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3

The arrow in the expression $\sqrt{n}D\rightarrow K$ means that $K$ is the asymptotic distribution of $\sqrt{n}D$, and you can consider it to be a good approximation of your test statistic's distribution only when $n$ is big enough. Hence the need for a table that considers the distribution of $D$ when $n$ is little.


1

By goodness of fit in this context we mean to evaluate if the model used for the analysis is reasonable, that is, it the underlying assumptions of the analysis is not to badly broken. For that we cannot just look at the parameter estimates---the fixed effects---the estimation algorithm will give us some estimates, however broken is the model assumptions. ...


1

Goodness of fit is usually meant as an expression to test whether the model is sufficiently likely to be not too incorrect. If the description of your data and the parametrization is correct, then $\chi^2$ minimization allows of the strongest tests that exists. It consists of two parts: analyze the distribution of the standardized residuals as you ...


0

While I agree with all the answers and comments, I believe the example I gave using Anderson-Darling test to assess the distribution is incorrect. I did not apply the ad.test function correctly. Below is from the documentation of the ad.test function from the goftest package. By default, the test assumes that all the parameters of the null distribution ...


1

Firstly, I must agree with the other answerers: anything that tests your distribution against some fixed $H_0$ and returns a p-value is not the right answer for you. You're not interested in asking "do I have enough evidence to prove that this is not exactly this distribution" (which is what the p-value would be asking). The geniuses on here might be able ...


5

The short answer is that such a regression is completely meaningless. See this question for a great discussion of it. Basically, since $y$ is always the same value, you don't observe any variation in it, and so intuitively you will always find that the intercept is equal to $y$, and all the other $\beta = 0$. Basically, you conclude that changing $x$ has no ...


2

Clearly, you are not really interested in the null hypothesis - given your concern about small deviations leading to a rejection. If the null hypothesis were really what you care about, a powerful test that can pick up on the slightest deviation given the large dataset would be great. Somehow fiddling around in some weird way to make the test less powerful ...


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