General chi-square tests

Imagen tomada de Lifeder.

Statistical Odds & Ends

In this previous post, I wrote about the asymptotic distribution of the Pearson $latex chi^2$ statistic. Did you know that the Pearson $latex chi^2$ statistic (and the related hypothesis test) is actually a special case of a general class of $latex chi^2$ tests? In this post we describe the general $latex chi^2$ test. The presentation follows that in Chapters 23 and 24 of Ferguson (1996) (Reference 1). I’m leaving out the proofs, which can be found in the reference.

(Warning: This post is going to be pretty abstract! Nevertheless, I think it’s worth a post since I don’t think the idea is well-known.)

Let’s define some quantities. Let $latex Z_1, Z_2, dots in mathbb{R}^d$ be a sequence of random vectors whose distribution depends on a $latex k$-dimensional parameter $latex theta$ which lies in a parameter space $latex Theta$. $latex Theta$ is assumed to be a non-empty open subset…

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Dos soluciones al problema de la transformación de valores a precios de producción

Alejandro Valle Baeza En 2021, Jesús Rojo organizó una presentación de dos soluciones al llamado problema de la transformación de valores a precios de producción formulado por Marx en el tomo III de El capital. Hay dos clases de soluciones al problema de la transformación: las que critican la teoría del valor marxiana: por contradictoria […]

Dos soluciones al problema de la transformación de valores a precios de producción