OneStep : Le Cam's One-step Estimation Procedure

Abstract

The OneStep package proposes principally an eponymic function that numerically computes Le Cam's one-step estimator, which is asymptotically efficient and can be computed faster than the maximum likelihood estimator for large datasets. Monte Carlo simulations are carried out for several examples (discrete and continuous probability distributions) in order to exhibit the performance of Le Cam's one-step estimation procedure in terms of efficiency and computational cost on observation samples of finite size.

Speeding up the Training of Neural Networks with the One-Step Procedure

“…In this setting, for a initial sequence which is neither asymptotically rate nor variance efficient, the new sequence is asymptotically rate and variance efficient. This result allows to use the numerical computation of the Maximum Likelihood estimation (MLE) on a subsample (of size n δ , 1 2 < δ ≤ 1) as a fast initial sequence of guess estimators (see [4] for the practical application in the i.i.d. setting).…”

New closed‐form efficient estimator for multivariate gamma distribution

“…A significant advantage of the $$$ {\mathrm{MLE}}_{\mathrm{CE}} $$$ of the univariate gamma distribution derived in Ferguson (2002, chapter 20) and packaged by Brouste, Dutang, and Mieniedou (2021), OneStep only for some univariate distributions, is that it can be computed faster than the MLE for large datasets. According to Table 1 from Brouste et al (2021), $$$ {\mathrm{MLE}}_{\mathrm{CE}} $$$ is between 20 and 55 times faster than MLE. See Brouste et al (2021) for more information.…”

“…According to Table 1 from Brouste et al (2021), $$$ {\mathrm{MLE}}_{\mathrm{CE}} $$$ is between 20 and 55 times faster than MLE. See Brouste et al (2021) for more information.…”

One-step closed-form estimator for generalized linear model with categorical explanatory variables

“…In such procedure, an initial guess estimator is proposed which is fast to be computed but not asymptotically efficient. Then, a single step of the gradient descent method is done on the log-likelihood function in order to correct the initial estimation and reach asymptotic efficiency, see Brouste et al (2021). With some recent developments, the one-step procedure has been successfully generalized to more sophisticated statistical experiments as diffusion processes in Kamatani & Uchida (2015), Gloter & Yoshida (2021), ergodic Markov chains in Kutoyants & Motrunich (2016), inhomogeneous Poisson counting processes in Dabye et al (2018), fractional Gaussian and stable noises observed at high frequency in Brouste & Masuda (2018), Brouste, Soltane & Votsi (2020).…”