---
title: "True Estimation of ATE"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{True Estimation of ATE}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

## Introduction

This vignette demonstrates the usage of the `True_Estimation` function in the `ATE.ERROR` package. The `True_Estimation` function provides a method for estimating the Average Treatment Effect (ATE) using the generated values for X and Y.


## Generating Simulated Data

First, we generate our simulated data using the `data(Simulated_data)` syntax.

```{r setup}
library(ATE.ERROR)
set.seed(1)
data(Simulated_data)
Y <- Simulated_data$Y
A <- Simulated_data$T
Z <- Simulated_data$Z
X <- Simulated_data$X
```

## True Estimation of ATE

Now we use the `True_Estimation` function.

```{r}
True_ATE <- True_Estimation(Y, A, Z, X)
print(True_ATE)
```

The `True_Estimation` function calculates the ATE by considering the true values of X and Y and adjusting for the misclassification probabilities.