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| Format: | Preprint |
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2019
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| Online Access: | https://arxiv.org/abs/1908.02193 |
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| _version_ | 1866911121125933056 |
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| author | Das, Nabaneet Bhandari, Subir K. |
| author_facet | Das, Nabaneet Bhandari, Subir K. |
| contents | In this paper,our main focus is to obtain an asymptotic bound on the family wise error rate (FWER) for Bonferroni-type procedure in the simultaneous hypotheses testing problem when the observations corresponding to individual hypothesis are correlated. In particular, we have considered the sequence of null hypotheses H_{0i} : X_i follows N(0,1) , (i=1,2,....,n) and equicorrelated structure of the sequence (X_1,....,X_n). Distribution free bound on FWER under equicorrelated setup can be found in Tong(2014). But the upper bound provided in Tong(2014) is not a bounded quantity as the no. of hypotheses(n) gets larger and larger and as a result,FWER is highly overestimated for the choice of a particular distribution (e.g.- normal). In the equicorrelated normal setup, we have shown that FWER asymptotically is a convex function (as a function of correlation (rho)) and hence an upper bound on the FWER of Bonferroni-(alpha) procedure is alpha(1-ρ).This implies,Bonferroni's method actually controls the FWER at a much smaller level than the desired level of significance under the positively correlated case and necessitates a correlation correction. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1908_02193 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Bound on FWER for correlated normal distribution Das, Nabaneet Bhandari, Subir K. Statistics Theory In this paper,our main focus is to obtain an asymptotic bound on the family wise error rate (FWER) for Bonferroni-type procedure in the simultaneous hypotheses testing problem when the observations corresponding to individual hypothesis are correlated. In particular, we have considered the sequence of null hypotheses H_{0i} : X_i follows N(0,1) , (i=1,2,....,n) and equicorrelated structure of the sequence (X_1,....,X_n). Distribution free bound on FWER under equicorrelated setup can be found in Tong(2014). But the upper bound provided in Tong(2014) is not a bounded quantity as the no. of hypotheses(n) gets larger and larger and as a result,FWER is highly overestimated for the choice of a particular distribution (e.g.- normal). In the equicorrelated normal setup, we have shown that FWER asymptotically is a convex function (as a function of correlation (rho)) and hence an upper bound on the FWER of Bonferroni-(alpha) procedure is alpha(1-ρ).This implies,Bonferroni's method actually controls the FWER at a much smaller level than the desired level of significance under the positively correlated case and necessitates a correlation correction. |
| title | Bound on FWER for correlated normal distribution |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/1908.02193 |