Consider $K$ processes, each generating a sequence of identical and independent random variables. The probability measures these processes have parameters that must be estimated. Specifically, they share parameter notation="LaTeX">$\theta$ common to all measures. Additionally, process notation="La...

Sometimes in order to estimate population parameters such as mean and total values, we extract a random sample by cluster sampling method, and after completing sampling, we are interested in using the same sample to estimate the desired parameters in a subset of the population, which is said subpopulation. In this paper, we try to estimate subpopulation parameters in different cases when one-st...

We explain three random sampling techniques that are simple but widely applicable for various problems involving huge data sets. The first technique is an immediate application of large deviation bounds. The second and the third ones are sequential sampling or adaptive sampling techniques. We fix one simple problem and explain these techniques by demonstrating algorithms for this problem and di...

Sequential sample selection methods are distinguished from conventional methods in the manner in which random numbers are used to determine the sample. Conventionally, a sample of size n is selected from a sampling frame of N sampling units by selecting n random numbers and mapping then into n of the labels in the sampling frame. Sequential methods require each sampling unit in the sampling fra...

A sequential sampling algorithm or adaptive sampling algorithm is a sampling algorithm that obtains instances sequentially one by one and determines from these instances whether it has already seen enough number of instances for achieving a given task. In this paper, we present two typical sequential sampling algorithms. By using simple estimation problems for our example, we explain when and h...