delicatessen 0.4

Generalized M-Estimation

Delicatessen

The one-stop sandwich (variance) shop in Python. delicatessen is a Python 3.6+ library for the generalized calculus of M-estimation.

Citation: Zivich PN, Klose M, Cole SR, Edwards JK, & Shook-Sa BE. (2022). Delicatessen: M-Estimation in Python. arXiv:2203.11300 [stat.ME]

M-Estimation and Estimating Equations

Here, we provide a brief overview of M-estimation theory. For a more detailed and formal introduction to M-estimation, I highly recommend chapter 7 of Boos & Stefanski (2013). M-estimation is a generalization of robust inference (here robust refers to allowing for misspecification of secondary assumptions does not invalidate inference) for likelihood-based methods to a general context. M-estimators are solutions to estimating equations. A large number of consistent and asymptotically normal statistics can be put into the M-Estimation framework. Some examples include: mean, regression, delta method, and among others.

To apply the M-Estimator, we solve the stacked estimating equations using observed data. This is similar to other approaches, but the key advantage of M-Estimators is the straightforward estimation of the variance via the sandwich variance.

While M-Estimation is a powerful tool, the derivatives and matrix algebra can quickly become unwieldy. This is where delicatessen comes in. delicatessen takes an array of stacked estimating equations and data and works through the root-finding, numerically approximating the partial derivatives, and matrix calculations. Therefore, M-Estimation can be more widely adopted without needing to solve every derivative for your particular problem. We can let the computer do all that hard math for us.

In addition to implementing a general M-estimator, delicatessen also comes with a variety of built-in estimating equations. See the delicatessen website for the full set of available estimating equations and how to use them.

Installation

Installing:

You can install via python -m pip install delicatessen

Dependencies:

There are only two dependencies: numpy, scipy

To replicate the tests located in tests/, you will additionally need to install: panda, statsmodels, and pytest

While delicatessen is expected to work with older versions of NumPy and SciPy, this has not been formally tested. Therefore, it is recommended to use numpy >= 1.18.0 and scipy >= 1.4.0 as there is no currently reported testing on previous versions.

Getting started

To demonstrate delicatessen, below is a simple demonstration of calculating the mean for the following data

import numpy as np
y = np.array([1, 2, 3, 1, 4, 1, 3, -2, 0, 2])

Loading the M-estimator functionality from deli, building the estimating equation, and printing the results to the console

from delicatessen import MEstimator

def psi(theta):
    return y - theta

mestimate = MEstimator(psi, init=[0, ])
mestimate.estimate()

print(mestimate.theta)     # Estimate of the mean
print(mestimate.variance)  # Variance estimator for the mean

For full details on using delicatessen, see the full documentation and worked examples available at delicatessen website.