Bootstrap Estimate Of Standard Error
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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 bootstrap values that relies on random sampling with replacement. Bootstrapping allows assigning
Bootstrap Standard Error Estimates For Linear Regression
measures of accuracy (defined in terms of bias, variance, confidence intervals, prediction error or some
Bootstrap Standard Error Stata
other such measure) to sample estimates.[1][2] This technique allows estimation of the sampling distribution of almost any statistic using random sampling methods.[3][4] Generally, it falls in
Bootstrap Standard Error R
the 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 approximating distribution is the empirical distribution function of the observed data. In the case where a bootstrap standard error matlab 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 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: Movin
whether or not the person got a speeding ticket. The data for women that received a ticket are shown below. Women, ticket:Sample: 103, 104, 109, 110, 120 Suppose we are interested in the following estimations: bootstrap standard error formula Estimate the population mean μ and get the standard deviation of the sample mean \(\bar{x}\). bootstrap standard error heteroskedasticity Estimate the population median η and get the standard deviation of the sample median. For (1), we have already found in the bootstrap standard error in sas previous section 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 https://en.wikipedia.org/wiki/Bootstrapping_(statistics) interested in the standard deviation of the M. We can easily find the sample median by finding the middle observation of the 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. https://onlinecourses.science.psu.edu/stat464/node/80 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 = observations from 103, 104, 109, 110, 120 with replacement. Sampling with replacement is important. If we did not sample with replacement, we would always get the same sample median as the observed value. The sample we get from sampling from the data with replacement is called the bootstrap sample. Summary of Steps: Replace the population with the sample Sample with replacement B times Compute sample medians each time Mi Compute the SD of M1, ... , MB. Example I created a function in R to generate a sample of size n = 5 observations from 103, 104, 109, 110, 120
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 http://stats.stackexchange.com/questions/26088/explaining-to-laypeople-why-bootstrapping-works 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 Here's how it works: Anybody can ask a question Anybody can answer The best answers standard error are voted up and rise to the top Explaining to laypeople why bootstrapping works up vote 181 down vote favorite 146 I recently used bootstrapping to estimate confidence intervals for a project. Someone who doesn't know much about statistics recently asked me to explain why bootstrapping works, i.e., why is it that resampling the same sample over and over gives good results. I realized that although I'd spent a lot of bootstrap standard error time understanding how to use it, I don't really understand why bootstrapping works. Specifically: if we are resampling from our sample, how is it that we are learning something about the population rather than only about the sample? There seems to be a leap there which is somewhat counter-intuitive. I have found a few answers to this question here which I half-understand. Particularly this one. I am a "consumer" of statistics, not a statistician, and I work with people who know much less about statistics than I do. So, can someone explain, with a minimum of references to theorems, etc., the basic reasoning behind the bootstrap? That is, if you had to explain it to your neighbor, what would you say? bootstrap communication share|improve this question edited Jun 25 '12 at 1:49 rolando2 6,91312238 asked Apr 8 '12 at 21:04 Alan H. 1,35631217 10 (+1) You might mention briefly the questions you have looked at, but that don't quite satisfy you. There are lots of questions on the bootstrap here. :) –cardinal♦ Apr 8 '12 at 21:11 @cardinal Thanks, I updated the original post. Hopefully it is more clear. :) –Alan H. Apr 9 '12 at 3:17 One thing to note - bootstrapping doesn't work easily for
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