Bradley Efron and Robert Tibshirani. 1986. Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical Accuracy. Statistical Science, 1(1). pp. 54--77.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....independence of the observations is crucial. It is easily seen that they give incorrect answers if dependence is neglected, compare Remark 2.1 of Singh (1981) Recently the two methods have been extended to ARMA models by reducing to innovations which are i.i.d. see Davis (1977) Freedman (1984) Efron and Tibshirani (1986), Section 6. Still ARMA processes are not able to model essential features of many observed time series, compare Priestley (1981) Chapter 11. Fitting models which go beyond ARMA is however an extremely difficult task, and it seems impossible to take the effects of parameter estimation or ....

....choice for is (n) j 1 provided the model (5.2) holds. If it does not hold, the influence functions are correlated and we have to let increase with n in order to obtain consistency. 27 5.2.l The sunspot numbers As an example with real data we consider Wolf s sunspot numbers from 17701889. Efron and Tibshirani (1986) used the same data set so that we can compare our procedure with theirs. The results are summarized in Table 2 . For p = 1 there are two groups of methods. The first one estimates the standard error close to 0.05 and contains methods 1.a, 2.a, 3.a, 4, and 5. The remaining methods estimate the ....

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Efron, B. and Tibshirani, R.J. (1986). Bootstrap methods for standard errors, confidence intervals and other measures of statistical accuracy. Statist. Sci.

....neighbourhood approximation to the PPD, and write it as, PNA(m) Specifically we have PNA(m) P (p i ) 14) where p i is the model in the input ensemble which is closest to the point m. It is interesting to note that the approximation, PNA(m) is related to the bootstrap method (Efron 1982; Efron Tibshirani 1986), used for determining measures of statistical accuracy. The philosophy behind the bootstrap is similar to that here; that is, reconstruct a probability distribution from a finite set of realizations. In the bootstrap it is achieved as a sum of Dirac delta functions centered on the members of the ....

Efron, B. & Tibshirani, R., 1986. Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy, Stat. Sci., 1, 54--77.

....of tt pp matrix whose rows are the resampling points in the least favourable family. The abc confidence points are the function tt evaluated at these points References Efron, B, and DiCiccio, T. 1992) More accurate confidence intervals in exponential families. Biometrika 79, pages 231 245. Efron, B. and Tibshirani, R. 1993) An Introduction to the Bootstrap. Chapman and Hall, New York, London. Examples # compute abc intervals for the mean x rnorm(10) theta function(p,x) sum(p x) sum(p) results abcnon(x, theta) # compute abc intervals for the correlation x matrix(rnorm(20) ncol=2) theta ....

....value of tt, estimated standard error and estimated bias constants list consisting of a=acceleration constant, z0=bias adjustment, cq=curvature component References Efron, B, and DiCiccio, T. 1992) More accurate confidence intervals in exponential families. Bimometrika 79, pages 231 245. Efron, B. and Tibshirani, R. 1993) An Introduction to the Bootstrap. Chapman and Hall, New York, London. Examples # binomial # x is a p vector of successes, n is a p vector of # number of trials S matrix(0,nrow=p,ncol=p) S[row(S) col(S) x (1 x n) mu function(eta,n) n (1 exp(eta) etahat log(x (n x) ....

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Efron, B. and Tibshirani, R. (1986). The Bootstrap Method for standard errors, confidence intervals, and other measures of statistical accuracy. Statistical Science, Vol 1., No. 1, pp 1-35.

....of tt pp matrix whose rows are the resampling points in the least favourable family. The abc confidence points are the function tt evaluated at these points References Efron, B, and DiCiccio, T. 1992) More accurate confidence intervals in exponential families. Biometrika 79, pages 231 245. Efron, B. and Tibshirani, R. 1993) An Introduction to the Bootstrap. Chapman and Hall, New York, London. Examples # compute abc intervals for the mean x rnorm(10) theta function(p,x) sum(p x) sum(p) results abcnon(x, theta) # compute abc intervals for the correlation x matrix(rnorm(20) ncol=2) theta ....

....value of tt, estimated standard error and estimated bias constants list consisting of a=acceleration constant, z0=bias adjustment, cq=curvature component References Efron, B, and DiCiccio, T. 1992) More accurate confidence intervals in exponential families. Bimometrika 79, pages 231 245. Efron, B. and Tibshirani, R. 1993) An Introduction to the Bootstrap. Chapman and Hall, New York, London. Examples # binomial # x is a p vector of successes, n is a p vector of # number of trials S matrix(0,nrow=p,ncol=p) S[row(S) col(S) x (1 x n) mu function(eta,n) n (1 exp(eta) etahat log(x (n x) ....

[Article contains additional citation context not shown here]

Efron, B. and Tibshirani, R. (1986). The Bootstrap Method for standard errors, confidence intervals, and other measures of statistical accuracy. Statistical Science, Vol 1., No. 1, pp 1-35.

....of tt pp matrix whose rows are the resampling points in the least favourable family. The abc confidence points are the function tt evaluated at these points References Efron, B, and DiCiccio, T. 1992) More accurate confidence intervals in exponential families. Biometrika 79, pages 231 245. Efron, B. and Tibshirani, R. 1993) An Introduction to the Bootstrap. Chapman and Hall, New York, London. 1 2 abcpar Examples # compute abc intervals for the mean x rnorm(10) theta function(p,x) sum(p x) sum(p) results abcnon(x, theta) # compute abc intervals for the correlation x matrix(rnorm(20) ncol=2) ....

....of tt, estimated standard error and estimated bias constants list consisting of a=acceleration constant, z0=bias adjustment, cq=curvature component bcanon 3 References Efron, B, and DiCiccio, T. 1992) More accurate confidence intervals in exponential families. Bimometrika 79, pages 231 245. Efron, B. and Tibshirani, R. 1993) An Introduction to the Bootstrap. Chapman and Hall, New York, London. Examples # binomial # x is a p vector of successes, n is a p vector of # number of trials S matrix(0,nrow=p,ncol=p) S[row(S) col(S) x (1 x n) mu function(eta,n) n (1 exp(eta) etahat log(x (n x) ....

[Article contains additional citation context not shown here]

Efron, B. and Tibshirani, R. (1986). The Bootstrap Method for standard errors, confidence intervals, and other measures of statistical accuracy. Statistical Science, Vol 1., No. 1, pp 1-35.

....from the empirical distribution function is also not generally appropriate and extending the bootstrap to non iid situations requires special arguments. The most studied problem in the bootstrap literature is that of determining reliable confidence limits; see, for examples Efron (1987) Efron Tibshirani (1986), DiCiccio Romano (1988) and DiCiccio Efron (1996) In the iid situation, basic bootstrap methods are asymptotically correct to first order and various approaches have been suggested to obtain higher order accuracy. For example, the BC a , the classical bootstrap percentile t method and the ....

B. Efron & R. J. Tibshirani (1986). Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy. Statistical Science, 1, 54--77.

....PDB is concentrated in a single sequence (fold 4) Thus, the presence or absence of this sequence would greatly affect the composition of the PDB. One imagines that the actual PDB (clustered PDB) is somewhere between these extremes. The compositional bias of the PDB can be quantified by resampling [44,98,99]. One begins with the 1135 sequences in the soluble PDB (data set PS in Table 10) Then one randomly picks the 1135 sequences with replacement to make a new soluble PDB, called the bootstrap sample PS 2 . One calculates the composition PS 2 and then continues the procedure N times (here N = ....

Efron, B. & Tibshirani, R. (1986). Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy. Stat. Sci. 1, 54-77.

....we pulled independent random samples from the population of severity 1 and 2. Each sample was large enough to allow the necessary categorization. We then combined the results from the severity 1 and 2 samples in the proportion they are represented in the population. We used boot strapping [Efron86] to combine the samples rather than a simple weighted average. Boot strapping has the advantage that when used to make confidence interval estimates it does not depend on assumptions about the distribution of the parent population. In all, we classified 150 APARs in the Regular sample and 91 from ....

B. Efron and R. Tibshirani. Bootstrap Methods for Standard Errors, Confidence Intervals, ... Statistical Science, 1(1), 1986.

....it is natural to consider point estimates, and subsequently interval estimates, of functions of #. Several di#erent approaches might be suggested which would enable us to avoid deriving the observed information directly. For example, we could use one of the resampling methods described by Efron and Tibshirani (1986) to construct a confidence interval for the parameter of interest. A second approach is based on the technique suggested by Turnbull and Mitchell (1984) Alternatively, the observed information can be computed indirectly, using the approach outlined by Louis (1982) In the remainder of this ....

Efron, B., and Tibshirani, R. J. (1986). Bootstrap methods for standard errors, confidence intervals and other measure of statistical accuracy. Statist. Sci. 1, 54--77.

....and Romano (1994) and the matched block bootstrap of Carlstein, Do, Hall, Hesterberg and Kunsch (1996) On the other hand, there exists an extensive literature on model based bootstrap methods in the time series context. Under the assumption of i.i.d. innovations in a linear autoregressive model, Efron and Tibshirani (1986) proposed to generate bootstrap series by drawing bootstrap innovations independently with replacement from the set of mean adjusted residuals. Kreiss and Franke (1992) generalized this to autoregressive moving average models. Furthermore, there exists a series of proposals for bootstrapping ....

....chains; see the brief survey in Section 3. There also exist several semiparametric methods. For example, Kreiss (1988) approximated linear autoregressive processes by a bootstrap process of finite, but increasing order. Franke and Wendel (1992) and Kreutzberger (1993) generalized the method of Efron and Tibshirani (1986) to the case of nonlinear autoregressive processes. 2 Concerning universality, blockwise bootstrap schemes with a block length tending to infinity dominate model based methods since they do not require structural assumptions on the data generating process to be fulfilled. They are nearly ....

Efron, B. and Tibshirani, R. J. (1986). Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy. Statist. Science 1, 54--77.

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Bradley Efron and Robert Tibshirani. 1986. Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical Accuracy. Statistical Science, 1(1). pp. 54--77.

No context found.

Efron, Bradley and Robert Tibshirani. 1986. Bootstrap Methods for Standard Errors, Confidence Intervals and Other Measures of Statistical Accuracy. Statistical Science, 1:54--77.

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