caa a22 4500 60546183X CHVBK 20210128100245.0 cr unu---uuuuu 210128e20150401xx s 000 0 eng 10.1007/s10114-015-3326-5 doi (NATIONALLICENCE)springer-10.1007/s10114-015-3326-5 Inferences in linear mixed models with skew-normal random effects [Elektronische Daten] [Ren Ye, Tong Wang] For the linear mixed model with skew-normal random effects, this paper gives the density function, moment generating function and independence conditions. The noncentral skew chi-square distribution is defined and its density function is shown. The necessary and sufficient conditions under which a quadratic form is distributed as noncentral skew chi-square distribution are obtained. Also, a version of Cochran's theorem is given, which modifies the result of Wang et al. (2009) and is used to set up exact tests for fixed effects and variance components of the proposed model. For illustration, our main results are applied to a real data problem. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg, 2015 Linear mixed model nationallicence moment generating function nationallicence Cochran's theorem nationallicence noncentral skew chi-square distribution nationallicence noncentral skew F distribution nationallicence Ye Ren College of Economics, Hangzhou Dianzi University, 310018, Zhejiang, P. R. China aut Wang Tong Innovation Experimental College, Northwest A&F University, 712100, Shannxi, P. R. China aut Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/4(2015-04-01), 576-594 1439-8516 31:4<576 2015 31 10114 https://doi.org/10.1007/s10114-015-3326-5 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10114-015-3326-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Ye Ren College of Economics, Hangzhou Dianzi University, 310018, Zhejiang, P. R. China aut NATIONALLICENCE 700 1- Wang Tong Innovation Experimental College, Northwest A&F University, 712100, Shannxi, P. R. China aut NATIONALLICENCE 773 0- Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/4(2015-04-01), 576-594 1439-8516 31:4<576 2015 31 10114