Bootstrap Estimator Standard Error Mean
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standard deviation and the median absolute deviation (both measures of dispersion) distributions. In statistics, bootstrapping can refer to any test or metric that relies on random sampling with replacement. Bootstrapping allows assigning measures of accuracy (defined in terms of bias, bootstrap standard error estimates for linear regression variance, confidence intervals, prediction error or some other such measure) to sample estimates.[1][2] bootstrap standard error stata This technique allows estimation of the sampling distribution of almost any statistic using random sampling methods.[3][4] Generally, it falls in the
Bootstrap Standard Error R
broader class of resampling methods. Bootstrapping is the practice of estimating properties of an estimator (such as its variance) by measuring those properties when sampling from an approximating distribution. One standard choice for an
Bootstrap Standard Error Matlab
approximating distribution is the empirical distribution function of the observed data. In the case where a set of observations can be assumed to be from an independent and identically distributed population, this can be implemented by constructing a number of resamples with replacement, of the observed dataset (and of equal size to the observed dataset). It may also be used for constructing hypothesis tests. It is often used as bootstrap standard error formula an alternative to statistical inference based on the assumption of a parametric model when that assumption is in doubt, or where parametric inference is impossible or requires complicated formulas for the calculation of standard errors. Contents 1 History 2 Approach 3 Discussion 3.1 Advantages 3.2 Disadvantages 3.3 Recommendations 4 Types of bootstrap scheme 4.1 Case resampling 4.1.1 Estimating the distribution of sample mean 4.1.2 Regression 4.2 Bayesian bootstrap 4.3 Smooth bootstrap 4.4 Parametric bootstrap 4.5 Resampling residuals 4.6 Gaussian process regression bootstrap 4.7 Wild bootstrap 4.8 Block bootstrap 4.8.1 Time series: Simple block bootstrap 4.8.2 Time series: Moving block bootstrap 4.8.3 Cluster data: block bootstrap 5 Choice of statistic 6 Deriving confidence intervals from the bootstrap distribution 6.1 Bias, asymmetry, and confidence intervals 6.2 Methods for bootstrap confidence intervals 7 Example applications 7.1 Smoothed bootstrap 8 Relation to other approaches to inference 8.1 Relationship to other resampling methods 8.2 U-statistics 9 See also 10 References 11 Further reading 12 External links 12.1 Software History[edit] The bootstrap was published by Bradley Efron in "Bootstrap methods: another look at the jackknife" (1979).[5][6][7] It was inspired by earlier work on the jackknife.[8][9][10] Improved estimates of the variance were developed later.[11][12] A Bayesian extension was developed in 1981.[13
whether or not the person got a speeding ticket. The data for women that received a ticket are shown
Bootstrap Standard Error Heteroskedasticity
below. Women, ticket:Sample: 103, 104, 109, 110, 120 Suppose we are bootstrap standard error in sas interested in the following estimations: Estimate the population mean μ and get the standard deviation of bootstrap standard deviation the sample mean \(\bar{x}\). Estimate the population median η and get the standard deviation of the sample median. For (1), we have already found in the previous section https://en.wikipedia.org/wiki/Bootstrapping_(statistics) that the sampling distribution of \(\bar{X}\) is approximately Normal (under certain conditions) with \[\begin{align}& \bar{x}=109.2\\& \text{SD}=6.76\\& n=5\\& \text{SD}(\bar{x})=\frac{s}{\sqrt{n}}=\frac{6.76}{\sqrt{5}}=3.023\end{align}\] What about the estimate of the population median, η. Let's denote the estimate M. We are interested in the standard deviation of the M. We can easily find the sample median by finding the middle observation of the https://onlinecourses.science.psu.edu/stat464/node/80 ordered data. Thus, M = 109. But what about the standard deviation of the sample median? If we knew the underlying distribution of driving speeds of women that received a ticket, we could follow the method above and find the sampling distribution. To do this, we would follow these steps. Obtain a random sample of size n = 5 and calculate the sample median, M1. Gather another sample of size n = 5 and calculate M2. Repeat steps the steps until we obtained a desired number of sample medians, say 1000). Obtain the approximate distribution of the sample median and from there an estimate of the standard deviation. We can approximate the distribution by creating a histogram of all the sample medians. The trouble with this is that we do not know (nor want to assume) what distribution the data come from. A solution is to let the observed data represent the population and sample data from the original data. Therefore, we would sample n
Tour 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 this site About Us Learn more about Stack Overflow the company Business http://stats.stackexchange.com/questions/22472/use-of-standard-error-of-bootstrap-distribution 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 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 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 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 bootstrap standard error = boot(x, function(x, inds) mean(x[inds]), 1000)) # which is simply the standard *deviation* of the bootstrap distribution... sd(x.bs$t) However, what I'm wondering is, can it be useful/valid(?) to look to the standard error of a bootstrap distribution in certain situations? The situation I'm dealing with is a relatively noisy nonlinear function, such as: # Simulate dataset set.seed(12345) n = 100 x = runif(n, 0, 20) y = SSasymp(x, 5, 1, -1) + rnorm(n, sd=2) dat = data.frame(x, y) Here the model doesn't even converge using the original data set, > (fit = nls(y ~ SSasymp(x, Asym, R0, lrc), dat)) Error in numericDeriv(form[[3L]], names(ind), env) : Missing value or an infinity produced when evaluating the model so the statistics I'm interested in instead are more stabilized estimates of these nls parameters - perhaps their means across a number of bootstrap replications. # Obtain mean bootstrap nls parameter estimates fit.bs = boot(dat, function(dat, inds) tryCatch(coef(nls(y ~ SSasymp(x, Asym, R0, lrc), dat[inds, ])), error=function(e) c(NA, NA, NA)), 100) pars = colMeans(fit.bs$t, na.rm=T) Here these are, indeed, in the ball park of what I used to simulate the original data: > pars [1] 5.606190 1.859591 -1.390816 A plotted version looks like: # Plot with(dat, plot(x, y)) newx = seq(min(x), max(x), len=100) lines(newx, SSasymp(newx, pars[1], pars[2], pars[3])) lines(newx, SSasymp(newx, 5, 1, -1), col='red') legend('bottomright', c('Actual', 'Predicted'), bty='n', lty=1, col=2:1) Now, if
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