We consider uniform minimum variance unbiased (UMVU) estimation of an unbiased estimable function of distribution parameters for bivariate truncation (non-regular) parameter families. In particular, we derive the UMVU estimator of the probability that Y is less than X ....
The objective is to minimize the variance in the atomic basis and keep it as an unbiased estimator of the original gradient. AdaQS [77,78] uses the MSDR value of gradient elements as a metric to determine the quantization ratio of QSGD. MSDR can reflect the “signal-to-noise ratio” ...
Minimum variance unbiased estimation of the distribution function admitting a sufficient statistic Let a real-valued random variable X have the distribution function (df) F(x; 0) where 0 is a scalar or a vector parameter. The situations where one wants to estimate g(O)=F(a; O) with "a"...
8a). We note that the variance can be larger or smaller than the mean in ssPoisson distribution (see Supplementary Table 3 for the simulation). PIC model—diploid cells For diploid cells, we use Ws1 and Ws2 to denote the observed PIC count in two alleles, with insertion rates X1 and X...
For a population according to a uniform distribution U[kθ,(k+1)θ] where k is known, Thomas Yageen (1996) derived an efficient estimator for θ. Here for the case when both k and θ'are unknown, we obtain uniformly minimum variance unbiased (UMVU) estimators for them. Moreover, for...
We derive the uniformly minimum variance unbiased estimator (UMVUE) of S. We also consider three natural estimators N, 1, N, 2, and N, 3 of S which are, respectively, based on the maximum likelihood estimators, UMVUEs, and minimum risk equivariant estimators for component estimation problems...
Three natural estimators of θS based on the maximum likelihood estimators, uniformly minimum variance unbiased estimators, and minimum risk equivariant estimators are considered. The generalized Bayes estimator of θS with respect to a non-informative prior is derived. Under the ASE loss function, a...
Uniformly minimum variance unbiased estimatorSufficiency, conditionality, and invariance are basic principles of statistical inference. Current mathematical statistics courses do not devote much teaching time to these classical principles, and even ignore the latter two, in order to teach modern methods. ...
The minimum within each group is given as , i.e., the number of biased items within each group. In empirical applications of robust Haebara linking it can be expected that the bias decreases with decreasing values of p. Obviously, the reasoning relies on asymptotic arguments, and it is of...