AbstractInference for a scalar interest parameter in the presence of nuisance parameters is considered in terms of the conditional maximum‐likelihood estimator developed by Cox and Reid (1987). Parameter orthogonality is assumed throughout. The estimator is analyzed by means of stochastic asymptotic expansions in three cases: a scalar nuisance parameter, m nuisance parameters from m independent samples, and a vector nuisance parameter. In each case, the expansion for the conditional maximum‐likelihood estimator is compared with that for the usual maximum‐likelihood estimator. The means and variances are also compared. In each of the cases, the bias of the conditional maximum‐likelihood estimator is unaffected by the nuisance parameter to first order. This is not so for the maximum‐likelihood estimator. The assumption of parameter orthogonality is crucial in attaining this result. Regardless of parametrization, the difference in the two estimators is first‐order and is deterministic to