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. |