On Asymptotic Normality in Stochastic Approximation

Asymptotic normality of randomly truncated stochastic algorithms

Asymptotic Normality of Maximum Likelihood and its Variational Approximation for Stochastic Blockmodels

Variational methods for parameter estimation are an active research area, potentially offering computationally tractable heuristics with theoretical performance bounds. We build on recent work that applies such methods to network data, and establish asymptotic normality rates for parameter estimates of stochastic blockmodel data, by either maximum likelihood or variational estimation. The resul...

On asymptotic normality of sequential

For estimating the unknown parameters in an unstable autoregressive AR(p), the paper proposes sequential least squares estimates with a special stopping time defined by the trace of the observed Fisher information matrix. The limiting distribution of the sequential LSE is shown to be normal for the parameter vector lying both inside the stability region and on some part of its boundary in contr...

Asymptotic Normality of Statistics on Permutation Tableaux

Abstract. In this paper we use a probabilistic approach to derive the expressions for the characteristic functions of basic statistics defined on permutation tableaux. Since our expressions are exact, we can identify the distributions of basic statistics (like the number of unrestricted rows, the number of rows, and the number of 1s in the first row) exactly. In all three cases the distribution...

Consistency and Asymptotic Normality

The consistency and asymptotic normality of minimum contrast estimation (which includes the maximum likelihood estimation as a special case) is established if the sample is from a renewal process and the observation time tends to innnity. It is shown, that the conditions for consistency and asymptotic normality for maximum likelihood estimation are fulllled if the distribution of the time betwe...