diff --git a/R/lpcde/DESCRIPTION b/R/lpcde/DESCRIPTION
index 4f14b3d..cc8cb83 100644
--- a/R/lpcde/DESCRIPTION
+++ b/R/lpcde/DESCRIPTION
@@ -14,7 +14,7 @@ Encoding: UTF-8
 LazyData: false
 SystemRequirements: GNU make
 Roxygen: list(markdown = TRUE)
-RoxygenNote: 7.1.2
+RoxygenNote: 7.3.2
 Imports:
     Rcpp (>= 0.12.8),
     ggplot2,
diff --git a/R/lpcde/R/lpcde_fns.R b/R/lpcde/R/lpcde_fns.R
index 148b741..3ddc30a 100644
--- a/R/lpcde/R/lpcde_fns.R
+++ b/R/lpcde/R/lpcde_fns.R
@@ -32,9 +32,10 @@ lpcde_fn = function(y_data, x_data, y_grid, x, p, q, p_RBC, q_RBC, bw, mu, nu,
   my = mean(y_data)
   #y_data = (y_data - my)/sd_y
   #y_grid = (y_grid-my)/sd_y
+  d = ncol(x_data)
   x_data = sweep(x_data, 2, mx)/sd_x
-  x = as.matrix(x)
-  x = sweep(x, 2, mx)/sd_x
+  x = matrix(x, ncol=d)
+  x = sweep(x, MARGIN=2, STATS=matrix(mx, ncol=d))/sd_x
   # initializing output vectors
   est = matrix(0L, nrow = length(y_grid), ncol = 1)
   se = matrix(0L, nrow = length(y_grid), ncol = 1)
@@ -52,7 +53,7 @@ lpcde_fn = function(y_data, x_data, y_grid, x, p, q, p_RBC, q_RBC, bw, mu, nu,
                    mu=mu, nu=nu, h=bw, kernel_type=kernel_type)
   covMat = covmat$cov
   c_flag = covmat$singular_flag
-  se = sqrt(abs(diag(covMat)))*sd_y*sd_x
+  se = sqrt(abs(diag(covMat)))*sd_y*mean(sd_x)
 
   if (rbc){
     est_rbc = matrix(0L, nrow = length(y_grid), ncol = 1)
@@ -80,7 +81,7 @@ lpcde_fn = function(y_data, x_data, y_grid, x, p, q, p_RBC, q_RBC, bw, mu, nu,
                        kernel_type=kernel_type)
       covMat_rbc = covmat_rbc$cov
       c_rbc_flag = covmat_rbc$singular_flag
-      se_rbc = sqrt(abs(diag(covMat_rbc)))*sd_y*sd_x
+      se_rbc = sqrt(abs(diag(covMat_rbc)))*sd_y*mean(sd_x)
     }
 
     # with rbc results
diff --git a/R/lpcde/man/lpbwcde.Rd b/R/lpcde/man/lpbwcde.Rd
index 19a7319..2dc3292 100644
--- a/R/lpcde/man/lpbwcde.Rd
+++ b/R/lpcde/man/lpbwcde.Rd
@@ -63,7 +63,7 @@ bandwidth selected for each grid point)}
 }
 \description{
 \code{\link{lpbwcde}} implements the bandwidth selection methods for local
-polynomial based conditionaldensity (and derivatives) estimation proposed and studied
+polynomial based conditional density (and derivatives) estimation proposed and studied
 in \insertCite{bernoulli}{lpcde}.
 
 Companion command: \code{\link{lpcde}} for estimation and robust bias-corrected inference.
diff --git a/todo.org b/todo.org
index f84179f..457328e 100644
--- a/todo.org
+++ b/todo.org
@@ -9,7 +9,8 @@
 ** TODO add more unit tests
 *** TODO checking integrates to 1
 *** TODO checking non-negativity
-** TODO ggplot deprecated warnings
+** DONE ggplot deprecated warnings
+** DONE multivariate warning
 ** DONE add missing doi
 ** DONE fix main paper reference
 ** DONE spelling mistake on pg 2