Measuring and managing market, credit and Op risk [105]

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Bullet points include: Suppose k restrictions (constraints) on parameters expressed as C(theta) = 0 (where 0 is a k-vector of zeros) If these restrictions really hold then imposing them should not reduce likelihood by much Estimate model with and without restrictions Ratio LR = LR/LU of restricted likelihood LR to unrestricted likelihood LU Provides a statistic about the validity or otherwise of the restrictions – 2 log(LR) asymptotically chi-squared (with k degrees of freedom) LR Test: reject restriction at alpha-quantile if:

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