fun.sigijj12 {HeterFunctionalData}

Unbiased estimate of $sigma_ijj1^2$

Description

This function calculatess an unbiased estimate of $sigma_ijj1^2$ using the u-statisitic of vectors $x=(x_1, x_2, ..., x_ni)$ and $y=(y_1, y_2, ..., y_ni)$, where $X_j$ and $Y_j$ are correlated, but $X_j$ and $Y_j1$ are independent if $j ne j1$. Note: $sum_k1 ne k2 ne k3 ne k4 (x_k1-x_k2))(y_k1-y_k2)) (x_k3-x_k4)) (y_k3-y_k4))$ is an unbiased est. of $4*ni*(ni-1)*(ni-2)*(ni-3) [E(X_ijk-mu_ij u_ij1k) ]^2$.

Usage

fun.sigijj12(x, y)

Arguments

x

a vector

y

a vector

Value

A list containing two variables sigmaijj12 and ssijj1 in it. The sigmaijj12 variable gives an unbiased estimate of $sigma_ijj1^2$. The ssijj1 variable gives an unbiased estimate of $sigma_ijj sigma_ij_1j_1$.