Derivative Estimation Based on Difference Sequence via Locally Weighted Least Squares Regression

Authors: WenWu Wang, Lu Lin

JMLR 2015 | Venue PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental In simulations our estimators have less bias and mean square error than its main competitors, especially second order derivative estimator. Section 5. Simulations
Researcher Affiliation Academia Wen Wu Wang EMAIL Lu Lin EMAIL Qilu Securities Institute for Financial Studies & School of Mathematics Shandong University Jinan, 250100, China
Pseudocode No The paper describes methods mathematically and textually using equations and detailed explanations, but does not contain any clearly labeled pseudocode or algorithm blocks.
Open Source Code No The paper discusses the use of third-party R packages (locpol, pspline) for comparisons but does not provide specific access information or a release statement for the authors' own source code implementation of their proposed methodology.
Open Datasets No The data sets are of size n = 500 and generated from model (1) with ̈ N(0, ̃2) for ̃ = 0.1. Simulated data set of size 300 from model (1) with equidistant xi [0.25, 1], x(1 x) sin((2.1π)/(x + 0.05)), ̈i iid N(0, 0.12), and the true mean function (bold line). The paper describes how data was simulated using mathematical functions but does not provide access information for a pre-existing open dataset.
Dataset Splits No where xi s are equidistantly designed, that is, xi = i/n, Yi s are random response variables, m( ) is an unknown smooth mean function, ̈i s are independent and identically distributed random errors with E[̈i] = 0 and V ar[̈i] = ̃2. The paper describes how data was simulated based on a model with equidistantly designed points, but it does not specify any training/test/validation splits for a dataset.
Hardware Specification No The paper describes simulation studies and their results but does not provide any specific details about the hardware (CPU, GPU, etc.) used to perform these computations.
Software Dependencies Yes local polynomial regression with p = 5 (R-package: locpol, Cabrera, 2012) and penalized smoothing splines with norder = 6 and method = 4 (R packages pspline, Ramsay and Ripley, 2013) and in references J.L.O. Cabrera. locpol: Kernel local polynomial regression. R packages version 0.6-0, 2012. J. Ramsay and B. Ripley. pspline: Penalized smoothing splines. R packages version 1.0-16, 2013.
Experiment Setup Yes We consider three sample sites n = 50, 200, 1000, corresponding to small, moderate, and large sample sizes, three standard deviations ̃ = 0.1, 0.5, 2, two frequencies f = 1, 2, and two amplitudes A = 1, 10. The number of repetitions is set as 1000. We consider four sample sizes, n {50, 100, 250, 500}, and three standard deviations, ̃ {0.02, 0.1, 0.5}. The number of repetitions is set as 100.