ASYMPTOTIC-DISTRIBUTION OF THE LIKELIHOOD RATIO TEST THAT A MIXTURE OF 2 BINOMIALS IS A SINGLE BINOMIAL
ASYMPTOTIC-DISTRIBUTION OF THE LIKELIHOOD RATIO TEST THAT A MIXTURE OF 2 BINOMIALS IS A SINGLE BINOMIAL
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DOI：
10.1016/0378-3758(94)00006-h
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发表时间：
1995-01-01
影响因子：
0.9
通讯作者：
LANDER, E
中科院分区：
文献类型：
--
作者：
CHERNOFF, H;LANDER, E
遗传学中感兴趣的一个问题是检验两个二项分布B-i(k，p)和B-i(k，1/2)的混合是否仅仅是纯分布B-i(k，1/2)。这个问题出现在确定我们是否有一个负责异质性特征的基因的遗传标记时，这是一个由几个基因中的任何一个引起的特征。在这种情况下，我们将有一个涉及0无穷远的非平凡混合，似然比的对数的两倍的渐近分布对应于均值为0，方差为1的高斯随机过程的上确界的平方，并且具有良好的协方差函数。当k-->；无穷大时，该极限分布以logk随机增长。
A problem of interest in genetics is that of testing whether a mixture of two binomial distributions B-i(k, p) and B-i(k, 1/2) is simply the pure distribution B-i(k, 1/2). This problem arises in determining whether we have a genetic marker for a gene responsible for a heterogeneous trait, that is a trait which is caused by any one of several genes. In that event we would have a nontrivial mixture involving 0infinity, the asymptotic distribution of twice the logarithm of the likelihood ratio corresponds to the square of the supremum of a Gaussian stochastic process with mean 0, variance 1 and a well behaved covariance function. As k-->infinity this limiting distribution grows stochastically as log k.