James-Stein estimator improves accuracy and sample efficiency in human kinematic and metabolic data

In the associated manuscript, we show that James-Stein estimator helps improve statistical estimates for kinematic and metabolic problems by pooling data from multiple subjects. We considered three types of estimation problems: foot placement control, metabolic cost of walking in circles and metabolic cost of resting. In this dataset, we have shared the individual statistical estimates for each subject for each type of data, for each trial duration, along with their standard errors. The data in MATLAB's .mat format and can be opened with MATLAB, or free software such as octave and python.

Methods
The estimates and standard errors were computed as follows:

Foot placement control sensitivities was estimated from linear regression over motion capture data, using methods identical to those in Yang and Srinivasan [1], Perry and Srinivasan [2], Joshi and Srinivasan [3], and Seethapathi and Srinivasan [4]. The estimates and standard errors were obtained from the linear regression software fitlm in MATLAB.
The resting metabolic data just involves simple averages and are from Hanford and Srinivasan [5], Seethapathi and Srinivasan [6], and Brown, Seethapathi, and Srinivasan [7]. The estimates and standard errors were obtained by elementary formulas for mean and standard error.
The exponential fit to the walking metabolic rate is performed using fminunc in MATLAB to minimize a mean squared error between an exponential a0 + a1*exp(-lambda t) and the data [7].

References

[1] Wang, Yang, and Manoj Srinivasan. "Stepping in the direction of the fall: the next foot placement can be predicted from current upper body state in steady-state walking." Biology letters 10, no. 9 (2014): 20140405.

[2] Perry, Jennifer A., and Manoj Srinivasan. "Walking with wider steps changes foot placement control, increases kinematic variability and does not improve linear stability." Royal Society open science 4, no. 9 (2017): 160627.

[3] Joshi, Varun, and Manoj Srinivasan. "A controller for walking derived from how humans recover from perturbations." Journal of The Royal Society Interface 16, no. 157 (2019): 20190027.

[4] Seethapathi, Nidhi, and Manoj Srinivasan. "Step-to-step variations in human running reveal how humans run without falling." Elife 8 (2019): e38371.

[5] Handford, Matthew L., and Manoj Srinivasan. "Sideways walking: preferred is slow, slow is optimal, and optimal is expensive." Biology letters 10, no. 1 (2014): 20131006.

[6] Seethapathi, Nidhi, and Manoj Srinivasan. "The metabolic cost of changing walking speeds is significant, implies lower optimal speeds for shorter distances, and increases daily energy estimates." Biology letters 11, no. 9 (2015): 20150486.

[7] Brown, Geoffrey L., Nidhi Seethapathi, and Manoj Srinivasan. "A unified energy-optimality criterion predicts human navigation paths and speeds." Proceedings of the National Academy of Sciences 118, no. 29 (2021): e2020327118.