Performance of sequential sampling schemes for some independent and dependent models.

摘要

This dissertation considers three different statistical inference problems. In all of these, however, a common connecting theme is that sample size cannot be specified in advance to develop inference procedures. In such circumstances, we show that sequential sampling can provide an alternative, yet useful, way to develop efficient inference procedures.; We begin with the problem of counting a large, but pre-specified, number of items using the weight of a small sample. One encounters these problems in manufacturing industries where it is often necessary to count out large numbers of items produced/ordered with both speed and accuracy. Since weighing the items in a small sample could save considerable time and energy, the problem then reduces to selecting the size of a small sample. Two criteria, one based on estimation and the other based on fixed-width confidence interval estimation, are used to obtain optimal sample sizes. It is shown that these optimal samples sizes depend on the unknown coefficient of variation of the weight distribution and, hence, cannot be of use in practice. To overcome this, sequential sampling schemes that mimic the form of the optimal sample sizes are proposed. These schemes are shown to be as efficient as the ones available in the literature with an added attractive feature that the number of sampling operations required are few.; Next, we consider the problem of constructing a fixed-width confidence interval for a parameter based on minimum Hellinger distance (MHD) estimator, with a prespecified coverage probability. Unlike other robust estimators it has been shown in the literature that MHD estimators simultaneously achieve efficiency at the parametric model and possess desirable robustness properties under gross-error contamination. This once again leads to consideration of sequential sampling rules. Through extensive simulations we assess the effect of gross-error contamination on the expected sample size and coverage probability of the procedures based on MHDE. These are then compared with the performance of similar procedures based on MLE. It is shown that sequential sampling rules based on MHDE continue to perform well even under contamination while the procedures based on MLE perform poorly under contamination.; Finally, we consider the problem of constructing a fixed-size confidence region for parameters of Exponential Autoregressive (EAR) model of order one. EAR models are members of a whole class of nonlinear autoregressive models which have been shown to provide a systematic way of modeling certain discrete time series data. Our aim here is to construct a sufficiently precise confidence ellipsoid such that the length of the major axis is fixed and the coverage probability is approximately equal to a pre-specified number. Sequential sampling procedure based on the minimum eigenvalue of the observed Fisher information matrix is proposed. It is shown that the sequential fixed-size confidence region and the expected sample size are asymptotically consistent and efficient, respectively, as the size of the region becomes small.