Title: Statistical inference in binomial time series when the number of trials is small
Authors: Takis Besbeas - Athens University of Economics and Business (Greece) [presenting]
Fiori Labrinakou - Athens University fo Economics and Business (Greece)
Abstract: Many authors have studied the problem of estimating the parameters in Bernoulli trials with Markov dependence. We consider the problem of analysing dependent count data arising from a series of binomial experiments, which includes dependent Bernoulli trials as a special case. We adopt a parameter-driven approach to modelling the data, involving a generalized linear model (GLM) for the binomial response based on an autoregressive AR(1) latent process to introduce autocorrelation. We focus on the case where the number of trials at time $t$, $n_t$, is small, and consider model-fitting by maximum likelihood using different estimation methods. Using theory and simulation, we show that the likelihood contains a ridge when $n_t=1$ but the MLE is typically not located on the ridge. However, the estimation can be highly uncertain, even for large sample sizes. Further, we illustrate that estimation improves dramatically even for $n_t$ as low as 2, which may provide a more pragmatic sampling alternative to obtaining a large binary sample in practice. An application to a rainfall example is given, allowing for different hypotheses on the probability of rain across years to be tested.