A List Sequential Sampling Method Suitable for Real-Time Sampling

Abstract.  A flexible list sequential π ps sampling method is introduced and studied. It can reproduce any given sampling design without replacement, of fixed or random sample size. The method is a splitting method and uses successive updating of inclusion probabilities. The main advantage of the method is in real-time sampling situations where it can be used as a powerful alternative to Bernoulli and Poisson sampling and can give any desired second-order inclusion probabilities and thus considerably reduce the variability of the sample size.     

Resampling m-Dependent Random Variables with Applications to Forecasting

Resampling methods are proposed to estimate the distributions of sums of m -dependent possibly differently distributed real-valued random variables. The random variables are allowed to have varying mean values. A non parametric resampling method based on the moving blocks bootstrap is proposed for the case in which the mean values are smoothly varying or 'asymptotically equal'. The idea is to resample blocks in pairs. It is also confirmed that a 'circular' block resampling scheme can be used in the case where the mean values are 'asymptotically equal'. A central limit resampling theorem for each of the two cases is proved. The resampling methods have a potential application to time series analysis, to distinguish between two different forecasting models. This is illustrated with an example using Swedish export prices of coated paper products.     

Stability theorems for maxima of dependent sequences

Three stability theorems due to Gnedenko (1943), Barndorff-Nielsen (1963), and Tomkins (1986) are extended to the sample maxima of identically distributed ?-mixing and m-dependent sequences.     

Adaptive wavelet estimation of a function from an m-dependent process with possibly unbounded m

The estimation of a multivariate function from a stationary m-dependent process is investigated, with a special focus on the case where m is large or unbounded. We develop an adaptive estimator based on wavelet methods. Under flexible assumptions on the nonparametric model, we prove the good performances of our estimator by determining sharp rates of convergence under two kinds of errors: the pointwise mean squared error and the mean integrated squared error. We illustrate our theoretical result by considering the multivariate density estimation problem, the derivatives density estimation problem, the density estimation problem in a GARCH-type model and the multivariate regression function estimation problem. The performance of proposed estimator has been shown by a numerical study for a simulated and real data sets.