Wald test of H0: theta = theta0 against a two-sided alternative

Formula: W = (theta_hat - theta0)/se; reject when |W| > z_{alpha/2}; p = 2(1 - Phi(|W|))

Usage

Waldstat(theta_hat, se, theta0 = 0, level = 0.95)

Arguments

theta_hat: The estimate.
se: Its estimated standard error, se > 0.
theta0: The null value.
level: Confidence level for the returned interval.

Value

List with statistic, p_value, estimate, se, ci_lower, ci_upper, z_critical, reject.

References

Wasserman (2004), All of Statistics, Definition 10.3 and equation (10.5), with Theorem 10.4 giving the asymptotic size.

Examples

Waldstat(theta_hat = c(1, 2, 3, 4, 5, 6, 7, 8), se = 5L)
#> $statistic
#> [1] 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
#> 
#> $p_value
#> [1] 0.8414806 0.6891565 0.5485062 0.4237108 0.3173105 0.2301393 0.1615133
#> [8] 0.1095986
#> 
#> $estimate
#> [1] 1 2 3 4 5 6 7 8
#> 
#> $se
#> [1] 5
#> 
#> $ci_lower
#> [1] -8.79982 -7.79982 -6.79982 -5.79982 -4.79982 -3.79982 -2.79982 -1.79982
#> 
#> $ci_upper
#> [1] 10.79982 11.79982 12.79982 13.79982 14.79982 15.79982 16.79982 17.79982
#> 
#> $z_critical
#> [1] 1.959964
#> 
#> $reject
#> [1] 0 0 0 0 0 0 0 0
#> 
#> $method
#> [1] "Wald test, Wasserman Definition 10.3"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"