Question

9. Bootstrap (a) (1 mark) Give an advantage of the bootstrap estimate of the standard error. (b) (3 marks) Describe the bootstrap percentile method for constructing a confidence interval. (c) (3 marks) For regression describe how to generate bootstrap samples by resampling from the errors.

Answer 1

g With deviation will be Low biased & with boot strapping estinates of standard I approximate the sampling distribution of your the true distribution of your data. The more sample your the closer your empirical distribution will be to the actual your small samples, your very you can estimates by treating your sample as an have, distribution, hence allowing ever more more accurate error approximation of estimates . would To see have of b Lets discuss this method by an example how this method works, here's how you use it to estimate the SE and 95% CI of the mean and the median of the 20 IQ valus. you have to (*:61,88,8989, 90, 92,93,94, 98, 98,101 102 ,/05) 108,109,113,114,115,120,138). These no 100.85 and median 99.5. Step 1 Write each of your measurements on a separate slip of paper & put them all into a bag. step27 Reach in and draw out one slip, write that no. down & but the slip back. Step 3 Repeat steps 2 as many times as need to match measurements you have returning the slip to the bag each time Step 4 > Calculate the desired sample statistie of the resampled numbers from step 2 & 3, and record that number Step 5 Repeat steps 2 through 4 many thousands time Step 6→ Calculate the standard deviation of your Scanned thousands of values of the sample statistic the no of CS CamScanner

Step I obtain the 2,5th and 97.5th percentiles of the thousands of values of the stample statistic, You can try this by any software program dike Statistic los". You can centre your observed results and tell it to generate , say, 100,000 resampled data sets of then calculate and save mean & the median from each one then calculate the SD and the 25th & 97.5th centiles of those 100,000 means & Joo, ooo medians. Bootstrapping is conceptually simple, but its not full- proof The method involves certain assumptions & limitations, © Above escample, you generate a new resample data set from which calculate and record the desired sample. you statistics in this case the mean & median of the resampled data set), you wind up with thousands of values for the mean and thousands of values of the meadian. CS Scanned with CamScanner