DESCRIPTION

-Original file line number
+Diff line change
@@ Expand Up / @@ -15,7 +15,7 @@ Authors@R: c( @@
     License: GPL-3
     Encoding: UTF-8
     LazyLoad: yes
-    RoxygenNote: 7.3.2
+    RoxygenNote: 7.3.3
     Depends:
       R (>= 3.6.0)
     Roxygen: list(markdown = TRUE)
@@ Expand Down @@

NAMESPACE

-Original file line number
+Diff line change
@@ -1,5 +1,8 @@
     # Generated by roxygen2: do not edit by hand
+    export(CCovEst)
+    export(CEllGenEst)
+    export(CMeanEst)
     export(Convert_g1_To_Fg1)
     export(Convert_g1_To_Qg1)
     export(Convert_g1_To_f1)
@@ Expand Down @@

R/CCovEst.R

-Original file line number
+Diff line change
@@ -0,0 +1,196 @@
+    #' Conditional Covariance Estimator
+    #'
+    #' This function estimates the conditional covariance matrix
+    #' \deqn{\Sigma(z) = \mathrm{Cov}(X \mid Z = z)}
+    #' of a multivariate response variable \eqn{X} given a conditioning variable
+    #' \eqn{Z}, using kernel smoothing. Three different estimators are provided.
+    #'
+    #' The kernel weights are defined as
+    #' \deqn{
+    #'   w_{n,i}(z) =
+    #'   \frac{K\!\left( \frac{Z_i - z}{h} \right)}
+    #'        {\sum_{j=1}^n K\!\left( \frac{Z_j - z}{h} \right)} ,
+    #' }
+    #' where \eqn{K} is the chosen kernel and \eqn{h} is the bandwidth.
+    #'
+    #' The supported estimators are:
+    #'
+    #' \describe{
+    #'   \item{type = 1}{
+    #'     Covariance estimator using the conditional mean evaluated at the grid point:
+    #'     \deqn{
+    #'       \widehat{\Sigma}_n(z)
+    #'       = \sum_{i=1}^n w_{n,i}(z)
+    #'         \bigl(X_i - \widehat{\mu}_n(z)\bigr)
+    #'         \bigl(X_i - \widehat{\mu}_n(z)\bigr)^\top .
+    #'     }
+    #'   }
+    #'
+    #'   \item{type = 2}{
+    #'     Covariance estimator using the conditional mean evaluated at each observation:
+    #'     \deqn{
+    #'       \widetilde{\Sigma}_n(z)
+    #'       = \sum_{i=1}^n w_{n,i}(z)
+    #'         \bigl(X_i - \widehat{\mu}_n(Z_i)\bigr)
+    #'         \bigl(X_i - \widehat{\mu}_n(Z_i)\bigr)^\top .
+    #'     }
+    #'   }
+    #'
+    #'   \item{type = 3}{
+    #'     Pairwise covariance estimator:
+    #'     \deqn{
+    #'       \widecheck{\Sigma}_n(z)
+    #'       =
+    #'       \frac{\sum_{i<j} w_{n,i}(z) w_{n,j}(z)
+    #'             (X_i - X_j)(X_i - X_j)^\top}
+    #'            {2 \sum_{i<j} w_{n,i}(z) w_{n,j}(z)} .
+    #'     }
+    #'   }
+    #' }
+    #'
+    #'
+    #' @param dataMatrix a matrix of size \eqn{n \times d} containing the \eqn{n}
+    #' observations of the \eqn{d}-dimensional response variable \eqn{X}. The pairs
+    #' \eqn{(X_i, Z_i)} are assumed to be i.i.d. realizations of a joint random vector.
+    #'
+    #' @param observedZ vector with \eqn{n} observations of the conditioning
+    #' variable \eqn{Z}.
+    #'
+    #' @param gridZ vector of points \eqn{z} at which the conditional covariance matrix
+    #' \eqn{\Sigma(z) = \mathrm{Cov}(X \mid Z = z)} is estimated.
+    #'
+    #' @param h bandwidth of the kernel.
+    #'
+    #' @template param-Kernel
+    #'
+    #' @param type integer in \{1,2,3\} indicating which estimator to compute.
+    #'
+    #' @return An array of dimension \eqn{d \times d \times \code{length(gridZ)}},
+    #' \eqn{\widehat{\Sigma}_n(z)} containing the estimated conditional covariance
+    #' matrices of the \eqn{d}-dimensional random variable \eqn{X} at each point of `gridZ`.
+    #'
+    #' @examples
+    #' # Comparison between the estimated and true conditional covariance
+    #'
+    #' n = 10000
+    #' Z = runif(n, -2, 2)
+    #' sigma12 = 0.3 * Z
+    #' X1 = rnorm(n)
+    #' X2 = sigma12 * X1 + sqrt(1 - sigma12^2) * rnorm(n)
+    #' X = cbind(X1, X2)
+    #' gridZ = seq(-2, 2, length.out = 50)
+    #' h = 0.2
+    #'
+    #' Sigma_est = CCovEst(X, Z, gridZ, h, type = 1)
+    #' cov_X1X2 = sapply(1:length(gridZ), function(i) Sigma_est[1,2,i])
+    #' true_cov = 0.3 * gridZ
+    #'
+    #' plot(gridZ, cov_X1X2, type = "l", col = "blue", lwd = 2,
+    #'      ylab = "Cov(X1,X2|Z)", xlab = "Z", ylim = range(c(cov_X1X2, true_cov)))
+    #' lines(gridZ, true_cov, col = "red", lwd = 2, lty = 2)
+    #' legend("topleft", legend = c("Estimated", "True"), col = c("blue", "red"),
+    #'        lty = c(1,2), lwd = 2)
+    #'
+    #' @export
+    #'
+    CCovEst <- function(dataMatrix, observedZ, gridZ, h , Kernel = "epanechnikov",
+                              type = 1)
+    {
+      d = ncol( dataMatrix )
+      n = nrow( dataMatrix )
+      nz = length( gridZ )
+      if(length(observedZ) != n) {
+        stop(errorCondition(
+          message = paste0("The length of observedZ and the number of rows in ",
+                           "'dataMatrix'must be equal. Here they are respectively: ",
+                           length(observedZ), ", ", n),
+          class = "DifferentLengthsError") )
+      }
+      if(type == 1){
+        meanEst = CMeanEst(
+          dataMatrix = dataMatrix, observedZ = observedZ,
+          gridZ = gridZ, h = h,
+          Kernel = Kernel)
+        matrixWeights = matrix(data = NA, nrow = n, ncol = nz)
+        for(i in 1:nz){
+          matrixWeights[,i] = computeWeights(
+            vectorZ = observedZ,h = h,
+            pointZ = gridZ[i], Kernel = Kernel,
+            normalization = TRUE)
+        }
+        estimate = array(data = NA, dim = c(d,d,nz))
+        for(i in 1:nz){
+          S = matrix(0,d,d)
+          for(j in 1:n){
+            diff = dataMatrix[j,] - meanEst[,i]
+            S = S + matrixWeights[j,i] * (diff %*% t(diff))
+          }
+          estimate[,,i] = S
+        }
+      }
+      if(type == 2){
+        matrixWeights = matrix(data = NA, nrow = n, ncol = nz)
+        for(i in 1:nz){
+          matrixWeights[,i] = computeWeights(
+            vectorZ = observedZ, h = h,
+            pointZ = gridZ[i], Kernel = Kernel,
+            normalization = TRUE)
+        }
+        estimate = array(data = NA, dim = c(d,d,nz))
+        for(i in 1:nz){
+          meanEst = CMeanEst(
+            dataMatrix = dataMatrix, observedZ = observedZ,
+            gridZ = observedZ[i], h = h,
+            Kernel = Kernel)
+          S = matrix(0,d,d)
+          for(j in 1:n){
+            diff = dataMatrix[j,] - meanEst
+            S = S + matrixWeights[j,i] * (diff %*% t(diff))
+          }
+          estimate[,,i] = S
+        }
+      }
+      if(type == 3){
+        matrixWeights = matrix(data = NA, nrow = n, ncol = nz)
+        for(i in 1:nz){
+          matrixWeights[,i] = computeWeights(
+            vectorZ = observedZ, h = h,
+            pointZ = gridZ[i], Kernel = Kernel,
+            normalization = FALSE)
+        }
+        estimate = array(data = NA, dim = c(d,d,nz))
+        for(i in 1:nz){
+          S = matrix(0,d,d)
+          denom = 0
+          for(j in 1:(n-1)){
+            for(k in (j+1):n){
+              w = matrixWeights[j,i] * matrixWeights[k,i]
+              diff = dataMatrix[j,] - dataMatrix[k,]
+              S = S + w * (diff %*% t(diff))
+              denom = denom + w
+            }
+          }
+          S = S/ (2* denom)
+          estimate[,,i] = S
+        }
+      }
+      return(estimate)
+    }

Added CMeanEst, CCovEst, and CEllGenEst #6

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Merged

AlexisDerumigny merged 1 commit into AlexisDerumigny:main from Rutgervdspek:feature/new_branch

Nov 20, 2025

-Original file line number
+Diff line change
@@ Expand Up / @@ -15,7 +15,7 @@ Authors@R: c( @@
     License: GPL-3
     Encoding: UTF-8
     LazyLoad: yes
-    RoxygenNote: 7.3.2
+    RoxygenNote: 7.3.3
     Depends:
       R (>= 3.6.0)
     Roxygen: list(markdown = TRUE)
@@ Expand Down @@

-Original file line number
+Diff line change
@@ -1,5 +1,8 @@
     # Generated by roxygen2: do not edit by hand
+    export(CCovEst)
+    export(CEllGenEst)
+    export(CMeanEst)
     export(Convert_g1_To_Fg1)
     export(Convert_g1_To_Qg1)
     export(Convert_g1_To_f1)
@@ Expand Down @@

-Original file line number
+Diff line change
@@ -0,0 +1,196 @@
+    #' Conditional Covariance Estimator
+    #'
+    #' This function estimates the conditional covariance matrix
+    #' \deqn{\Sigma(z) = \mathrm{Cov}(X \mid Z = z)}
+    #' of a multivariate response variable \eqn{X} given a conditioning variable
+    #' \eqn{Z}, using kernel smoothing. Three different estimators are provided.
+    #'
+    #' The kernel weights are defined as
+    #' \deqn{
+    #'   w_{n,i}(z) =
+    #'   \frac{K\!\left( \frac{Z_i - z}{h} \right)}
+    #'        {\sum_{j=1}^n K\!\left( \frac{Z_j - z}{h} \right)} ,
+    #' }
+    #' where \eqn{K} is the chosen kernel and \eqn{h} is the bandwidth.
+    #'
+    #' The supported estimators are:
+    #'
+    #' \describe{
+    #'   \item{type = 1}{
+    #'     Covariance estimator using the conditional mean evaluated at the grid point:
+    #'     \deqn{
+    #'       \widehat{\Sigma}_n(z)
+    #'       = \sum_{i=1}^n w_{n,i}(z)
+    #'         \bigl(X_i - \widehat{\mu}_n(z)\bigr)
+    #'         \bigl(X_i - \widehat{\mu}_n(z)\bigr)^\top .
+    #'     }
+    #'   }
+    #'
+    #'   \item{type = 2}{
+    #'     Covariance estimator using the conditional mean evaluated at each observation:
+    #'     \deqn{
+    #'       \widetilde{\Sigma}_n(z)
+    #'       = \sum_{i=1}^n w_{n,i}(z)
+    #'         \bigl(X_i - \widehat{\mu}_n(Z_i)\bigr)
+    #'         \bigl(X_i - \widehat{\mu}_n(Z_i)\bigr)^\top .
+    #'     }
+    #'   }
+    #'
+    #'   \item{type = 3}{
+    #'     Pairwise covariance estimator:
+    #'     \deqn{
+    #'       \widecheck{\Sigma}_n(z)
+    #'       =
+    #'       \frac{\sum_{i<j} w_{n,i}(z) w_{n,j}(z)
+    #'             (X_i - X_j)(X_i - X_j)^\top}
+    #'            {2 \sum_{i<j} w_{n,i}(z) w_{n,j}(z)} .
+    #'     }
+    #'   }
+    #' }
+    #'
+    #'
+    #' @param dataMatrix a matrix of size \eqn{n \times d} containing the \eqn{n}
+    #' observations of the \eqn{d}-dimensional response variable \eqn{X}. The pairs
+    #' \eqn{(X_i, Z_i)} are assumed to be i.i.d. realizations of a joint random vector.
+    #'
+    #' @param observedZ vector with \eqn{n} observations of the conditioning
+    #' variable \eqn{Z}.
+    #'
+    #' @param gridZ vector of points \eqn{z} at which the conditional covariance matrix
+    #' \eqn{\Sigma(z) = \mathrm{Cov}(X \mid Z = z)} is estimated.
+    #'
+    #' @param h bandwidth of the kernel.
+    #'
+    #' @template param-Kernel
+    #'
+    #' @param type integer in \{1,2,3\} indicating which estimator to compute.
+    #'
+    #' @return An array of dimension \eqn{d \times d \times \code{length(gridZ)}},
+    #' \eqn{\widehat{\Sigma}_n(z)} containing the estimated conditional covariance
+    #' matrices of the \eqn{d}-dimensional random variable \eqn{X} at each point of `gridZ`.
+    #'
+    #' @examples
+    #' # Comparison between the estimated and true conditional covariance
+    #'
+    #' n = 10000
+    #' Z = runif(n, -2, 2)
+    #' sigma12 = 0.3 * Z
+    #' X1 = rnorm(n)
+    #' X2 = sigma12 * X1 + sqrt(1 - sigma12^2) * rnorm(n)
+    #' X = cbind(X1, X2)
+    #' gridZ = seq(-2, 2, length.out = 50)
+    #' h = 0.2
+    #'
+    #' Sigma_est = CCovEst(X, Z, gridZ, h, type = 1)
+    #' cov_X1X2 = sapply(1:length(gridZ), function(i) Sigma_est[1,2,i])
+    #' true_cov = 0.3 * gridZ
+    #'
+    #' plot(gridZ, cov_X1X2, type = "l", col = "blue", lwd = 2,
+    #'      ylab = "Cov(X1,X2|Z)", xlab = "Z", ylim = range(c(cov_X1X2, true_cov)))
+    #' lines(gridZ, true_cov, col = "red", lwd = 2, lty = 2)
+    #' legend("topleft", legend = c("Estimated", "True"), col = c("blue", "red"),
+    #'        lty = c(1,2), lwd = 2)
+    #'
+    #' @export
+    #'
+    CCovEst <- function(dataMatrix, observedZ, gridZ, h , Kernel = "epanechnikov",
+                              type = 1)
+    {
+      d = ncol( dataMatrix )
+      n = nrow( dataMatrix )
+      nz = length( gridZ )
+      if(length(observedZ) != n) {
+        stop(errorCondition(
+          message = paste0("The length of observedZ and the number of rows in ",
+                           "'dataMatrix'must be equal. Here they are respectively: ",
+                           length(observedZ), ", ", n),
+          class = "DifferentLengthsError") )
+      }
+      if(type == 1){
+        meanEst = CMeanEst(
+          dataMatrix = dataMatrix, observedZ = observedZ,
+          gridZ = gridZ, h = h,
+          Kernel = Kernel)
+        matrixWeights = matrix(data = NA, nrow = n, ncol = nz)
+        for(i in 1:nz){
+          matrixWeights[,i] = computeWeights(
+            vectorZ = observedZ,h = h,
+            pointZ = gridZ[i], Kernel = Kernel,
+            normalization = TRUE)
+        }
+        estimate = array(data = NA, dim = c(d,d,nz))
+        for(i in 1:nz){
+          S = matrix(0,d,d)
+          for(j in 1:n){
+            diff = dataMatrix[j,] - meanEst[,i]
+            S = S + matrixWeights[j,i] * (diff %*% t(diff))
+          }
+          estimate[,,i] = S
+        }
+      }
+      if(type == 2){
+        matrixWeights = matrix(data = NA, nrow = n, ncol = nz)
+        for(i in 1:nz){
+          matrixWeights[,i] = computeWeights(
+            vectorZ = observedZ, h = h,
+            pointZ = gridZ[i], Kernel = Kernel,
+            normalization = TRUE)
+        }
+        estimate = array(data = NA, dim = c(d,d,nz))
+        for(i in 1:nz){
+          meanEst = CMeanEst(
+            dataMatrix = dataMatrix, observedZ = observedZ,
+            gridZ = observedZ[i], h = h,
+            Kernel = Kernel)
+          S = matrix(0,d,d)
+          for(j in 1:n){
+            diff = dataMatrix[j,] - meanEst
+            S = S + matrixWeights[j,i] * (diff %*% t(diff))
+          }
+          estimate[,,i] = S
+        }
+      }
+      if(type == 3){
+        matrixWeights = matrix(data = NA, nrow = n, ncol = nz)
+        for(i in 1:nz){
+          matrixWeights[,i] = computeWeights(
+            vectorZ = observedZ, h = h,
+            pointZ = gridZ[i], Kernel = Kernel,
+            normalization = FALSE)
+        }
+        estimate = array(data = NA, dim = c(d,d,nz))
+        for(i in 1:nz){
+          S = matrix(0,d,d)
+          denom = 0
+          for(j in 1:(n-1)){
+            for(k in (j+1):n){
+              w = matrixWeights[j,i] * matrixWeights[k,i]
+              diff = dataMatrix[j,] - dataMatrix[k,]
+              S = S + w * (diff %*% t(diff))
+              denom = denom + w
+            }
+          }
+          S = S/ (2* denom)
+          estimate[,,i] = S
+        }
+      }
+      return(estimate)
+    }

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