AddInf-package: The package functions implement statistical estimation with...

In starima74/AddInf: The package functions implement statistical estimation with the use of additional information

The package functions implement statistical estimation with the use of additional information The use of additional information in statistical estimation

Description

The package functions implement statistical estimation with the use of additional information. This additional information can come from multiple indepedent data sources. Each source is reported in form of a vector of means and a variance covariance matrix. The package functions implement statistical estimation with the use of additional information. This additional information can come from multiple indepedent data sources. Additional Each source is reported in form of a vector of means and a variance covariance matrix.

Details

This package include several functions (such as MVAR and MMSE) which incorparate external information in statistical estimation.

Author(s)

Sergey Tarima Maintainer: Sergey Tarima <[e-mail]>

References

Tarima SS and Pavlov D, Using auxiliary information in statistical function estimation, ESAIM: Probability and Statistics; 10, 11-23, 2006

Tarima SS, Slavova SS, Fritsch TA, and Hall L, Probability estimation when some observations are grouped, Statistics in Medicine; 26 (8), 1745-61, 2007

Tarima S.S. and Dmitriev Y.G. Statistical estimation with possibly incorrect model assumptions. The Bulletin of Tomsk State University: control, computing, informatics 2009, 3(8):87-99

Tarima S.S., Vexler A., Singh S., Robust mean estimation under a possibly incorrect log-normality assumption. Communications in Statistics - Simulation and Computation, 42: 316-326, 2013

Examples

### data (an available dataset of patient ages)

dd <- data.frame(age = c(66,59,61,76,35,59,37,47,71,63,
                         41,56,49,58,48,79,87,50,57,58,32,
                         52,57,61,62,42,67,77,66,79))
                         
### the objective is to estimate proportion of pateints 
### younder than 40, 50, 60 and 70 years of age      
times1 <- c(40,50,60,70)

### this function estimates these proportions on a dataset d, 
### defined in its first argument
theta.f <- function(d,times) {
  ecdf(c(d)[[1]])(times)
}

### (Empty) Additional Information
Add.Info.Means <- list()
Add.Info.Vars <- list()
Add.Info.Functions <- list()
Add.Info.Biases <- list()

#### the first additional data source says that average of patients
### is 58.58 years of age with variance = 0.09, 
### and this information is possibly biased
Add.Info.Means[[1]] <- 58.58
Add.Info.Vars[[1]] <- 0.09
Add.Info.Functions[[1]] <- function(d) mean(d[[1]],na.rm = TRUE)
Add.Info.Biases[[1]] <- 1 # biased additional information

#### the second additional data source says that the proportion of patients
### 55 years of age or older is 70 percent, this information is unbiased

Add.Info.Means[[2]] <- 0.70
Add.Info.Vars[[2]] <- 0.0001
Add.Info.Functions[[2]] <- function(d) mean(d[[1]]>=55,na.rm = TRUE)
Add.Info.Biases[[2]] <- 0 # unbiased additional information

### create the data frame where the additional information will be saved
Add.Info <- data.frame(Means = rep(NA,2), 
                       Vars = rep(NA,2), 
                       Functions = rep(NA,2),
                       Biases = rep(NA,2))

### Adding the additional information to the data frame
Add.Info$Means = Add.Info.Means
Add.Info$Vars = Add.Info.Vars
Add.Info$Functions = Add.Info.Functions
Add.Info$Biases = Add.Info.Biases

### using both available dataset and additional information for estimation
res <- MMSE(dd, theta.f, Add.Info, nboots = 500, 
               eig.cutoff = 1, times = times1)

### calculating new estimates and pointwise confidence intervals
lo  <- res$Theta.Est - 1.96*sqrt(diag(res$Theta.Est.Var))
cdf <- res$Theta.Est
hi  <- res$Theta.Est + 1.96*sqrt(diag(res$Theta.Est.Var))

### calculating empirical (no additional information) estimates 
### and pointwise confidence intervals
theta_lo  <- res$Theta.Hat - 1.96*sqrt(diag(res$Theta.Hat.Var))
theta_cdf <- res$Theta.Hat
theta_hi  <- res$Theta.Hat + 1.96*sqrt(diag(res$Theta.Hat.Var))

### plot
plot(cdf ~ times1, type = "l", ylab="Proportions", 
          main = paste("Means and 95 percent confidence intervals\n", 
                   "with (dashed) and without (solid) additional information"), 
          xlab="Age", lty = 2, ylim= c(0,1))
lines(lo ~ times1, type = "l", lty = 2)
lines(hi ~ times1, type = "l", lty = 2)
points(cdf ~ times1)
points(lo ~ times1)
points(hi ~ times1)

lines(theta_cdf ~ times1, type = "l")
lines(theta_lo ~ times1, type = "l")
lines(theta_hi ~ times1, type = "l")
points(theta_cdf ~ times1)
points(theta_lo ~ times1)
points(theta_hi ~ times1)

starima74/AddInf documentation built on June 13, 2022, 12:08 p.m.