the asymptotic distribution theory. The purpose of this paper is to provide
theoretical justifications for the use of bootstrap as a semiparametric
inferential tool. We show that, under general conditions, the bootstrap is
asymptotically consistent in estimating the distribution of the -estimate of
Euclidean parameter; that is, the bootstrap distribution asymptotically
imitates the distribution of the -estimate. We also show that the bootstrap
confidence set has the asymptotically correct coverage probability. These
general conclusions hold, in particular, when the nuisance parameter is not
estimable at root- rate, and apply to a broad class of bootstrap methods
with exchangeable bootstrap weights. This paper provides a first general
theoretical study of the bootstrap in semiparametric models.Comment: Published in at http://dx.doi.org/10.1214/10-AOS809 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
A Residual Bootstrap for Conditional Value-at-Risk
This paper proposes a fixed-design residual bootstrap method for the two-step
estimator of Francq and Zako\"ian (2015) associated with the conditional
Value-at-Risk. The bootstrap's consistency is proven for a general class of
volatility models and intervals are constructed for the conditional
Value-at-Risk. A simulation study reveals that the equal-tailed percentile
bootstrap interval tends to fall short of its nominal value. In contrast, the
reversed-tails bootstrap interval yields accurate coverage. We also compare the
theoretically analyzed fixed-design bootstrap with the recursive-design
bootstrap. It turns out that the fixed-design bootstrap performs equally well
in terms of average coverage, yet leads on average to shorter intervals in
smaller samples. An empirical application illustrates the interval estimation
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