This paper is concerned with steady-state risk-sensitive filtering, prediction and smoothing problems for discrete-time singular systems. it is shown that a risk-sensitive estimator can be obtained by ensuring the minimum of an indefinite quadratic form to be maximum (minimum) when the risk-sensitivity parameter 0 is negative (positive). An auxiliary state-space signal model and an innovation sequence in Krein space are introduced to simplify the derivation of the estimator. The estimator is calculated based on one J-spectral factorization for risk-seeking (theta < 0) or one H-2 spectral factorization for risk-averse (θ > 0). A numerical example is given to demonstrate the applicability of the result.