Bootstrap Median Standard Error
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Bootstrap Standard Error Estimates For Linear Regression
Bootstrap Method for Standard Errors and Confidence Intervals Key Concepts in Human Biology and Physiology Chronic Pain bootstrap standard error matlab and Individual Differences in Pain Perception Pain-Free and Hating It: Peripheral Neuropathy Neurotransmitters That Reduce or Block Pain Load more EducationScienceBiologyThe Bootstrap Method for Standard Errors and Confidence Intervals
Bootstrap Standard Error Formula
The Bootstrap Method for Standard Errors and Confidence Intervals Related Book Biostatistics For Dummies By John Pezzullo You can calculate the standard error (SE) and confidence interval (CI) of the more common sample statistics (means, proportions, event counts and rates, and regression coefficients). But an SE and CI exist (theoretically, at least) for any number you could possibly wring bootstrap standard error heteroskedasticity from your data -- medians, centiles, correlation coefficients, and other quantities that might involve complicated calculations, like the area under a concentration-versus-time curve (AUC) or the estimated five-year survival probability derived from a survival analysis. Formulas for the SE and CI around these numbers might not be available or might be hopelessly difficult to evaluate. Also, the formulas that do exist might apply only to normally distributed numbers, and you might not be sure what kind of distribution your data follows. Consider a very simple problem. Suppose you've measured the IQ of 20 subjects and have gotten the following results: 61, 88, 89, 89, 90, 92, 93, 94, 98, 98, 101, 102, 105, 108, 109, 113, 114, 115, 120, and 138. These numbers have a mean of 100.85 and a median of 99.5. Because you're a good scientist, you know that whenever you report some number you've calculated from your data (like a mean or median), you'll also want to indicate the precision of that value in the form of an SE an
programs The R program (as a text file) for the code on this page. In order to see more than just the results from the computations of the functions (i.e. if you want to see the functions echoed back in console as they are processed) use the echo=T
Bootstrap Standard Error In Sas
option in the source function when running the program. source("d:/stat/bootstrap.txt", echo=T) Introduction Bootstrapping can be a very
Bootstrap Median Confidence Interval
useful tool in statistics and it is very easily implemented in R. Bootstrapping comes in handy when there is doubt that the usual distributional assumptions and bootstrap median r asymptotic results are valid and accurate. Bootstrapping is a nonparametric method which lets us compute estimated standard errors, confidence intervals and hypothesis testing. Generally bootstrapping follows the same basic steps: 1. Resample a given data set a specified number of times 2. http://www.dummies.com/education/science/biology/the-bootstrap-method-for-standard-errors-and-confidence-intervals/ Calculate a specific statistic from each sample 3. Find the standard deviation of the distribution of that statistic The sample function A major component of bootstrapping is being able to resample a given data set and in R the function which does this is the sample function.
sample(x, size, replace, prob) The first argument is a vector containing the data set to be resampled or the indices of the data to be resampled. The size option specifies the sample size with the default being the http://www.ats.ucla.edu/stat/r/library/bootstrap.htm size of the population being resampled. The replace option determines if the sample will be drawn with or without replacement where the default value is FALSE, i.e. without replacement. The prob option takes a vector of length equal to the data set given in the first argument containing the probability of selection for each element of x. The default value is for a random sample where each element has equal probability of being sampled. In a typical bootstrapping situation we would want to obtain bootstrapping samples of the same size as the population being sampled and we would want to sample with replacement. #using sample to generate a permutation of the sequence 1:10 sample(10) [1] 4 8 3 5 1 10 6 2 9 7 #bootstrap sample from the same sequence sample(10, replace=T) [1] 1 3 9 4 10 3 5 1 6 4 #boostrap sample from the same sequence with #probabilities that favor the numbers 1-5 prob1 <- c(rep(.15, 5), rep(.05, 5)) prob1 [1] 0.15 0.15 0.15 0.15 0.15 0.05 0.05 0.05 0.05 0.05 sample(10, replace=T, prob=prob1) [1] 4 2 1 7 6 5 4 4 2 9 #sample of size 5 from elements of a matrix #creating the data matrix y1 [,1] [,2] [,3] [,4] [,5] [1,] 6 4 6 4 5 [2,] 6 5 5 7 4 [3,] 5 4 5 7 6 [4,] 5 3 6 6 6 [5,] 3 4 4 5 5 #saving the sample of size 5 in the vector x1 x1 <- y1[sample(25, 5)] x1 [1Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of http://stats.stackexchange.com/questions/22472/use-of-standard-error-of-bootstrap-distribution this site About Us Learn more about Stack Overflow the company Business Learn more about hiring developers or posting ads with us Cross Validated Questions Tags Users Badges Unanswered Ask Question _ Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. Join them; it only takes a minute: Sign up standard error Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top Use of standard error of bootstrap distribution up vote 18 down vote favorite 7 (ignore the R code if needed, as my main question is language-independent) If I want to look at the variability of a simple statistic (ex: mean), I bootstrap standard error know I can do it via theory like: x = rnorm(50) # Estimate standard error from theory summary(lm(x~1)) # same as... sd(x) / sqrt(length(x)) or with the bootstrap like: library(boot) # Estimate standard error from bootstrap (x.bs = boot(x, function(x, inds) mean(x[inds]), 1000)) # which is simply the standard *deviation* of the bootstrap distribution... sd(x.bs$t) However, what I'm wondering is, can it be useful/valid(?) to look to the standard error of a bootstrap distribution in certain situations? The situation I'm dealing with is a relatively noisy nonlinear function, such as: # Simulate dataset set.seed(12345) n = 100 x = runif(n, 0, 20) y = SSasymp(x, 5, 1, -1) + rnorm(n, sd=2) dat = data.frame(x, y) Here the model doesn't even converge using the original data set, > (fit = nls(y ~ SSasymp(x, Asym, R0, lrc), dat)) Error in numericDeriv(form[[3L]], names(ind), env) : Missing value or an infinity produced when evaluating the model so the statistics I'm interested in instead are more stabilized estimates of these nls parameters - perhaps their means across a number of bootstrap replications. # Obtain mean bootstrap nls parameter estimates fit.bs = boot(dat, function(dat, inds