Zuk et al. (2012) have shown that their method for estimating additive heritability is unbiased; however, the proof presented in Zuk et al. implicitly assumes that the population is homogenous.
We now state our first result for the mean convergence of g n ( x ), which, on the opinion of statistics, is asymptotically unbiased of g ( x ) in the proof of Theorem 3.1.
This work demonstrates the successful application of macroarray methodology using randomly primed and sequence-nonspecific amplified cDNAs derived from grapevine total RNA extracts, and provides a proof-of-principal for unbiased multiplex detection using a single robust platform.
Similarly is an unbiased estimator of Γ k. ■ In the above proof, is a non-central Chi-square distribution with 'n' degrees of freedom and 'c' being the non-centrality parameter; ⟨Z⟩ is the expectation of the random variable Z.
Discovery of BCL11A as a HbF QTL was proof of principle that GWAS could be used as an unbiased tool to define genotype-phenotype relationships.
The proof uses the framework of Seely [1970a. Linear spaces and unbiased estimation. Ann. Math. Statist. 41, 1725 1734], in which quadratic estimators are expressed as inner products of symmetric matrices.
Fortunately, based on the careful design of Algorithm 2, the following theorem shows that, if we apply a significance level α ' = α / 1 + α where α is the targeted false positive rate (FPR), an unbiased estimation and detection results can be readily obtained using Algorithm 2 (see formal proof in Appendix A).
Theorem : Tk and Bk are the unbiased estimators of and respectively under the assumption that the noise in X ijk follows N 0, ) Proof: As E k is an unbiased estimator of, is an unbiased estimator of β k.
Two modifiers identified in an unbiased manner from these screens, par-1 and shaggy, are known tau kinases (24, 25, 90– 92), providing a proof of principle that our approach can identify bona fide tau modifiers.
The present proof of concept study seeks to establish the feasibility of surface-based MRI morphometry to detect, in an unbiased, automated fashion, known areas of structural abnormality in individual patients with a range of epileptogenic cortical malformations.
