Subsample and half-sample methods

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Abstract

Hartigan's subsample and half-sample methods are both shown to be inefficient methods of estimating the sampling distributions. In the sample mean case the bootstrap is known to correct for skewness. But irrespective of the population, the estimates based on the subsample method, have skewness factor zero. This problem persists even if we take only samples of size less than or equal to half of the original sample. For linear statistics it is possible to correct this by considering estimates based on subsamples of size νn, when the sample size is n. In the sample mean case ν can be taken as {Mathematical expression}. In spite of these negative results, the half-sample method is useful in estimating the variance of sample quantiles. It is shown that this method gives as good an estimate as that given by the bootstrap method. A major advantage of the half-sample method is that it is shown to be robust in estimating the mean square error of estimators of parameters of a linear regression model when the errors are heterogeneous. Bootstrap is known to give inconsistent results in this case; although, it is more efficient in the case of homogeneous errors.

Original languageEnglish (US)
Pages (from-to)703-720
Number of pages18
JournalAnnals of the Institute of Statistical Mathematics
Volume44
Issue number4
DOIs
StatePublished - Dec 1992

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Sample mean
Skewness
Bootstrap
Estimate
Sample Quantiles
Sampling Distribution
Bootstrap Method
Less than or equal to
Linear Regression Model
Mean square error
Inconsistent
Sample Size
Statistics
Estimator
Zero

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics(all)

Cite this

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title = "Subsample and half-sample methods",
abstract = "Hartigan's subsample and half-sample methods are both shown to be inefficient methods of estimating the sampling distributions. In the sample mean case the bootstrap is known to correct for skewness. But irrespective of the population, the estimates based on the subsample method, have skewness factor zero. This problem persists even if we take only samples of size less than or equal to half of the original sample. For linear statistics it is possible to correct this by considering estimates based on subsamples of size νn, when the sample size is n. In the sample mean case ν can be taken as {Mathematical expression}. In spite of these negative results, the half-sample method is useful in estimating the variance of sample quantiles. It is shown that this method gives as good an estimate as that given by the bootstrap method. A major advantage of the half-sample method is that it is shown to be robust in estimating the mean square error of estimators of parameters of a linear regression model when the errors are heterogeneous. Bootstrap is known to give inconsistent results in this case; although, it is more efficient in the case of homogeneous errors.",
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Subsample and half-sample methods. / Babu, G. Jogesh.

In: Annals of the Institute of Statistical Mathematics, Vol. 44, No. 4, 12.1992, p. 703-720.

Research output: Contribution to journalArticle

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AU - Babu, G. Jogesh

PY - 1992/12

Y1 - 1992/12

N2 - Hartigan's subsample and half-sample methods are both shown to be inefficient methods of estimating the sampling distributions. In the sample mean case the bootstrap is known to correct for skewness. But irrespective of the population, the estimates based on the subsample method, have skewness factor zero. This problem persists even if we take only samples of size less than or equal to half of the original sample. For linear statistics it is possible to correct this by considering estimates based on subsamples of size νn, when the sample size is n. In the sample mean case ν can be taken as {Mathematical expression}. In spite of these negative results, the half-sample method is useful in estimating the variance of sample quantiles. It is shown that this method gives as good an estimate as that given by the bootstrap method. A major advantage of the half-sample method is that it is shown to be robust in estimating the mean square error of estimators of parameters of a linear regression model when the errors are heterogeneous. Bootstrap is known to give inconsistent results in this case; although, it is more efficient in the case of homogeneous errors.

AB - Hartigan's subsample and half-sample methods are both shown to be inefficient methods of estimating the sampling distributions. In the sample mean case the bootstrap is known to correct for skewness. But irrespective of the population, the estimates based on the subsample method, have skewness factor zero. This problem persists even if we take only samples of size less than or equal to half of the original sample. For linear statistics it is possible to correct this by considering estimates based on subsamples of size νn, when the sample size is n. In the sample mean case ν can be taken as {Mathematical expression}. In spite of these negative results, the half-sample method is useful in estimating the variance of sample quantiles. It is shown that this method gives as good an estimate as that given by the bootstrap method. A major advantage of the half-sample method is that it is shown to be robust in estimating the mean square error of estimators of parameters of a linear regression model when the errors are heterogeneous. Bootstrap is known to give inconsistent results in this case; although, it is more efficient in the case of homogeneous errors.

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