I have fitted a censored regression model in R which whose outputs look like this
library(carx) SAmodel <- carx(y=SAdata$CC, x=SAdata[,c("CPI","LI","FDI","FPI", "OI")], lcl=1.996866, p=2, CI.compute = FALSE, CI.level = 0.95) summary(SAmodel) Call: carx.default(y = SAdata$CC, x = SAdata[, c("CPI", "LI", "FDI", "FPI", "OI")], lcl = 1.996866, p = 2, CI.compute = FALSE, CI.level = 0.95) Coefficients Estimate CPI 0.0804 LI -0.0088 FDI -0.0395 FPI -0.0166 OI 0.0488 AR1 1.6324 AR2 -0.7097 sigma 0.4286 AIC:  -72.92045
The outputs come with no standard errors and no confidence intervals, those can be obtained by bootstrapping which could take tremendous time, probably more than a day, so I decided to manually calculate the standard errors. I know how standard errors are calculated for the coefficients in multiple regression and based on that I did the following calculations
#Calculating the residuals of the fitted model SAres = residuals(SAmodel,type="raw") # Find the sum of the squared residuals rss <- sum(SAres^2) # find the estimate of sigma^2, commonly called S S <- sqrt(rss / (length(SAres) - length(SAmodel$coefficients))) # Make the X matrix; a column of 1s for the intercept and one for each variable X <- cbind(rep( nrow(SAdata)), SAdata$CPI, SAdata$LI,SAdata$FDI, SAdata$FPI, SAdata$OI) # Multiply matrices using %*%, transpose them with t(), # and invert them with solve(); and directly apply the formula above with: std.errors <- S * sqrt(diag(solve(t(X) %*% X))) std.errors  0.001232184 0.037669933 0.010483153 0.068843648 0.040779940 0.063888636
But I don't know how to apply this to a model where there are additional parameters such as sigma and autoregressive terms. What is the formula to calculate the standard errors for these terms?