Is the Wald test Parametric?
This variant of the test is sometimes called the Wald Chi-Squared Test to differentiate it from the Wald Log-Linear Chi-Square Test, which is a non-parametric variant based on the log odds ratios.
What is H0 and H1 hypothesis?
Alternative Hypothesis: H1: The hypothesis that we are interested in proving. Null hypothesis: H0: The complement of the alternative hypothesis. Type I error: reject the null hypothesis when it is correct. It is measured by the level of significance α, i.e., the probability of type I error.
Why is asymptotic theory important?
A primary goal of asymptotic analysis is to obtain a deeper qualitative understanding of quantitative tools. The conclusions of an asymptotic analysis often supplement the conclusions which can be obtained by numerical methods.
What are the assumptions of large sample theory?
A larger sample size means the distribution of results should approach a normal bell-shaped curve. The final assumption is homogeneity of variance. Homogeneous, or equal, variance exists when the standard deviations of samples are approximately equal.
How does the asymptotic theory of Statistics begin?
Most statistical problems begin with a dataset of size n. The asymptotic theory proceeds by assuming that it is possible (in principle) to keep collecting additional data, thus that the sample size grows infinitely, i.e. n → ∞. Under the assumption, many results can be obtained that are unavailable for samples of finite size.
Can a numerical method be used in asymptotic analysis?
In many cases, highly accurate results for finite samples can be obtained via numerical methods (i.e. computers); even in such cases, though, asymptotic analysis can be useful. This point was made by Small (2010, §1.4), as follows.
Is the sequence of estimators said to have the asymptotic distribution?
then the sequence of estimators is said to have the asymptotic distribution G . Most often, the estimators encountered in practice are asymptotically normal, meaning their asymptotic distribution is the normal distribution, with an = θ0, bn = √n, and G = N(0, V) :