Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
Linear Approximations01:23

Linear Approximations

For a differentiable function of two variables, linear approximation estimates values near a known point by replacing the curved surface with its tangent plane. Consider the function\begin{equation*}f(x,y)=x^2+3y^2\end{equation*}near the point (2, 1). The exact value at this point is f(2, 1) = 22 + 3(1)2 = 4 + 3 = 7.The linear approximation of f(x, y)) near (a, b) is\begin{equation*}L(x,y)=f(a,b)+f_x(a,b)(x-a)+f_y(a,b)(y-b)\end{equation*}First, compute the partial derivatives: fx(x, y) = 2x and...
Linearization and Approximation01:26

Linearization and Approximation

Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...
Introduction to Polynomial Functions01:26

Introduction to Polynomial Functions

Polynomial functions are fundamental elements in algebra and calculus, defined by expressions that combine variables and constants through addition, subtraction, and multiplication, with the variable raised to nonnegative integer exponents. A general polynomial function of degree n is given byWhere an ≠ 0. The term anxn is the leading term, and an is the leading coefficient, while a0 is referred to as the constant term.Characteristics and ClassificationPolynomials are categorized by their...
Routh-Hurwitz Criterion II01:19

Routh-Hurwitz Criterion II

In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first column of the Routh...
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same authorSame journal

Nonparametric Density Estimation of a Long-Term Trend from Repeated Semicontinuous Data.

Journal of the American Statistical Association·2026
Same author

Generative AI-assisted Bayesian-frequentist Hybrid Inference in Single-cell RNA Sequencing Analysis for Genes Associated with Alzheimer's Disease.

medRxiv : the preprint server for health sciences·2026
Same author

Application of the Total Nutrient Index as a Precision Nutrition Tool to Address Dietary Recommendations Across the Life Course.

Journal of the Academy of Nutrition and Dietetics·2026
Same author

Anomalous Saturation of CO Adsorption at 26% on Cu(111) Governed by Nanometer-Scale Substrate-Mediated Interactions.

Journal of the American Chemical Society·2025
Same author

Valid and efficient inference for nonparametric variable importance in two-phase studies.

Biometrics·2025
Same author

Accelerometer measurement error in a randomized physical activity intervention trial in breast cancer survivors was nondifferential but attenuated the intervention effect.

The international journal of behavioral nutrition and physical activity·2025
Same journal

Instrumental Variable Estimation of Marginal Structural Mean Models for Time-Varying Treatment.

Journal of the American Statistical Association·2026
Same journal

Semiparametric Joint Modeling for Survival Analysis with Longitudinal Covariates.

Journal of the American Statistical Association·2026
Same journal

Dimension Reduction for Large-Scale Federated Data: Statistical Rate and Asymptotic Inference.

Journal of the American Statistical Association·2026
Same journal

Facilitating Heterogeneous Effect Estimation via Statistically Efficient Categorical Modifiers.

Journal of the American Statistical Association·2026
Same journal

Functional Integrative Bayesian Analysis of High-dimensional Multiplatform Clinicogenomic Data.

Journal of the American Statistical Association·2026
See all related articles

Related Experiment Video

Updated: Jun 14, 2026

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

A Design-Adaptive Local Polynomial Estimator for the Errors-in-Variables Problem.

Aurore Delaigle1, Jianqing Fan, Raymond J Carroll

  • 1Aurore Delaigle is Reader, Department of Mathematics, University of Bristol, Bristol BS8 1TW, UK and Department of Mathematics and Statistics, University of Melbourne, VIC, 3010, Australia (E-mail: aurore.delaigle@bri-s.ac.uk ).

Journal of the American Statistical Association
|March 31, 2010
PubMed
Summary
This summary is machine-generated.

This study introduces a novel local polynomial estimator for errors-in-variables regression, solving a 15-year-old problem. The new method advances nonparametric regression techniques and derivative estimation in challenging data settings.

More Related Videos

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Related Experiment Videos

Last Updated: Jun 14, 2026

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Area of Science:

  • Statistics
  • Nonparametric Regression
  • Errors-in-Variables Models

Background:

  • Local polynomial estimators are widely used in nonparametric regression.
  • Extending these estimators to errors-in-variables models, especially higher orders, has been a significant challenge for 15 years.
  • The local constant estimator is adaptable to errors-in-variables, but higher-order generalizations remain an open problem.

Purpose of the Study:

  • To propose an innovative local polynomial estimator applicable to errors-in-variables regression for any order.
  • To address a long-standing open problem in the field of nonparametric statistics.
  • To provide methodological advancements in errors-in-variables regression, including derivative estimation.

Main Methods:

  • Development of a novel local polynomial estimator for errors-in-variables regression.
  • Derivation of design-adaptive asymptotic properties for the proposed estimator.
  • Finite sample performance evaluation using simulated datasets.

Main Results:

  • Successful proposal of a local polynomial estimator of any order for errors-in-variables regression.
  • Demonstration of the estimator's asymptotic properties.
  • Validation of the method's performance through simulations.

Conclusions:

  • The study resolves a 15-year-old open problem in nonparametric regression.
  • The proposed estimator offers a significant methodological contribution to errors-in-variables regression.
  • The work includes novel approaches to local polynomial estimation of derivative functions in this context.