Examples of bootstrapping method in the following topics:
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Hypotheses about two paired means or densities
- Network>Compare densities>Paired (same node) compares the densities of two relations for the same actors, and calculates estimated standard errors to test differences by bootstrap methods.
- Results for both the standard approach and the bootstrap approach (this time, we ran 10,000 sub-samples) are reported in the output.
- The standard error of the difference by the classical method is .0697; the standard error by bootstrap estimate is .1237.
- By the bootstrap method, we can see that there is a two-tailed probability of .0178.
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Single-Population Inferences
- Two notable nonparametric methods of making inferences about single populations are bootstrapping and the Anderson–Darling test.
- Two notable nonparametric methods of making inferences about single populations are bootstrapping and the Anderson–Darling test.
- Bootstrapping is a method for assigning measures of accuracy to sample estimates.
- This technique allows estimation of the sampling distribution of almost any statistic using only very simple methods.
- The simplest bootstrap method involves taking the original data set of $N$ heights, and, using a computer, sampling from it to form a new sample (called a 'resample' or bootstrap sample) that is also of size $N$.
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Financing Company Operations
- Many successful companies including Dell Computers and Facebook were founded using financial bootstrapping.
- Financial bootstrapping is a term used to cover different methods for avoiding the use of financial resources that come from external investors.
- The use of private credit card debt is the most known form of bootstrapping, but a wide variety of methods are available for entrepreneurs.
- While bootstrapping involves a risk for the founders, the absence of any other stakeholder gives the founders more freedom to develop the company.
- Many successful companies, including Dell Computers and Facebook, were founded using financial bootstrapping.
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Hypotheses about one mean or density
- The parameter "Number of samples" is used for estimating the standard error for the test by the means of "bootstrapping" or computing estimated sampling variance of the mean by drawing 5000 random sub-samples from our network, and constructing a sampling distribution of density measures.
- However, if we use the bootstrap method of constructing 5000 networks by sampling random sub-sets of nodes each time, and computing the density each time, the mean of this sampling distribution turns out to be .4893, and its standard deviation (or the standard error) turns out to be .1201.
- The classical formula gives an estimate of the standard error (.0528) that is much smaller than than that created by the bootstrap method (.1201).
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Spot Rates, Forward Rates, and Cross Rates
- For bonds, spot rates are estimated via the bootstrapping method, which uses prices of the securities currently trading in market, that is, from the cash or coupon curve.
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Distribution-Free Tests
- distribution free methods, which do not rely on assumptions that the data are drawn from a given probability distribution. ( As such, it is the opposite of parametric statistics.
- Non-parametric methods are widely used for studying populations that take on a ranked order (such as movie reviews receiving one to four stars).
- The use of non-parametric methods may be necessary when data have a ranking but no clear numerical interpretation, such as assessing preferences.
- In terms of levels of measurement, non-parametric methods result in "ordinal" data.
- Distribution-free statistical methods are mathematical procedures for testing statistical hypotheses which, unlike parametric statistics, make no assumptions about the probability distributions of the variables being assessed.
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Interpreting a Confidence Interval
- For users of frequentist methods, various interpretations of a confidence interval can be given.
- Descriptive statistics - This is closely related to the method of moments for estimation.
- Estimating equations - The estimation approach here can be considered as both a generalization of the method of moments and a generalization of the maximum likelihood approach.
- Bootstrapping - In situations where the distributional assumptions for the above methods are uncertain or violated, resampling methods allow construction of confidence intervals or prediction intervals.
- For users of frequentist methods, various interpretations of a confidence interval can be given:
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References
- Tape-assisted reciprocal teaching: Cognitive bootstrapping for poor decoders.
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Valuing Notes Receivable
- Companies have two methods available to them for measuring the net value of accounts receivable: the allowance method and the direct write-off method.
- Companies have two methods available to them for measuring the net value of accounts receivable--the allowance method and the direct write-off method.
- The first method is the allowance method, which establishes a contra-asset account, allowance for doubtful accounts, or bad debt provision, that has the effect of reducing the balance for accounts receivable.
- The second method is the direct write off method.
- Differentiate between the allowance method and the write off method for valuing notes receivable
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Newton's Method
- Newton's Method is a method for finding successively better approximations to the roots (or zeroes) of a real-valued function.
- In numerical analysis, Newton's method (also known as the Newton–Raphson method), named after Isaac Newton and Joseph Raphson, is a method for finding successively better approximations to the roots (or zeroes) of a real-valued function.
- This algorithm is first in the class of Householder's methods, succeeded by Halley's method.
- The method can also be extended to complex functions and to systems of equations.
- Use "Newton's Method" to find successively more accurate estimates for a function's $x$-intercept