Sample Analogs to Multidimensional Coverages with Applications to Prediction

Abstract

Let X ₁, …, X_n and Y ₁, …, Y_m be two independent random samples of a multidimensional random variable X with distribution function F(x). Let B ₁, …, B _{n + 1} be statistically equivalent blocks constructed from X ₁, …, X_n . Let U_mi (i = 1, …, n + 1) be the proportion of Y_j 's that lie in B_i . The U_mi 's are the sample analogs of the multidimensional coverages U_i = ∫ _Bi dF. Small and large sample properties of the sample coverages are studied and found to be similar to those of their population counterparts. The sample coverages are used to construct prediction regions for future observations.

Key Words:

• Statistically equivalent blocks
• Multidimensional coverages
• Prediction of future observations