# Boostrap CGAIM Generates bootstrap replicates of a `cgaim` object. ```r boot.cgaim(object, boot.type = c("residuals", "wild", "pairs"), bsamples = NULL, B = 100, l = 1, nc = 1) ``` ## Arguments - `object`: A `cgaim` object. - `boot.type`: The type of bootstrap to perform. Currently available type are `"residuals"`, `"wild"` and `"pairs"`. See details - `bsamples`: A numerical matrix of observation indices specifying bootstrap samples. Rows indicate observations and columns bootstrap samples. If `NULL` (the default), samples are generated internally. - `B`: Number of bootstrap samples to generate when `bsamples = NULL`. - `l`: Block length for block-bootstrap. Samples are generated by resampling block of observation of length `l`. The classical bootstrap corresponds to `l = 1` (the default). - `nc`: Positive integer. If `nc > 1`, the function is parallelized with `nc` indicating the number of cores to use. ## Returns A `boot.cgaim` object with components - **`boot`**: The bootstrap result. A list that includes all `B` replications of `alpha`, `beta`, `gfit` and `indexfit` organized in arrays. - **`obs`**: The original `object` passed to the function. - **`samples`**: The bootstrap samples. A matrix with indices corresponding to original observations. - **`boot.type`**: The type of bootstrap performed. - **`B`**: The number of bootstrap replications. - **`l`**: The block length for block bootstrap. ## Details This function fits the `cgaim` on bootstrap samples. It is called internally by the `confint.cgaim` function, but can also be called directly to generate various statistics. Three types of bootstrap are currently implemented. `"residuals"` (the default) resamples the residuals in `object` to then be added to fitted values, creating alternative response vectors. The `cgaim` is then fitted on these newly generated y values with the original x. `"wild"` is similar except that residuals are multiplied by random draws from a standard normal distribution before being added to fitted values. `"pairs"` resamples directly pairs of y and x to create bootstrap samples. Bootstrap samples can either be prespecified by the user through `bsamples` or generated internally. In the former case, the columns of `bsamples` indicate the number of replications `B` and the rows should match the original number of observations. Internally generated bootstrap samples are controlled by the number of replications `B` and block length `l`, implementing block bootstrap. The latter is particularly recommended for time series data. As fitting a large number of `cgaim` models can be computationally intensive, the function can be run in parallel, using the `doParallel` package. This can be done by setting the argument `nc` to a value greater than 1, controlling the number of cores used in parallelization. ## Examples ```r # A simple CGAIM n <- 200 x1 <- rnorm(n) x2 <- x1 + rnorm(n) z <- x1 + x2 y <- z + rnorm(n) df1 <- data.frame(y, x1, x2) ans <- cgaim(y ~ g(x1, x2, acons = list(monotone = 1)), data = df1) # Use function to compute confidence intervals (B should be increased) set.seed(1989) boot1 <- boot.cgaim(ans, B = 10) ci1 <- confint(boot1) # Produces the same result as set.seed(1989) ci2 <- confint(ans, type = "boot", B = 10) # Create sampling beforehand bsamp <- matrix(sample(1:n, n * 10, replace = TRUE), n) boot2 <- boot.cgaim(ans, bsamples = bsamp) # Parallel computing (two cores) boot3 <- boot.cgaim(ans, nc = 2) ```

boot.cgaim function