TAILIEUCHUNG - Computational Statistics Handbook with MATLAB phần 5

SE θ là sai số chuẩn cho thống kê θ thu được bằng cách sử dụng dây đeo khởi động [Mooney và Duval, 1993]. Khoảng tin cậy trong phương trình 6,21 có thể được sử dụng khi phân phối cho θ phát hành bình thường hoặc giả định bình thường là chính đáng. | Similar to this the bootstrap standard confidence interval is given by 0 - z 1 -a 2 SE0 0 - z a 2 SE0 where SE0 is the standard error for the statistic 0 obtained using the bootstrap Mooney and Duval 1993 . The confidence interval in Equation can be used when the distribution for 0 is normally distributed or the normality assumption is plausible. This is easily coded in MATLAB using previous results and is left as an exercise for the reader. Bootstrap-t Confidence Interval The second type of confidence interval using the bootstrap is called the boot-strap-t. We first generate B bootstrap samples and for each bootstrap sample the following quantity is computed n b n zb i0 0 . SE As before 0 b js the bootstrap replicate of 0 but SE b is the estimated standard error of 0 b for that bootstrap sample. If a formula exists for the standard error of 0 b then we can use that to determine the denominator of Equation . For instance if 0 is the mean then we can calculate the standard error as explained in Chapter 3. However in most situations where we have to resort to using the bootstrap these formulas are not available. One option is to use the bootstrap method of finding the standard error keeping in mind that you are estimating the standard error of 0 b using the bootstrap sample x b. In other words one resamples with replacement from the bootstrap sample x b to get an estimate of SE b. Once we have the B bootstrapped z b values from Equation the next step is to estimate the quantiles needed for the endpoints of the interval. The a 2 a 2 -th quantile denoted by t of the z b is estimated by a 2 zb ta 2 B This says that the estimated quantile is the V 2 such that 100 a 2 of the points z b are less than this number. For example if B 100 and a 2 then t0 05 could be estimated as the fifth largest value of the z b B a 2 100 5 . One could also use the quantile estimates discussed previously in Chapter 3 or some other suitable estimate. We .

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