An Alternative to Maximum Likelihood Based on Spacings

Consider a scalar continuously distributed random variable x with probability density function (PDF) f(x) ≡ f(x, θ) and corresponding cumulative distribution function (CDF) F (x) ≡ F (x, θ) known up to a possibly multidimensional parameter θ ∈ Θ. Denote the true value of the parameter by θ0. Suppose that a random sample x1, · · · , xn is available. To estimate θ0, one usually uses the Maximum Likelihood (ML) estimator θ̂ML = arg max θ∈Θ QML (θ), wher