联系我们： 手动添加方式: 微信>添加朋友>企业微信联系人>13262280223 或者 QQ: 1483266981

Coverage of the main parametric and non-parametric and techniques used in statistics. Uniformly minimum variance estimation. Cramer-Rao inequality, Lehmann-Scheffe theorem. Monotone likelihood ratio distributions and uniformly most powerful unbiased tests. Generalised likelihood ratio tests, exact tests and large sample tests. Bayesian point estimation, interval estimation and hypothesis testing. Robustness and bootstrap resampling. Order statistics, goodness of fit, contingency tables. Statistical inference based on ranks. One sample, two sample and k-sample problems, blocked data, independence and association.

这是一份unsw新南威尔士大学MATH3911 的成功案例

高级统计推理|MATH3911 Higher Statistical Inference
问题 1.

The t(n-1)t(n-1) density decreases away from 0 , so the weirdest observations are far from 0 .

The pp value is the probability of observing a test statistic as weird or weirder than we actually saw. In the illustration, because the t(n-1)t(n-1) density is symmetric about 0 , with T_{o b s} equiv T left(y_{o b s} right)T_{o b s} equiv T left(y_{o b s} right) the pp value is p= operatorname{Pr} left[T leq- left|T_{o b s} right| right]+ operatorname{Pr} left[T geq left|T_{o b s} right| right] . p= operatorname{Pr} left[T leq- left|T_{o b s} right| right]+ operatorname{Pr} left[T geq left|T_{o b s} right| right] .

证明 .

A small pp value suggests that something is wrong with the model. Perhaps the mean is not 0 but perhaps the data are not normal, are not independent, or are heteroscedastic. Interestingly, this two-sided t(n-1)t(n-1) test, when using the alternative test statistic T^{2}T^{2}, corresponds to a one-sided F(1, n-1)F(1, n-1) test, because the mode of an F(1, n-1)F(1, n-1) distribution is at 0 .In general, with W_{o b s} equiv W left(y_{o b s} right)W_{o b s} equiv W left(y_{o b s} right), the pp value is p= operatorname{Pr} left[f(W) leq f left(W_{o b s} right) right] p= operatorname{Pr} left[f(W) leq f left(W_{o b s} right) right] For a less standard illustration, assume y_{1}, ldots, y_{n}y_{1}, ldots, y_{n} iid N( mu, 4)N( mu, 4). With a test statistic W= frac{(n-1) s^{2}}{4} sim chi^{2}(n-1), W= frac{(n-1) s^{2}}{4} sim chi^{2}(n-1), denote the density chi^{2}(w mid n-1) chi^{2}(w mid n-1). For n-1>2n-1>2, unless W_{o b s}W_{o b s} happens to be the mode, there are two values w_{1}