Bayesian analysis for outliers in survey sampling
The present paper develops an outlier model suitable for problems wherein identification of outliers is essential and, applied areas of statistics are abound with such examples. One of the peculiarities of outliers in survey sampling is that there could be observed as well as unobserved outliers; the paper assumes that there are no unobserved outliers. We use a generalized linear model (GLM) with higher variances for the outlying units. Count data are treated through overdispersed GLM of Gelfand and Dalal (1990). Error components of the link function are assumed to have scale mixtures of normal distributions. The framework covers both standard survey sampling and small area estimation problems. The number as well as the set of outliers are assumed to be unknown. Posterior joint distribution is found using the reversible jump Markov chain and MetropolisHastings algorithm. We also use properties of the deviance function of GLM (West, 1985) for posterior computations. The basic framework is extended to various models appropriate in survey sampling such as double sampling and conditional autoregressive models. The method is illustrated using leukaemia patients data of Cox and Snell (1981), Scottish lip cancer data, Missouri lung cancer data and Baltimore census data.
glm overdispersed glm scale mixtures of normal distributions deviance function double sampling reversible jump mcmc stable regression