An intensive survey of two farmer-managed corn and soybean fields in eastern Nebraska was conducted to investigate parametric sequential sampling of weed seedling populations using a multistage procedure to estimate k, of the negative binomial distribution. k is a nonspatial aggregation parameter related to the variance at a given mean value. Mean weed seedling density ranged from 0.18 to 3.11 plants 0.38 m−2 (linear meter of crop row) based on 806 sampling locations. The average value of k, derived from 200 multistage estimation procedures, ranged from 0.17 to 0.32. A sequential sampling plan was developed with the goal of estimating the mean with a coefficient of variation (CV) of 10, 20, 30, and 40% of the sample mean. A sampling plan was also constructed to estimate the mean within a specified distance H of the true mean (H(x̄)= 0.10, 0.50 and 1.0 plants 0.38 m−2) with 80, 85, and 90% confidence. Estimating mean weed seedling density within a specified CV of the true mean CV(x̄) using parametric sequential sampling techniques was superior to estimating the mean within a specified distance (H(x̄)) of the true mean when considering the frequency of sampling and probability of error, especially at intermediate k values. At a k: value of 0.32 and 0.25, the difference between the actual CV(x̄) obtained from sampling and the CV(x̄) specified by the sampler was minimal. However, the accuracy of weed seedling density estimates was reduced with decreasing k values below 0.25, especially as the specified CV(x̄) increased.

Let I1,I2,…,In be independent indicator functions on some probability space We suppose that these indicators can be observed sequentially. Furthermore, let T be the set of stopping times on (Ik), k=1,…,n, adapted to the increasing filtration where The odds algorithm solves the problem of finding a stopping time τ ∈ T which maximises the probability of stopping on the last Ik=1, if any. To apply the algorithm, we only need the odds for the events {Ik=1}, that is, rk=pk/(1-pk), where The goal of this paper is to offer tractable solutions for the case where the pk are unknown and must be sequentially estimated. The motivation is that this case is important for many real-world applications of optimal stopping. We study several approaches to incorporate sequential information. Our main result is a new version of the odds algorithm based on online observation and sequential updating. Questions of speed and performance of the different approaches are studied in detail, and the conclusiveness of the comparisons allows us to propose always using this algorithm to tackle selection problems of this kind.

Spodoptera frugiperda (J.E. Smith) is a major pest in maize fields in Argentina. However, a sampling method that accounts for spatial pattern and allows reliable pest density estimations is still lacking. This paper addresses the issue of how sampling unit size can influence the characterization of S. frugiperda spatial pattern and the performance of sampling plans. An intensive sampling programme for S. frugiperda larvae was carried out in maize fields from October until March in four growing seasons. On each sampling date, 12 to 20 sampling units were taken at random. Each unit consisted of 1, 2, 4, 6, 8, 10 or 12 consecutive plants along a row. The linearized version of the Taylor's power law (TPL) was fitted to mean and variance estimated for each sampling date and data set through least squares regression. In general, b values from TPL were significantly >1 (P<0.05), indicating an aggregated sampling distribution. Regression slopes (b) ranged from 1.28 to 1.48 in small larvae and from 1.06 to 1.24 in large larvae, indicating stronger clumping in the former. TPL parameters were used to develop constant precision sampling plans. The efficiency of these plans in terms of expected total cost (searching and handling sampling units) was very sensitive to the size of the sampling units with small larvae but not with large larvae. The influence of sampling unit size and spatial pattern on TPL parameters and sampling costs is discussed.

Some concepts of dependence have recently been introduced by Ebrahimi (1987) to explore the structural properties of the hitting times of bivariate processes. In this framework, the special case of univariate processes has curious features. New properties are derived for this case. Some applications to sequential inference and inequalities for Brownian motion and new better than used (NBU) processes are also provided.

Let {Xt}t≧0 (t may be discrete or continuous) be a random process whose finite-dimensional distributions are of exponential type. The first-passage time inf{t:Xt≧f(t)}, where f(t) is a positive, continuous function, such that f(t)= o(t) as t↑∞, is considered. The problem of finiteness of its moments is solved for both the case that {Xt}t≧0 has stationary independent increments as well as the case in which no assumptions are made about stationarity and independence for the increments of the process. Applications to sequential estimation are also given.

Consider N sources, each of which transmits signals according to a renewal process with a common, known, underlying distribution. Sequential point estimators for N, which are asymptotically efficient in comparison to the best fixed stopping strategy, are derived. Confidence statements for N, and applications to the problem of estimating finite populations are discussed.

The exact limiting distribution, and moments, of the stopping time we use, which was suggested by Starr, are derived.