Consider inference with a small number of potentially heterogeneous clusters. Suppose estimating the model on each cluster yields q asymptotically unbiased, independent Gaussian estimators with potentially heterogeneous variances. Following Ibragimov and Müller (2010), one can then conduct asymptotically valid inference with a standard t-test based on the q cluster estimators, since at conventi...

In statistic tests, the probability distribution of the statistics is important. When samples are drawn from population N (µ, σ(2)) with a sample size of n, the distribution of the sample mean X̄ should be a normal distribution N (µ, σ(2)/n). Under the null hypothesis µ = µ0, the distribution of statistics [Formula: see text] should be standardized as a normal distribution. When the variance of ...

introductionandobjective:the overall objective of the current study investigated teachers' attitudes towards performance appraisal system; the staff is trained in education branch. methods: all schools in the study sample middle school teacher education in the academic year 1390-1391 a total of 370 branch secretary is formed. of which 191 were randomly classified according to morgan being ...

Brownian motion is a stochastic process (Wt, t ≥ 0) such that • W0 = 0. • (Wt2 −Wt1) and (Wt4 −Wt3) are independent, for any t1 < t2 ≤ t3 < t4. • (Wt2 −Wt1) ∼ N(0, t2 − t1). • For almost all ω, the sample function t 7→Wt(ω) is continuous. Since Wt has stationary independent increments, we already know that EWt = 0 and that the covariance function is r(t, s) = t∧ s. Thus the covariance matrix of...