zbMATH — the first resource for mathematics

Short confidence intervals for variance components. (English) Zbl 0825.62194
Summary: Four approximate methods are proposed to construct confidence intervals for the estimation of variance components in unbalanced mixed models. The first three methods are modifications of the Wald, arithmetic and harmonic mean procedures, see Harville and Fenech (1985), while the fourth is an adaptive approach, combining the arithmetic and harmonic mean procedures. The performances of the proposed methods were assessed by a Monte Carlo simulation study. It was found that the intervals based on Wald’s method maintained the nominal confidence levels across all designs and values of the parameters under study. On the other hand, the arithmetic (harmonic) mean method performed well for small (large) values of the variance component, relative to the error variance component. The adaptive procedure performed rather well except for extremely unbalanced designs. Further, compared with equal tails intervals, the intervals which use special tables, e.g., Table 678 of Tate and Klett (1959), provided adequate coverage while having much shorter lengths and are thus recommended for use in practice.

MSC:
 62-XX Statistics
Full Text:
References:
 [1] DOI: 10.1002/bimj.4710230302 · Zbl 0477.62057 · doi:10.1002/bimj.4710230302 [2] Anderson R. L., Statistical theory in research (1952) · Zbl 0049.09803 [3] DOI: 10.2307/2529647 · Zbl 0286.62055 · doi:10.2307/2529647 [4] DOI: 10.1080/03610928608829315 · Zbl 0613.62046 · doi:10.1080/03610928608829315 [5] DOI: 10.2307/2286796 · Zbl 0373.62040 · doi:10.2307/2286796 [6] DOI: 10.2307/2530650 · Zbl 0607.62031 · doi:10.2307/2530650 [7] DOI: 10.2307/2529265 · Zbl 0399.62073 · doi:10.2307/2529265 [8] DOI: 10.1214/aos/1176343586 · Zbl 0344.62060 · doi:10.1214/aos/1176343586 [9] Searle S. R., Linear Models (1971) · Zbl 0218.62071 [10] DOI: 10.1214/aos/1176346069 · Zbl 0516.62028 · doi:10.1214/aos/1176346069 [11] DOI: 10.2307/1268135 · Zbl 0405.62051 · doi:10.2307/1268135 [12] DOI: 10.2307/2282545 · Zbl 0096.12801 · doi:10.2307/2282545 [13] DOI: 10.1214/aos/1176344202 · Zbl 0386.62057 · doi:10.1214/aos/1176344202 [14] DOI: 10.1214/aoms/1177730350 · Zbl 0029.30703 · doi:10.1214/aoms/1177730350
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.