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We discuss linear regression approaches to the estimation of law-invariant conditional risk measures. Two estimation procedures are considered and compared; one is based on residual analysis of the standard least-squares method, and the other is in the spirit of the M-estimation approach used in robust statistics. In particular, value-at-risk and average(More)
The main goal of this paper is to develop a numerical procedure for construction of covariance matrices such that for a given covariance structural model and a discrepancy function the corresponding minimizer of the discrepancy function has a specified value. Often construction of such matrices is a first step in Monte Carlo studies of statistical(More)
We consider a lender (bank) who determines the optimal loan price (interest rates) to offer to prospective borrowers under uncertain risk and borrower response. A borrower may or may not accept the loan at the price offered, and in the presence of default risk, both the principal loaned and the interest income become uncertain. We present a risk-based loan(More)
The noncentral chi-square approximation of the distribution of the likelihood ratio (LR) test statistic is a critical part of the methodology in structural equation modeling. Recently, it was argued by some authors that in certain situations normal distributions may give a better approximation of the distribution of the LR test statistic. The main goal of(More)
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