Local limit theorems without assuming finite third moment

Local limit theorems for finite and infinite urn models

Local limit theorems are derived for the number of occupied urns in general finite and infinite urn models under the minimum condition that the variance tends to infinity. Our results represent an optimal improvement over previous ones for normal approximation.

Moment Convergence in Conditional Limit Theorems

SVANTE JANSON Abstract. Consider a sum ∑N 1 Yi of random variables conditioned on a given value of the sum ∑N 1 Xi of some other variables, where Xi and Yi are dependent but the pairs (Xi, Yi) form an i.i.d. sequence. We consider here the case when each Xi is discrete. We prove, for a triangular array ((Xni, Yni)) of such pairs satisfying certain conditions, both convergence of the distribution...

Moment Convergence in Conditional Limit Theorems

Consider a sum P N 1 Y i of random variables conditioned on a given value of the sum P N 1 X i of some other variables, where X i and Y i are dependent but the pairs (X i ; Y i) form an i.i.d. sequence. We prove, for a triangular array (X ni ; Y ni) of such pairs satisfying certain conditions, both convergence of the distribution of the conditioned sum (after suitable normalization) to a normal...

Estimation of Conditional Moment Restrictions without Assuming Parameter Identifiability

A well known difficulty in estimating conditional moment restrictions is that the parameters of interest need not be globally identified by the implied unconditional moments. In this paper, we propose an approach to constructing a continuum of unconditional moments that can ensure parameter identifiability. These unconditional moments depend on the “instruments” generated from a “generically co...

Local Limit Theorems for Free