Lemma 3.3 Only under the assumptions of Lemma 3.1, the result of Lemma 3.2 is true, which ensures that the assumption is weaker than that in Lemma 3.2.
Even if deviation from the MAR assumption was weak (r = 0.7), the resulting change in inference is dramatic: 95%CIs widen somewhat and shift from 0.91-1.29 (Table 3) to 0.99-1.46 (Table 4), while the point estimate increases from 1.09 (Table 3) to 1.20 (Table 4).
"When you model something you make assumptions," Mr. Goglia said, "and if your assumptions are weak, your outcome is compromised".
The required assumptions are weak and allow for piecewise smooth parametrizations of the boundary, local mesh-refinement, and related standard piecewise polynomials as well as NURBS.
Our assumptions are weaker than the asymptotically contractive condition recently introduced by Jean-Paul Penot. Jean-Paul Penot
Still, this estimator underlying assumptions are weaker than those pertaining to the log-periodogram regression (LPR) estimator.
According to Corollaries 4.3 and 4.4, our assumptions are weaker than those of Song and Xu [11].
Our assumptions are weaker, as the comparison function is much more general, and we do not assume the spaces under consideration to be metric.
Second, though its assumptions are weaker than parametric models, model estimates still have good statistical properties, and the efficiency of statistical tests does not suffer greatly.
(iii) Since in the results of [1, 2] and [4], the spaces ( X, d ) are Hausdorff and complete, and the maps T : X → X are continuous, therefore, Theorems 4.1 and 4.2 are new generalizations of [1, 2] and [3], respectively; more precisely, the assertions are identical, but assumptions are weaker.
