全文链接：http:///?p=27695相关视频  参数引导：估计 MSE统计学问题：水平(k\)修剪后的平均值的MSE是多少？ result=rep(0,9)for(j in 1:9){
参数自抽样法：经验功效计算统计问题：随着零假设与现实之间的差异发生变化，功效如何变化？ 我们如何回答：绘制 t 检验的经验功效曲线。 _t 检验的原假设是 _
。另一种选择是
。 您将从具有
_ 的正态分布总体中抽取大小为 20 的样本。您将使用 0.05 的显着性水平。_ 显示当总体的实际平均值从 350 变为 650（增量为 10）时，功效如何变化。 y 轴是经验功效（通过 bootstrap 估计），x 轴是 \(\mu\) 的不同值（350、360、370 … 650）。 x <- rnorm(n, mean = muA, sd = sigma) #抽取平均值=450的样本 ts <- t.test(x, mu = mu0) #对无效的mu=500进行t检验 ts$p.value
点击标题查阅往期内容   左右滑动查看更多 参数自抽样法：经验功效计算统计问题：样本量如何影响功效？pvals <- replicate(m, pvalue())
参数自抽样法：经验置信水平统计问题：在制作 95% CI 时，如果我们的样本很小并且不是来自正态分布，我们是否仍有 95% 的置信度？我们如何回答：根据样本为总体的平均值创建一堆置信区间 (95%)。
您的样本大小应为 16，取自具有 2 个自由度的卡方分布。 for(i in 1:m){
非参数自抽样法置信区间统计问题：基于一个样本，我们可以为总体相关性创建一个置信区间吗？我们如何回答：为相关统计量创建一个 bootstrap t 置信区间估计。 boot.ti <-
自抽样法后的Jackknife统计问题：R 的标准误差的 bootstrap 估计的标准误差是多少？我们如何回答： indices <- matrix(0, nrow = B, ncol = n)
自测题Submit the rendered HTML file. Make sure all requested output (tables, graphs, etc.) appear in your document when you submit.Parametric Bootstrap: Estimate MSE Statistical question: What is the MSE of a level \(k\) trimmed mean? How we can answer it: Estimate the MSE of the level \(k\) trimmed mean for random samples of size 20 generated from a standard Cauchy distribution (t-distribution w/df = 1). The target parameter \(\theta\) is the center or median. The mean does not exist for a Cauchy distribution. Summarize the estimates of MSE in a table for \(k = 1, 2, ... 9\). Parametric Bootstrap: Empirical Power Calculations Statistical question: How does power change as the difference between the null hypothes and the reality changes? How we can answer it: Plot an empirical power curve for a t-test. The null hypothesis of the t-test is \(\mu = 500\). The alternative is \(\mu \ne 500\). You will draw samples of size 20, from a normally distributed population with \(\sigma = 100\). You will use a significance level of 0.05. Show how the power changes as the actual mean of the population changes from 350 to 650 (increments of 10). On the y-axis will be the empirical power (estimated via bootstrap) and the x-axis will be the different values of \(\mu\) (350, 360, 370 … 650). Parametric Bootstrap: Empirical Power Calculations Statistical question: How does sample size affect power? How we can answer it: Create more power curves as the actual mean varies from 350 to 650, but produce them for using samples of size n = 10, n = 20, n = 30, n = 40, and n = 50. Put all 5 power curves on the same plot. Parametric Bootstrap: Empirical Confidence Level Statistical question: When making a 95% CI, are we still 95% confident if our samples are small and do not come from a normal distribution? How we can answer it: Create a bunch of Confidence Intervals (95%) for the mean of a population based on a sample. \[\bar{x} \pm t^{*} \times \frac{s}{\sqrt{n}}\] Your samples should be of size 16, drawn from a chi-squared distribution with 2 degrees of freedom. Find the proportion of Confidence Intervals that fail to capture the true mean of the population. (Reminder: a chi-squared distribution with \(k\) degrees of freedom has a mean of \(k\).) Non Parametric Bootstrap Confidence Interval Statistical question: Based on one sample, can we create a confidence interval for the correlation of the population? How we can answer it: Create a bootstrap t confidence interval estimate for the correlation statistic. Jackknife after bootstrap Statistical question: What is the standard error of the bootstrap estimate of the standard error of R? How we can answer it: Use  |
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