To “ Fixed - Smoothing Asymptotics for Time Series
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چکیده
We assume the (i, j)th element and the (j, i)th element of Σ are functionally unrelated. The results can be extended to the case where symmetric matrix elements are considered functionally equal (see e.g., McCulloch [5]). In the following, we use ⊗ to denote the Kronecker product in matrix algebra and use vec to denote the operator that transforms a matrix into a column vector by stacking the columns of the matrix one underneath the other. For a vector y ∈ Rl×1 whose elements are differential functions of a vector x ∈ Rk×1, we define ∂y ∂x to be a k × l matrix with the (i, j)th element being ∂yj ∂xi . The notation u ≍ v represents u = O(v) and v = O(u). Lemma 1.1 and Lemma 1.2 below are straightforward consequences of matrix calculus (see e.g., Vetter [9], Brewer [1] and Turkington [8]).
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تاریخ انتشار 2013