500+ quant interview questions for Jane Street, Citadel, Two Sigma, DE Shaw, and other top quantitative finance firms.
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Difficulty: Hard
Category: Statistics & Regression
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Topics: statistics, likelihood-ratio-test, hypothesis-testing, asymptotic-distribution
Suppose you are building a statistical model to predict stock returns. You want to compare two nested models using the Likelihood Ratio Test (LRT). Model 0 is the simpler model with $p$ parameters, and Model 1 is a more complex model with $p + k$ parameters. Let $L_0$ be the maximized likelihood of Model 0, and $L_1$ be the maximized likelihood of Model 1. The likelihood ratio test statistic is defined as $Λ = -2 \ln(L_0 / L_1)$. Under the null hypothesis ($H_0$) that the simpler model (Model 0
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