diff --git a/README.md b/README.md index ed72b55..aaf0a4a 100644 --- a/README.md +++ b/README.md @@ -7,7 +7,7 @@ We present a detailed study of the asymptotic behavior of the distribution of th MATLAB -[OST /TST /WELCH /F ]+ComputeKg.m - compute Kg for the Student one- and two- sample t−, Welch, and F− statistics using adaptive Simpson or Lobatto quadratures. Here g is an arbitrary multivariate density.1 +[OST /TST /WELCH /F ]+ComputeKg.m - compute Kg for the Student one- and two- sample t−, Welch, and F− statistics using adaptive Simpson or Lobatto quadratures. Here g is an arbitrary multivariate density.1 [TST /WELCH /F ]+ComputeKgIS+.m - the same as above but for the case where samples are independent.2 @@ -17,7 +17,7 @@ RunSimulation+[IID/MVN ]+.m - perform simulation study for i.i.d. and dependent/ Wolfram Mathematica -[OST /TST /WELCH /F ]+ComputeKg.nb - compute the exact expression for Kg for an arbitrary multivariate density g and given sample size(s). We include a number of examples, such as evaluation of Kg for the zero-mean Gaussian case with an arbitrary covariance matrix Σ; the “unequal variances” case for the Student two-sample t− and Welch statistics; and evaluation of Kg. for the densities considered in the simulation study. +[OST /TST /WELCH /F ]+ComputeKg.nb - compute the exact expression for Kg for an arbitrary multivariate density g and given sample size(s). We include a number of examples, such as evaluation of Kg for the zero-mean Gaussian case with an arbitrary covariance matrix **Σ**; the “unequal variances” case for the Student two-sample t− and Welch statistics; and evaluation of Kg. for the densities considered in the simulation study. OSTComputeKgIID.nb - verifies the constants in Table 1 for the i.i.d. case of the Student one-sample t−statistic. @@ -27,9 +27,9 @@ Other Materials Supplementary-Materials.pdf - Remarks on Theorem 1.1 and its application to real data; extended version of the literature review; comparison of the result of Theorem 1.1 with the exact distribution of the Welch statistic; proof of Theorem 5.1. -______________________ -1For the F−statistic we use Monte Carlo integration. -2For the F−statistic and n1 > 3 we use Monte Carlo integration. +___ +1For the F−statistic we use Monte Carlo integration. +2For the F−statistic and n1 > 3 we use Monte Carlo integration. ## Reference Zholud, D. (2014). [**Tail approximations for the Student t−, F−, and Welch statistics for non-normal and not necessarily i.i.d. random variables**](http://www.zholud.com/articles/Tail-approximations-for-the-Student-t-,-F-,-and-Welch-statistics-for-non-normal-and-not-necessarily-i.i.d.-random-variables.pdf), **Bernoulli**, Vol. 20, No. 4, pp. 2102-2130