### 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 language | English (US) |
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Pages (from-to) | 703-720 |

Number of pages | 18 |

Journal | Annals of the Institute of Statistical Mathematics |

Volume | 44 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1992 |

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### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Mathematics(all)

### Cite this

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*Annals of the Institute of Statistical Mathematics*, vol. 44, no. 4, pp. 703-720. https://doi.org/10.1007/BF00053399

**Subsample and half-sample methods.** / Babu, G. Jogesh.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Subsample and half-sample methods

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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U2 - 10.1007/BF00053399

DO - 10.1007/BF00053399

M3 - Article

AN - SCOPUS:0011570572

VL - 44

SP - 703

EP - 720

JO - Annals of the Institute of Statistical Mathematics

JF - Annals of the Institute of Statistical Mathematics

SN - 0020-3157

IS - 4

ER -