Bootstrapping

Question 1

what is bootstrapping?

Answer 1

any test/metric that uses random sampling with replacement

Question 2

What is the empirical distribution function?

Answer 2

the distribution function associated with the empirical measure of a sample

Question 3

What is resampling?

Answer 3

any method for:

• estimating the precision of sample statistics (medians, variances, perecentiles) by using subsets of data (jackknifing) or drawing randomly (bootstrapping)
• validating models using random subsets (bootstrapping, cross validation)
• exchange labels on data points (for significance tests) = permutation tests

Question 4

intuition for bootstrap

Answer 4

• infer info about a population by resampling the sample data
• the ‘population’ is the sample and the quality of inference using resampled data can be measured

Question 5

what is variability?

Answer 5

aka dispersion, scatter

• is the extent to which a distribution is stretched or squeezed
• measures: variance, std deviation, interquantile range (IQR=Q3[75%] -Q1[25%]), median absolute deviation

Question 6

consistent? consistency?

Answer 6

• terms restricted to cases where the same procedure can be applied to any number of data items

Question 7

statistic/sample statistic

Answer 7

• single measure of some attribute of a sample

- calculated by applying a function (statistical algorithm) to the set of data = values of the items of the sample

Question 8

what is point estimation?

Answer 8

• use of sample data to calculate a single value (a ‘statistic’) which is to serve as the best guess/best estimate of an unknown population parameter

Question 9

recommendations for boostrap

Answer 9

• when the distribution of the statistic of interest is unknown or complex
• when the sample size for the unknown statistic is insufficient
• when power calculations have to be performed, and a small pilot sample is available
• MUST be sure that the distribution is NOT a power law/heavy tailed

Question 10

how to do bootstarp (simple case)?

Answer 10

• using MonteCarlo algorithm: resample with replacement, use the same data set size as the original, calculate the statistic of interest, repeat to increase estimate’s precision

Question 11

other bootstrap types?

Answer 11

• bayesian
• parametric
• wild
• gaussian process regression
• smooth