ABSTRACT
A collection {Yni; 1 ≤ i ≤ n} of random variables is called a double array if the probability distribution Pni of Yni depends on both i and n. An example is the regresssion model
Yni = α+ βnxni + εi
where βn = c/ √ n, n−1
∑ (xni− x¯n)2 → τ ∈ (0, 1) and ε1, . . . , εn are i.i.d. Such models
are used when investigating asymptotic power. See Section 6.3.2. Another example is the
“bootstrap” asymptotic theory of Section 10.3.4. A key result for double arrays is
1. The Lindeberg-Feller Central Limit Theorem.
