The comparison of competing estimating functions for a vector parameter of a stochastic process is discussed and the formation of combined quasi-likelihood estimating functions where this is advantageous. An example is given to illustrate the methodology.

The analysis of asymptotic behaviour of stochastic approximation procedures rests heavily on the use of martingale limit theory, although explicit recognition of this situation is notable for its absence in the literature. This point is emphasized and in illustration a martingale iterated...

In this paper we establish central limit theorems for the smoothed unbiased periodogram [integral operator][pi]-[pi]...[integral operator][pi]-[pi]g([omega],[theta]){I*T,X([omega])-EI*T,X([omega])}d[omega]1...d[omega]r, where {Xt} is a stationary r-dimensional random process or random field,...

The size of a closed population is to be estimated using data from a multiple recapture study in either continuous or discrete time. Here the use of maximum likelihood raises computational problems. However, a family of martingale estimating functions related to the score function is shown to...

Let {Xk} be a stationary ergodic sequence of nonnegative matrices. It is shown in this paper that, under mild additional conditions, the logarithm of the i, jth element of Xt···X1 is well approximated by a sum of t random variables from a stationary ergodic sequence. This representation...

Ordinary quasi-likelihood estimators are based on estimating functions with certain strong orthogonality properties. Asymptotic quasi-likelihood (AQL) estimators, introduced herein correspond to the case where the orthogonality results hold asymptotically but yet the estimators enjoy the same...

For scale mixtures of distributions it is possible to prescribe simple moment measures of distance. In the case of departure from the normal and exponential laws of scale mixtures of the normal and exponential, these distances may be taken as the kurtosis and half the squared coefficient of...

For a random walk on the integers define Rn as the number of (distinct) states visited in the first n steps and Zn as the number of states visited in the first n steps which are never revisited. Here we deal with transient walks. The increments of Zn form a stationary process and various central...