Table Of Contents
  • Asymptotic distributions
  • Edgeworth expansions
  • Randomization in statistics
  • Non-parametric function estimation

Asymptotic distributions

Also known as limiting or sequence distribution, asymptotic distribution is a hypothetical distribution used to identify a limiting distribution in a group or series of distributions. Fitting data to a model is not an easy task in real life, as there are so many limited sample sizes. A researcher’s best bet is therefore to use the information they have about the behavior of the data sample they are working with. The asymptotic distribution can be applied to this data instead to find out how a given variable is distributed. Asymptotic distributions are some of the most effective ways of identifying the right sample sizes.

Edgeworth expansions

Edgeworth expansion is a technique for predicting a probability distribution based on its cumulants. The data in the distribution is usually the same but the arrangement of various variables is different, which causes the accuracy of the truncating cumulants to differ. The whole idea behind the use of the Edgeworth expansion is to identify the distribution’s characteristic function. Essentially, the density function of the probability is estimated based on the distribution’s characteristic function and analyzed by inverting the Fourier transform. When values in distribution converge, the expansion is said to be asymptotic, because it becomes difficult to approximate the expansion error.

Randomization in statistics

Randomization in statistics is when samples to be used in an experiment are chosen randomly. For instance, one may use a simple, random sampling method where the participants are picked from a population where every person has an equal probability of being selected. When randomization is used in an experiment, there is reduced bias. For example, accidental bias and selection bias, which are the two most common types of bias are eliminated. It is also possible to perform various statistical tests on data when the chosen sample is randomized. Many types of randomization techniques are used today. The most common ones include simple random sampling, stratified random sampling, and permuted block randomization.

Non-parametric function estimation

Non-parametric function estimation is a technique in statistics that enables data analysts to obtain the functional form of a predefined fit to a set of data without applying any constraints or guidance from a theory. Due to the nature of this estimation, the procedures used have meaningless associated parameters. Kernel estimation and artificial neural networks are the most commonly used non-parametric techniques today. Artificial neural networks simulate unknown functions by illustrating them as a weighted sum of numerous sigmoids, often selected to be logit curves. Kernel estimation specifies conditional expectations without a defined parametric form and the error density is completely unspecified.