Related Experiment Video
Updated: Jun 7, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
Published on: July 3, 2020
Statistical inference under order restrictions in analysis of covariance using a modified restricted maximum
Joshua Betcher1, Shyamal D Peddada
1Quintiles Inc., Research Triangle Park, NC 27560, U.S.A.
None:
In this article we introduce a new procedure for estimating population parameters under inequality constraints (known as order restrictions) when the unrestricted maximum liklelihood estimator (UMLE) is multivariate normally distributed with a known covariance matrix. Furthermore, a Dunnett-type test procedure along with the corresponding simultaneous confidence intervals are proposed for drawing inferences on elementary contrasts of population parameters under order restrictions. The proposed methodology is motivated by estimation and testing problems encountered in the analysis of covariance models. It is well-known that the restricted maximum likelihood estimator (RMLE) may perform poorly under certain conditions in terms of quadratic loss. For example, when the UMLE is distributed according to multivariate normal distribution with means satisfying simple tree order restriction and the dimension of the population mean vector is large. We investigate the performance of the proposed estimator analytically as well as using computer simulations and discover that the proposed method does not fail in the situations where RMLE fails. We illustrate the proposed methodology by re-analyzing a recently published rat uterotrophic bioassay data.
Related Concept Videos
Friedman Two-way Analysis of Variance by Ranks
Censoring Survival Data
Statistical Inference Techniques in Hypothesis Testing: Parametric Versus Nonparametric Data
Parametric statistics, as the name suggests, assumes that data follow a specific distribution, often a normal distribution. This assumption enables robust hypothesis testing and estimation. Parametric methods, like the Student's t-test or Goodness-of-fit test, are frequently employed in biostatistics due to their robustness. For instance, comparing...
The Mantel-Cox Log-Rank Test
One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation
On...
Mechanistic Models: Compartment Models in Individual and Population Analysis
