Marginal estimates after running svy logistic

[PMUser]

This may be more of a statistical question than a Stata question... I am using the Canadian Community Health Survey (CCHS) which is a series of repeated cross-sections. Statistics Canada is the agency providing the data. Statistics Canada also supplies bootstrap weights (500 replicates) and recommends using bootstrapping to obtain unbiased standard errors.

If I survey set my data, then run a logistic regression with bootstrapping, will the following marginal estimates (for example predicted probabilities and elasticity estimates) also have unbiased standard errors? Here is an example of some sample code:

use cchs.dta, clear

/* Survey set data */
svyset _n [weight=fwt], vce(bootstrap) bsrweight(bswt1-bswt500)

/* Run svy logistic regression */
svy: logistic outcome xvarlist

/* Get marginal estimates */
margins , dydx(varx)
margins , eyex(varx)

Or will standard errors of marginal estimates only be unbiased if I use the margins command for each bootstrap replicate?

Thanks.

[Steve Samuels]

Writing margins commands after svy logistic, as you've done, is the correct approach. However nothing in the bootstrap theory promises that bootstrapped standard errors will be unbiased, though they can be nearly unbiased in some cases. See, e.g., Tables 1 and 2 in Efron and Tibshirani (1986).

Reference: Efron, Bradley, and R Tibshirani. 1986. Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical Accuracy: Rejoinde. Statistical Science 1, no. 1: 54-75. available at http://sites.fas.harvard.edu/~eps236/effron_bootstrap_1986.pdf

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[PMUser]

Thank you for the reference.