Slope consistency of quasi-maximum likelihood estimator for binary choice models
严格证明了在Ruud(1983)条件下，二元选择模型的拟极大似然估计量具有斜率一致性，从而为逻辑回归在机器学习中的广泛应用提供了理论支撑。
Although QMLE is generally inconsistent, logistic regression relying on the binary choice model (BCM) with logistic errors is widely used, especially in machine learning contexts with many covariates. This paper revisits the slope consistency of QMLE for BCMs. Ruud (1983) introduced a set of conditions under which QMLE may yield a constant multiple of the slope coefficient of BCMs asymptotically. However, he did not fully establish the slope consistency of QMLE, which requires the existence of a positive multiple of the true slope that maximizes the population QMLE likelihood over an appropriately restricted parameter space. We close this gap by providing a formal proof of slope consistency under the same set of conditions for BCMs identified as in Manski (1975, 1985). Our result implies that, under suitable conditions, logistic regression yields a consistent estimate of the slope coefficient for BCMs. • QMLE is generally inconsistent for binary choice models (BCMs). • Ruud (1983) proposed conditions for QMLE slope consistency in BCMs. • He did not fully establish slope consistency under those conditions. • We prove QMLE slope consistency for BCMs identified more generally in Manski (1985). • Probit/logit QMLE is thus slope consistent under suitable conditions.