Inverse probability weighted estimation for general missing data problems

I study inverse probability weighted M-estimation under a general missing data scheme. The cases covered that do not previously appear in the literature include M-estimation with missing data due to a censored survival time, propensity score estimation of the average treatment effect for linear exponential family quasi-log-likelihood functions, and variable probability sampling with observed retainment frequencies. I extend an important result known to hold in special cases: estimating the selection probabilities is generally more efficient than if the known selection probabilities could be used in estimation. For the treatment effect case, the setup allows for a simple characterization of a “double robustness” result due to Scharfstein, Rotnitzky, and Robins (1999): given appropriate choices for the conditional mean function and quasi-log-likelihood function, only one of the conditional mean or selection probability needs to be correctly specified in order to consistently estimate the average treatment effect.

Estimation/Imputation strategies for missing data in survival analysis

International audienceWe consider the problem of estimation from right-censored data, when the censoring indicator is possibly missing. We compare different estimatio/imputation strategies for recovering nuisance functional parameters. More precisely, we propose either a parametric strategy following a logistic model standard or a pure nonparametric regression strategy. We provide theoretical properties and numerical comparisons for these procedures

The cost for the default of a loan : Linking theory and practice

When calculating the cost of entering into a credit transaction the predominant stochastic component is the expected loss. Often in the credit business the one-year probability of default of the liable counterpart is the only reliable parameter. We use this probability to calculating the exact expected loss of trades with multiple cash ows. Assuming a constant hazard rate for the default time of the liable counterpart we show that the methodology used in practice is a linear Taylor approximation of our exact calculus. In a second stage we can generalize the calculation to arbitrary hazard rates for which we prove statistical evidence and develop an estimate from historical data. --