### Abstract

In this paper, we consider the one-sample problem of testing for the subvector of a mean vector with two-step monotone missing data. In the case that the data set consists of complete data with p(= p_{1} + p_{2} + p_{3}) dimensions and incomplete data with (p_{1} + p_{2}) dimensions, we derive the likelihood ratio criterion for testing the (p_{2}+p_{3}) mean vector under the given mean vector of p1 dimensions. Furthermore, we propose an approximation for the upper percentile of the likelihood ratio test (LRT) statistic. We investigate the accuracy and asymptotic behavior of this approximation using Monte Carlo simulation. An example is presented in order to illustrate the method.

Original language | English |
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Pages (from-to) | 21-39 |

Number of pages | 19 |

Journal | SUT Journal of Mathematics |

Volume | 52 |

Issue number | 1 |

Publication status | Published - 1 Jan 2016 |

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### Keywords

- Likelihood ratio test
- Maximum likelihood estimators
- Monte Carlo simulation
- Rao’s U statistic