mbbtest

The bootstrap is a way of estimating the variability of a statistic from a single data set by resampling it independently and with equal probabilities (Monte Carlo resampling). Allows the estimation of measures where the underlying distribution is unknown or where sample sizes are small. Their results are consistent with the statistical properties of those analytical methods (Efron and Tibshirani, 1993).

The name 'bootstrap' originates from the expression 'pulling yourself up by your own bootstraps' and refers to the basic idea of the bootstrap, sampling with replacement from the data. In this way a large number of 'bootstrap samples' is generated, each of the same size as the original data set. From each bootstrap sample the statistical parameter of interest is calculated (Wehrens and Van der Linden, 1997).

Here, we use the Non-parametric Bootstrap. Non-parametric bootstrap is simpler. It does not use the structure of the model to construct artificial data. The data is instead directly resampled with replacement.

As Silva et. al (2008) stated, here a m-file analytical procedure using bootstrap method is developed as an alternative to the homogeinity of covariance matrices test.

MBBTEST treats NaN values as missing values, and removes them.

Syntax: function mbbtest(X,t,alpha)

Inputs:
X - data matrix (Size of matrix must be n-by-(1+p); sample=
column 1, variables=column 2:p)
t - boot times or number of Bootstrap simulations (resamplings)
alpha - significance level (default = 0.05)

Output:
- Whether or not the homoscedasticity was met