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I have written an R script for obtaining bootstrapped standard errors in the linear regression setting.

In practice, first in a model building step I select the final model to be applied at each bootstrapped sample (for simplicity suppose that it is a simple univariate linear model).

Then I simulate B = 1000 bootstrap samples (with replacement from the initial true dataset). For each simulated sample I fit the initially defined univariate regression model to the simulated data and store the estimated coefficient of the covariate of interest in b_x.

Suppose now for simplicity that B = 10. At the end of the B simulations, I obtain the output matrix boot_out in this form:

boot_out <- read.table(text = "

iter      b_x
    1       1.19
    2       0.81
    3       1.21
    4       1.05
    5       0.99
    6       1.11
    7       1.09
    8       0.88
    9       0.91
    10      1.12",

header=TRUE)

Now I need to compute the bootstrapped standard error of the effect of the regressor of interest, call it se_boot.

To this aim, I used:

se_boot <- sd(boot_out[,"b_x"])
se_boot

but I get a unexpected result: the bootstrapped standard error of b_x is higher than the standard error estimated through the initial model fitted to the true data..

By looking at my b_x values I found that the estimates of the partial effect of interest vary within a wide range, but I guessed that 1000 bootstrap replications were sufficient for refining the estimated standard error of b_x..

Before trying to do even more replications, could you please tell me whether the above passages are right?

Thanks a lot for any help.

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