# Naive Estimation of ATE

## Introduction

This vignette demonstrates the usage of the `Naive_Estimation` function in the `ATE.ERROR` package. The `Naive_Estimation` function provides a simple method for estimating ATE.

## Generating Simulated Data

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

    library(ATE.ERROR)
    set.seed(1)
    data(Simulated_data)
    Y_star <- Simulated_data$Y_star
    A <- Simulated_data$T
    Z <- Simulated_data$Z
    X_star <- Simulated_data$X_star

## Naive Estimation of ATE

Now we use the `Naive_Estimation` function.

    Naive_ATE_XY <- Naive_Estimation(Y_star, A, Z, X_star)
    print(Naive_ATE_XY)
    #> [1] 0.09177131

The `Naive_Estimation` function calculates the ATE by ignoring the difference between {X^∗, Y^∗} and {X, Y}.