R/estimate_risk.R

In StevenGolovkine/SmoothCurves: Nonparametric Kernel Smoothing Methods for Functional Data

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#            Functions for risk estimation using regularity                    #
################################################################################


#' Perform an estimation of the risk on a set of curves at a particular point.
#' 
#' This function performs the estimation of the risk on a set of curves at a
#' particular sampling points \eqn{t_0}. Both the real and estimated curves have
#' to be sampled on the same grid. 
#' 
#' Actually, two risks are computed. They are defined as:
#' \deqn{MeanRSE(t_0) = \frac{1}{N}\sum_{n = 1}^{N}(X_n(t_0) - \hat{X}_n(t_0))^2}
#' and
#' \deqn{MeanRSE(t_0) = \max_{1 \leq n \leq N} (X_n(t_0) - \hat{X}_n(t_0))^2}
#'
#' @importFrom magrittr %>%
#' 
#' @param curves A list, where each element represents a real curve. Each curve 
#'  have to be defined as a list with two entries:
#'  \itemize{
#'   \item \strong{$t} The sampling points
#'   \item \strong{$x} The observed points.
#'  } 
#' @param curves_estim A list, where each element represents an estimated curve. 
#'  Each curve have to be defined as a list with two entries:
#'  \itemize{
#'   \item \strong{$t} The sampling points
#'   \item \strong{$x} The estimated points.
#'  } 
#' @param t0_list A vector of numerics, sampling points where the risk will be 
#'  computed. Can have a single value.
#' 
#' @return A list, with the mean and max residual squared error in \eqn{t_0}.
#' @export
#' @examples 
#' \dontrun{
#'  X <- generate_fractional_brownian(N = 1000, M = 300, H = 0.5, sigma = 0.05)
#'  X_smoothed <- smooth_curves(X)$smooth
#'  estimate_risk(X, X_smoothed, t0_list = 0.5)
#' }
estimate_risk <- function(curves, curves_estim, t0_list = 0.5) {
  risk_df <- dplyr::tibble(t0 = numeric(), 
                           MeanRSE = numeric(), 
                           MaxRSE = numeric())
  
  for(t0 in t0_list) {
    risk <- estimateRisk(curves, curves_estim, t0)
    risk_df <- risk_df %>% dplyr::add_row(t0 = t0, 
                                          MeanRSE = risk[[1]], 
                                          MaxRSE = risk[[2]])
  }
  risk_df
}


#' Perform an estimation of the risk on a set of curves along the sampling points.
#' 
#' This function performs the estimation of the risk on a set of curves along 
#' the sampling points. Both the real and estimated curves have to be sampled on
#' the same grid.
#' 
#' Actually, two risks are computed. They are defined as:
#' \deqn{MeanIntRSE = \frac{1}{N}\sum_{n = 1}^{N}\int(X_n(t) - \hat{X}_n(t))^2dt}
#' and
#' \deqn{MeanIntRSE = \max_{1 \leq n \leq N} \int(X_n(t) - \hat{X}_n(t))^2dt}
#'
#' @param curves A list, where each element represents a real curve. Each curve 
#'  have to be defined as a list with two entries:
#'  \itemize{
#'   \item \strong{$t} The sampling points
#'   \item \strong{$x} The observed points.
#'  } 
#' @param curves_estim A list, where each element represents an estimated curve. 
#'  Each curve have to be defined as a list with two entries:
#'  \itemize{
#'   \item \strong{$t} The sampling points
#'   \item \strong{$x} The estimated points.
#'  }
#'
#' @return A list, with the mean and max integrated residual squared error 
#'  in \eqn{t_0}.
#' @export
#' @examples 
#' \dontrun{
#'  X <- generate_fractional_brownian(N = 1000, M = 300, H = 0.5, sigma = 0.05)
#'  X_smoothed <- smooth_curves(X)$smooth
#'  estimate_risks(X, X_smoothed)
#' }
estimate_risks <- function(curves, curves_estim) {
  risk <- estimateRiskCurves(curves, curves_estim)
  c("MeanIntRSE" = risk[1], "MaxIntRSE" = risk[2])
}


#' Perform an estimation of the risk on one curve along the sampling points.
#' 
#' This function performs the estimation of the risk on one curve along 
#' the sampling points. Both the real and estimated curve have to be sampled on
#' the same grid.
#' 
#' Actually, one risk is computed. They are defined as:
#' \deqn{IntRSE = \int(X_n(t) - \hat{X}_n(t))^2dt}
#' 
#' @param curves A list, where each element represents a real curve. Each curve 
#'  have to be defined as a list with two entries:
#'  \itemize{
#'   \item \strong{$t} The sampling points
#'   \item \strong{$x} The observed points.
#'  } 
#' @param curves_estim A list, where each element represents an estimated curve. 
#'  Each curve have to be defined as a list with two entries:
#'  \itemize{
#'   \item \strong{$t} The sampling points
#'   \item \strong{$x} The estimated points.
#'  }
#'
#' @return Numeric, the integrated mean squared error
#' @export
#' @examples 
#' \dontrun{
#'  X <- generate_fractional_brownian(N = 1000, M = 300, H = 0.5, sigma = 0.05)
#'  X_smoothed <- smooth_curves(X)$smooth
#'  estimate_int_risk(X[[1]], X_smoothed[[1]])
#' }
estimate_int_risk <- function(curves, curves_estim) {
  estimateRiskCurve(curves, curves_estim)
}