Sentence examples for much weaker assumptions from inspiring English sources

Therefore, we proceed by estimating sibling-fixed effects, which need much weaker assumptions for identification.

The aim of this paper is to improve the above quoted results in [3] by obtaining a similar estimate under much weaker assumptions.

As we shall see, Kent's conclusion follows from much weaker assumptions, namely that (a) holds and f ¯ ( x, y ) decreases in y.

If one is only interested in upper O-estimates on N, the next theorem gives such bounds under much weaker assumptions on the symbol.

The radical one-child policy implemented in 1979 in China provides us with a unique opportunity to apply a regression discontinuity design method to examine this issue, which requires much weaker assumptions than the IV approaches used in previous studies.

This paper argues that many determinants of generic oligopoly market outcomes can be studied in bid-based wholesale electricity markets under much weaker assumptions than in other oligopoly industries because of their rich data, regulatory history, and clearly specified market rules.

However, it is shown in [21] that if T is assumed to be continuous in Theorem 4.3, then the assumption that lim sup n → ∞ k n < 2 may be replaced with the much weaker assumption that lim sup n → ∞ k n < ∞.

Second, it indicates that the efficiency of the residual error estimator ϱ ℓ holds at least under much weaker assumption than those of Theorem 13.

In other words, Assumption 2.5 is much weaker than Assumption 2.2.

Such an assumption is much weaker than the assumption of Hölder continuity; see [1, 2] for the case of sub-elliptic systems.

Further, the adaptive kernel non-parametric density estimation method developed for MCSA requires much weaker a-priori assumptions about the properties of the configurational densities than (quasi- harmonic approaches.