# Precomputation for wild bootstrap Implements key components for the wild bootstrap of the hqm estimator in preparation for obtaining confidence bands. ```r prep_boot(g_xt, alpha, Ni, Yi, size_s_grid, br_X, br_s, t, b, int_X, x, n) ``` ## Arguments - `g_xt`: A vector obtained by `g_xt`. - `alpha`: A vector of the marker only hazard on the marker grid obtained by `get_alpha`. - `Ni`: A matrix made by `make_Ni` indicating the occurence. - `Yi`: A matrix made by `make_Yi` indicating the exposure. - `size_s_grid`: Size of the time grid. - `br_X`: Vector of grid points for the marker values. - `br_s`: Time value grid points that will be used in the evaluatiuon. - `t`: Numeric value of the time the function should be evaluated. - `b`: Bandwidth. - `int_X`: Position of the linear interpolated marker values on the marker grid. - `x`: Numeric value of the last observed marker value. - `n`: Number of individuals. ## Details The function implements $$ A_B(t) = \frac{1}{\sqrt{n}} \sum_{i=1}^n \int^{T}_0 \hat{g}_{i,t,x_*}(X_i(s)) V_i\{dN_i(s) - \hat{\alpha}_i(X_i(s))Z_i(s)ds\}, $$ and $$ B_B(t) = \frac{1}{\sqrt{n}}\sum_{i = 1}^n V_i\{\hat{\Gamma}(t,x_*)^{-1}W_i(t,x_*) - \hat{h}_{x_*}(t)\}, $$ where $V \sim N(0,1)$, $$ W_i(t) =\int_0^T\hat{\alpha}_i(X_i(t+s))Z_i(t+s)Z_i(s)K_b(x_*,X_i(s))\mathrm {d}s, $$ and $$ \hat{\Gamma}(t,x) = \frac{1}{n} \sum_{i = 1}^n \int_{0}^{T-t} Z_i(t+s)Z_i(s) K_b(x,X_i(s))ds, $$ with $Z$ being the exposure and $X$ the marker. ## Returns A list of 5 items. The first two are vectors for calculating $A_B$ and the third one a vector for $B_B$. The 4th one is the value of the hqm estimator that can also be obtained by `h_xt` and the last one is the value of $\Gamma$. ## See Also `Conf_bands` ## Examples ```r pbc2_id = to_id(pbc2) size_s_grid <- size_X_grid <- 100 n = max(as.numeric(pbc2$id)) s = pbc2$year X = pbc2$serBilir XX = pbc2_id$serBilir ss <- pbc2_id$years delta <- pbc2_id$status2 br_s = seq(0, max(s), max(s)/( size_s_grid-1)) br_X = seq(min(X), max(X), (max(X)-min(X))/( size_X_grid-1)) X_lin = lin_interpolate(br_s, pbc2_id$id, pbc2$id, X, s) int_X <- findInterval(X_lin, br_X) int_s = rep(1:length(br_s), n) N <- make_N(pbc2, pbc2_id, br_X, br_s, ss, XX, delta) Y <- make_Y(pbc2, pbc2_id, X_lin, br_X, br_s, size_s_grid, size_X_grid, int_s, int_X, event_time = 'years', n) b = 1.7 alpha<-get_alpha(N, Y, b, br_X, K=Epan ) Yi <- make_Yi(pbc2, pbc2_id, X_lin, br_X, br_s, size_s_grid, size_X_grid, int_s, int_X, event_time = 'years', n) Ni <- make_Ni(br_s, size_s_grid, ss, delta, n) t = 2 x = 2 g = g_xt(br_X, br_s, size_s_grid, int_X, x, t, b, Yi, Y, n) Boot_all = prep_boot(g, alpha, Ni, Yi, size_s_grid, br_X, br_s, t, b, int_X, x, n) Boot_all ```

prep_boot function