Normalisation Watch

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Report Thread starter 7 years ago
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Consider the multiple regression model \displaystyle y=X\beta +u where \displaystyle E(u)=0 and \displaystyle V(u) = \sigma^2 I_n

where \displaystyle \beta is a \displaystyle K \times 1 vector, and \displaystyle X is a full rank \displaystyle n \times K non-stochastic matrix.

By using the fact that \displaystyle \lim_{n\to\infty}\sum_{i=1}^n i^\alpha  = \lim_{n\to\infty}\int_1^n x^\alpha \, dx for all \displaystyle \alpha>0

Find a suitable normalisation for \displaystyle \sum i and for \displaystyle \sum i^2 as \displaystyle n \to \infty and calculate the limit of the normalised sums.


I'll be truthful here... I've absolutely no idea what's being asked let alone how to proceed. Any help?
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