Estimation of parameters in linear structural relationships: Sensitivity to the choice of the ratio of error variances

Maximum likelihood estimation of parameters in linear structural relationships under normality assumptions requires knowledge of one or more of the model parameters if no replication is available. The most common assumption added to the model definition is that the ratio of the error variances of the response and predictor variates is known. The use of asymptotic formulae for variances and mean squared errors as a function of sample size and the assumed value for the error variance ratio is investigated

A Statistical Decision-Theoretical Perspective on the Two-Stage Approach to Parameter Estimation

One of the most important problems in system identification and statistics is how to estimate the unknown parameters of a given model. Optimization methods and specialized procedures, such as Empirical Minimization (EM) can be used in case the likelihood function can be computed. For situations where one can only simulate from a parametric model, but the likelihood is difficult or impossible to evaluate, a technique known as the Two-Stage (TS) Approach can be applied to obtain reliable parametric estimates. Unfortunately, there is currently a lack of theoretical justification for TS. In this paper, we propose a statistical decision-theoretical derivation of TS, which leads to Bayesian and Minimax estimators. We also show how to apply the TS approach on models for independent and identically distributed samples, by computing quantiles of the data as a first step, and using a linear function as the second stage. The proposed method is illustrated via numerical simulations.Comment: 7 pages, 6 figures, 1 tabl

Minimax Two-Stage Gradient Boosting for Parameter Estimation

Parameter estimation is an important sub-field in statistics and system identification. Various methods for parameter estimation have been proposed in the literature, among which the Two-Stage (TS) approach is particularly promising, due to its ease of implementation and reliable estimates. Among the different statistical frameworks used to derive TS estimators, the min-max framework is attractive due to its mild dependence on prior knowledge about the parameters to be estimated. However, the existing implementation of the minimax TS approach has currently limited applicability, due to its heavy computational load. In this paper, we overcome this difficulty by using a gradient boosting machine (GBM) in the second stage of TS approach. We call the resulting algorithm the Two-Stage Gradient Boosting Machine (TSGBM) estimator. Finally, we test our proposed TSGBM estimator on several numerical examples including models of dynamical systems.Comment: 6 page

Forming Maximally Diverse Workgroups: An Empirical Study

This work addresses two related important themes in business and business schools today: expanding diversity in the workplace and the increasing reliance on teams as an organizational structure. The paper describes an approach for creating student work groups where the objective is to maximize within group diversity based upon multiple criteria. This approach is an extension of a heuristic-based multiple-criteria decision support system (MCADSS) developed in earlier work (Weitz and Jelassi [1992]); that system was successfully implemented, and is currently in use, at the European Institute of Business Administration (INSEAD) in Fontainebleau, France. The heuristic has been modified here to incorporate a different set of criteria, and to allow for students placing out of core courses. This paper discusses the modified system, its implementation at the Stern School of Business at New York University (NYU), and an empirical experiment evaluating the performance of the system

Elastic Platonic Shells

On microscopic scales, the crystallinity of flexible tethered or cross-linked membranes determines their mechanical response. We show that by controlling the type, number, and distribution of defects on a spherical elastic shell, it is possible to direct the morphology of these structures. Our numerical simulations show that by deflating a crystalline shell with defects, we can create elastic shell analogs of the classical platonic solids. These morphologies arise via a sharp buckling transition from the sphere which is strongly hysteretic in loading or unloading. We construct a minimal Landau theory for the transition using quadratic and cubic invariants of the spherical harmonic modes. Our approach suggests methods to engineer shape into soft spherical shells using a frozen defect topology.Engineering and Applied SciencesMolecular and Cellular BiologyOrganismic and Evolutionary BiologyPhysic

Designer peptides to understand the mineralization of calcium salts

Recently, we reported the extraction, purification and amino acid sequence of ansocalcin, the major goose eggshell matrix protein. In vitro studies showed that ansocalcin induces spherical calcite crystal aggregates. We designed two peptides using the unique features of the sequence of ansocalcin and the role of these peptides in CaCO₃ crystallization was investigated. The peptides showed similar activities as compared to ansocalcin, but at a higher concentration. The full characterization of the peptides and a rational for the observed morphology for the calcite crystals are discussed in detail.Singapore-MIT Alliance (SMA

Eggshell Matrix Protein Mimetics: Elucidation of Molecular Mechanism of Goose Eggshell Calcification using Designed Peptides

Model peptides were designed, synthesized and conducted a detailed structure-property study to unravel the molecular mechanism of goose eggshell calcification. The peptides were designed based on the primary structural features of the eggshell matrix proteins ansocalcin and OC-17. In vitro CaCO₃ crystal growth experiments in presence of these peptides showed calcite crystal aggregation as observed in the case of the parent protein ansocalcin. The structure of these peptides in solution was established using intrinsic tryptophan fluorescence studies and quasi-elastic light scattering experiments. The structural features are correlated with observed results of the in vitro crystallization studies.Singapore-MIT Alliance (SMA

Correction to: The Activity of Polyhomoarginine against Acanthamoeba castellanii (Biology, (2022), 11, 12, (1726), 10.3390/biology11121726)

In the original publication [1], there was a mistake in the legend for ** Figure 1—4 **. **Using a two-sample t-test and two-tailed distribution**. The correct legend appears below. **i. Figure 1: Change “(** p < 0.001 using a two-sample t-test and two-tailed distribution).” to “(** p < 0.001 using one way ANOVA).” ii. Figure 2: Change “(** p < 0.001, * p < 0.05 using a two-sample t-test and two-tailed distribution).” to “(** p < 0.001, * p < 0.05 using one way ANOVA).” iii. Figure 3: change “(** p < 0.001, * p < 0.05 using a two-sample t-test and two-tailed distribution).” to “(** p < 0.001, * p < 0.05 using one way ANOVA).” iv. Figure 4: change “(** p < 0.001, * p < 0.05 using a two-sample t-test and two-tailed distribution).” to “(** p < 0.001, * p < 0.05 using one way ANOVA).” ** There was an error in the original publication. **Full name of PHMB missing in Introduction**. A correction has been made to **Introduction**, **Paragraph Number—3**: i. Change “PHMB or chlorhexidine are widely used to treat this infection as monotherapies or in combination” to “Polyhexamethylene biguanide or chlorhexidine are widely used to treat this infection as monotherapies or in combination”. The authors state that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated

Non-negative matrix factorization for parameter estimation in hidden Markov models

Hidden Markov models are well-known in analysis of random processes, which exhibit temporal or spatial structure and have been successfully applied to a wide variety of applications such as but not limited to speech recognition, musical scores, handwriting, and bio-informatics. We present a novel algorithm for estimating the parameters of a hidden Markov model through the application of a non-negative matrix factorization to the joint probability distribution of two consecutive observations. We start with the discrete observation model and extend the results to the continuous observation model through a non-parametric approach of kernel density estimation. For both the cases, we present results on a toy example and compare the performance with the Baum-Welch algorithm. ©2010 IEEE