Hypotheses and Test Statistics Sample Clauses

Hypotheses and Test Statistics. X1 denotes the average actively managed mutual fund return; X2 denotes the market return; X3 denotes the aggressive fund return; X4 denotes growth fund return; X5 denotes growth and income fund return; and X6 denotes income fund return. The hypothesis tested is whether or not one group of mutual funds or the market dominates the other. We examine the stochastic dominance relationship between all pairs of returns of Xk for k = 1 . . . 6. One example of the type of test we conduct is: H0: The market stochastically dominates average actively managed mutual fund, with the alternative being that there is no stochastic dominance. Next, we formalize these tests. Let χ denote the support of Xk for k = 1 . . . 6 and let s = 1, 2, 3 represent the order of stochastic dominance. Define: FK(x) = P (X ≤ x), (1.1) K D(1)(x) = FK(x), (1.2) ˆx K D(s)(x) = −∞
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