MVAR: Minimum variance estimation with additional information.

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

Minimum variance estimation with additional information.

Description

This function implements statistical estimation with the use of additional information. This additional information can come from multiple indepedent data sources. Each source is reported by a mean and its variance. Then, this additional information is used together with an estimating procedure theta.f applied to the dataset dd. A new estimator minimizes variance.

Usage

MVAR(dd, theta.f, Add.Inf, nboots = 500, eig.cutoff = 0.9, ...)

Arguments

dd	a data frame containing the variables used by function theta.f
theta.f	a function applied to the dataset dd to estimate a parameter of interest
Add.Inf	a data frame which consist of a columm of means (Means), a columm of variances (Vars), and a vector of functions (Functions). Functions column consists of functions used to calculate means in the additional data source; will be applied to the dataset dd.
nboots	a number of boostrap resamples to calculate variances and covariances
eig.cutoff	A percent cutoff for eigen values to approximate a matrix inverse.
...	additional parameters. These parameters can be used by function theta.f or by additional functions.

Value

Theta.Est	The estimate of the parameter of interest without the use of addtional information
Theta.Est.Var	Variance covariance matrix of Theta.Est
Theta.Hat	New estimate of the parameter of interest with the use of addtional information
Theta.Hat.Var	Variance covariance matrix of Theta.Hat

Author(s)

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

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)

### the function below 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()

#### the 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[[1]] <- 0.70
Add.Info.Vars[[1]] <- 0.0001
Add.Info.Functions[[1]] <- function(d) mean(d[[1]]>=55,na.rm = TRUE)

### create the data frame where the additional information will be saved
Add.Info <- data.frame(Means = rep(NA,1), 
                       Vars = rep(NA,1), 
                       Functions = rep(NA,1))

### 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

### using both available dataset and additional information for estimation
res <- MVAR(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.