Henderson's Method Research Articles

HPX filter: a hybrid of Hodrick–Prescott filter and multiple regression

Abstract This paper considers an extension of Hodrick–Prescott (HP) filter. It is a hybrid of HP filter and multiple regression. We refer to the filter as “HPX filter”. It is well known that HP filter has a unique global minimizer and the solution can be represented in matrix notation explicitly. Does HPX filter also have a unique global minimizer? Is it accomplished without any additional assumptions? Can the solution be expressed in matrix notation explicitly? In this paper, we answer these questions. In addition, this paper (i) provides an alternative perspective on the filter by representing it as a generalized ridge regression and (ii) gives an extension of it, which is a hybrid of Whittaker–Henderson method of graduation and multiple regression.

Nonlinear modeling of growth and study of a new characterization point applied to Timahdit breed sheep under uncertain paternity

The objectives of this study are to determine which model, among those of Brody, Logistic, Gompertz, Von Bertalanffy and Richards, is the most appropriate to describe the growth of this breed and to choose a point for this model which would be closest to the slaughter weight which have to be used as a selection criterion. Also, in preparation for genetic evaluation under uncertain paternity, Henderson's Average Numerator Relationship Matrix method was used and an R code was developed for the creation of the inverse matrix A which was replaced the pedigree in the animal model. To do this, 64,282 observations corresponding to 12,944 animals, collected between 2009 and 2016, were analyzed. The Von Bertalanffy function had the smallest AIC, BIC, and deviance criteria values, indicating better data representation for both sexes. Considering the average slaughter live weight of 29.4kg in the study area, the new point of characterization named f(tbm), later than the inflection point of the growth curve, is closer to the commercial target for females intended for regular slaughter supplying butchers and for animals of both sexes intended for religious festivals. Therefore, it would be appropriate to consider this point as a selection criterion for this breed. The developed R code will be integrated into a free R package allowing the estimation of the genetic parameters of the traits of the Von Bertalanffy model.

Henderson's method approach to Kernel prediction in partially linear mixed models

In this article, we propose Kernel prediction in partially linear mixed models by using Henderson's method approach. We derive the Kernel estimator and the Kernel predictor via the mixed model equations (MMEs) of Henderson's that they give the best linear unbiased estimation (BLUE) of the fixed effects parameters and the nonparametric function computationally easier and the best linear unbiased prediction (BLUP) of the random effects parameters as by-products. Additionally, asymptotic property of the Kernel estimator is investigated. A Monte Carlo simulation study is supported to illustrate the performance of Kernel prediction in partially linear mixed models and then, we finalize the article with the help of conclusion and discussion part to summarize the findings.

A modification of the Whittaker–Henderson method of graduation

This paper presents a modified Whittaker–Henderson (WH) Method of Graduation. After giving a closed-form solution, we show that it is of practical use because it provides not only a smoothed series identical to that of the WH graduation, but also an extrapolation beyond the sample limit of current data. In addition, we introduce two other penalized least squares problems and show that they provide the same results as those of the modified WH graduation.

Communication: Contact values of pair distribution functions in colloidal hard disks by test-particle insertion.

We apply Henderson's method for measuring the cavity distribution function y(r) [J. Henderson, Mol. Phys. 48, 389 (1983)] to obtain the pair distribution function at contact, g(σ+). In contrast to the conventional distance-histogram method, no approximate extrapolation to contact is required. The resulting equation of state from experiments and simulations of hard disks agrees well with the scaled particle theory prediction up to high fluid packing fractions. We also provide the first experimental measurement of y(r) inside the hard core, which will allow for a more complete comparison with theory. The method's flexibility is further illustrated by measuring the partial pair distribution functions of binary hard-disk mixtures in simulation. The equation for the contact values can be used to derive familiar results from statistical geometry.

Fast and robust estimators of variance components in the nested error model

Usual fitting methods for the nested error linear regression model are known to be very sensitive to the effect of even a single outlier. Robust approaches for the unbalanced nested error model with proved robustness and efficiency properties, such as M-estimators, are typically obtained through iterative algorithms. These algorithms are often computationally intensive and require robust estimates of the same parameters to start the algorithms, but so far no robust starting values have been proposed for this model. This paper proposes computationally fast robust estimators for the variance components under an unbalanced nested error model, based on a simple robustification of the fitting-of-constants method or Henderson method III. These estimators can be used as starting values for other iterative methods. Our simulations show that they are highly robust to various types of contamination of different magnitude.

Application of trajectories from growth curve in identification of longitudinal biomarker for the multivariate survival data

ABSTRACTIn clinical studies, the researchers measure the patients' response longitudinally. In recent studies, Mixed models are used to determine effects in the individual level. In the other hand, Henderson et al. [3,4] developed a joint likelihood function which combines likelihood functions of longitudinal biomarkers and survival times. They put random effects in the longitudinal component to determine if a longitudinal biomarker is associated with time to an event. In this paper, we deal with a longitudinal biomarker as a growth curve and extend Henderson's method to determine if a longitudinal biomarker is associated with time to an event for the multivariate survival data.

An extension of the Whittaker–Henderson method of graduation

We present an outline and historical summary of the Whittaker–Henderson method of graduation (or data smoothing), together with an extension of the method in which the graduated values are obtained by minimising a Whittaker–Henderson criterion subject to constraints. Examples are given, using data for the global average temperature anomaly and for a set of share prices, in which the proposed method appears to give good results.

The melodics of long poems

A tune is meaningless. Unless – it be deliberately made into, be coerced into becoming, some sign or symbol. So stands one orthodoxy of one kind of poetics, and so does poetics declare, upon every ...

Evaluation of immunization coverage within the Expanded Program on Immunization in Kita Circle, Mali: a cross-sectional survey

BackgroundIn 1986, the Government of Mali launched its Expanded Program on Immunization (EPI) with the goal of vaccinating, within five years, 80% of all children under the age of five against six target diseases: diphtheria, tetanus, pertussis, poliomyelitis, tuberculosis, and measles. The Demographic and Health Survey carried out in 2001 revealed that, in Kita Circle, in the Kayes region, only 13% of children aged 12 to 23 months had received all the EPI vaccinations. A priority program was implemented in 2003 by the Regional Health Department in Kayes to improve EPI immunization coverage in this area.MethodsA cross-sectional survey using Henderson's method (following the method used by the Demographic and Health Surveys) was carried out in July 2006 to determine the level of vaccination coverage among children aged 12 to 23 months in Kita Circle, after implementation of the priority program. Both vaccination cards and mothers' declarations (in cases where the mother cannot make the declaration, it is made by the person responsible for the child) were used to determine coverage.ResultsAccording to the vaccination cards, 59.9% [CI 95% (54.7-64.8)] of the children were fully vaccinated, while according to the mothers' declarations the rate was 74.1% [CI 95% (69.3-78.4)]. The drop-out rate between DTCP1 and DTCP3 was 5.5%, according to the vaccination cards. The rate of immunization coverage was higher among children whose mothers had received the anti-tetanus vaccine [OR = 2.1, CI 95% (1.44-3.28)]. However, our study found no difference associated with parents' knowledge about EPI diseases, distance from the health centre, or socio-economic status. Lack of information was one reason given for children not being vaccinated against the six EPI diseases.ConclusionThree years after the implementation of the priority program (which included decentralization, the active search for missing children, and deployment of health personnel, material and financial resources), our evaluation of the vaccination coverage rates shows that there is improvement in the EPI immunization coverage rate in Kita Circle. The design of our study did not, however, enable us to determine the extent to which different aspects of the program contributed to this increase in coverage. Efforts should nevertheless be continued, in order to reach the goal of 80% immunization coverage. in FrenchSee the full article online for a translation of this abstract in French.

Non‐iterative variance component estimation in QTL analysis

In variance component quantitative trait loci (QTL) analysis, a mixed model is used to detect the most likely chromosome position of a QTL. The putative QTL is included as a random effect and a method is needed to estimate the QTL variance. The standard estimation method used is an iterative method based on the restricted maximum likelihood (REML). In this paper, we present a novel non-iterative variance component estimation method. This method is based on Henderson's method 3, but relaxes the condition of unbiasedness. Two similar estimators were compared, which were developed from two different partitions of the sum of squares in Henderson's method 3. The approach was compared with REML on data from a European wild boar x domestic pig intercross. A meat quality trait was studied on chromosome 6 where a functional gene was known to be located. Both partitions resulted in estimated QTL variances close to the REML estimates. From the non-iterative estimates, we could also compute good approximations of the likelihood ratio curve on the studied chromosome.

Selective inhibitors of plasmepsin II of Plasmodium falciparum on the basis of pepstatin

A number of new inhibitors of plasmepsin II (PlmII) from Plasmodium falciparum, one of the key factors of malarial parasite survival, were synthesized. The inhibitors are analogues of pepstatin with various variants of Ala residue substitutions. Effects of the inhibitors on human PlmII and cathepsin D were studied. Inhibition of PlmII by the substrate was found, which required the use of the modified Henderson method for the determination of inhibition constants. Two synthesized inhibitors were shown to exhibit a pronounced selectivity to PlmII (K(i) = 5.5 and 5 nM) in comparison with cathepsin D (K(i) = 230 and 3000 nM, respectively).

Identifying differentially expressed genes in human acute leukemia and mouse brain microarray datasets utilizing QTModel

One of the essential issues in microarray data analysis is to identify differentially expressed genes (DEGs) under different experimental treatments. In this article, a statistical procedure was proposed to identify the DEGs for gene expression data with or without missing observations from microarray experiment with one- or two-treatment factors. An F statistic based on Henderson method III was constructed to test the significance of differential expression for each gene under different treatment(s) levels. The cutoff P value was adjusted to control the experimental-wise false discovery rate. A human acute leukemia dataset corrected from 38 leukemia patients was reanalyzed by the proposed method. In comparison to the results from significant analysis of microarray (SAM) and microarray analysis of variance (MAANOVA), it was indicated that the proposed method has similar performance with MAANOVA for data with one-treatment factor, but MAANOVA cannot directly handle missing data. In addition, a mouse brain dataset collected from six brain regions of two inbred strains (two-treatment factors) was reanalyzed to identify genes with distinct regional-specific expression patterns. The results showed that the proposed method could identify more distinct regional-specific expression patterns than the previous analysis of the same dataset. Moreover, a computer program was developed and incorporated in the software QTModel, which is freely available at http://ibi.zju.edu.cn/software/qtmodel .

Mapping the genetic architecture of complex traits in experimental populations

Understanding how interactions among set of genes affect diverse phenotypes is having a greater impact on biomedical research, agriculture and evolutionary biology. Mapping and characterizing the isolated effects of single quantitative trait locus (QTL) is a first step, but we also need to assemble networks of QTLs and define non-additive interactions (epistasis) together with a host of potential environmental modulators. In this article, we present a full-QTL model with which to explore the genetic architecture of complex trait in multiple environments. Our model includes the effects of multiple QTLs, epistasis, QTL-by-environment interactions and epistasis-by-environment interactions. A new mapping strategy, including marker interval selection, detection of marker interval interactions and genome scans, is used to evaluate putative locations of multiple QTLs and their interactions. All the mapping procedures are performed in the framework of mixed linear model that are flexible to model environmental factors regardless of fix or random effects being assumed. An F-statistic based on Henderson method III is used for hypothesis tests. This method is less computationally greedy than corresponding likelihood ratio test. In each of the mapping procedures, permutation testing is exploited to control for genome-wide false positive rate, and model selection is used to reduce ghost peaks in F-statistic profile. Parameters of the full-QTL model are estimated using a Bayesian method via Gibbs sampling. Monte Carlo simulations help define the reliability and efficiency of the method. Two real-world phenotypes (BXD mouse olfactory bulb weight data and rice yield data) are used as exemplars to demonstrate our methods. A software package is freely available at http://ibi.zju.edu.cn/software/qtlnetwork

Quadratic estimators of covariance components in a multivariate mixed linear model

It is known that the Henderson Method III (Biometrics 9:226–252, 1953) is of special interest for the mixed linear models because the estimators of the variance components are unaffected by the parameters of the fixed factor (or factors). This article deals with generalizations and minor extensions of the results obtained for the univariate linear models. A MANOVA mixed model is presented in a convenient form and the covariance components estimators are given on finite dimensional linear spaces. The results use both the usual parametric representations and the coordinate-free approach of Kruskal (Ann Math Statist 39:70–75, 1968) and Eaton (Ann Math Statist 41:528–538, 1970). The normal equations are generalized and it is given a necessary and sufficient condition for the existence of quadratic unbiased estimators for covariance components in the considered model.

A robust statistical procedure to discover expression biomarkers using microarray genomic expression data

Microarray has become increasingly popular biotechnology in biological and medical researches, and has been widely applied in classification of treatment subtypes using expression patterns of biomarkers. We developed a statistical procedure to identify expression biomarkers for treatment subtype classification by constructing an F-statistic based on Henderson method III. Monte Carlo simulations were conducted to examine the robustness and efficiency of the proposed method. Simulation results showed that our method could provide satisfying power of identifying differentially expressed genes (DEGs) with false discovery rate (FDR) lower than the given type I error rate. In addition, we analyzed a leukemia dataset collected from 38 leukemia patients with 27 samples diagnosed as acute lymphoblastic leukemia (ALL) and 11 samples as acute myeloid leukemia (AML). We compared our results with those from the methods of significance analysis of microarray (SAM) and microarray analysis of variance (MAANOVA). Among these three methods, only expression biomarkers identified by our method can precisely identify the three human acute leukemia subtypes.

Site characterization and assessment using the microgravity technique: a case history

A microgravity survey was undertaken to investigate the area surrounding the collapse of a riverbank retaining wall. Initial site investigation identified the presence of a void in the immediate area of the collapse. The objective of the geophysical survey was to assess the extent of the identified void and identify any similar features in the surrounding area. Several geophysical techniques were considered but due to the urban environment, the microgravity technique was chosen. Forward modelling using the data from the initial site investigation was undertaken to optimize the survey parameters. The gravity data was processed to the Bouguer anomaly and the terrain effects of the river‐channel morphology accounted for. Anomalies identified within the data set have been analysed using the Euler deconvolution method, which has provided estimates of the depth to the top of the anomalous areas. Inversion of the gravity data using the Cordell and Henderson method has provided an image of the 3D extent of the anomalous areas identified. Guided by this information, a secondary invasive site investigation was conducted which confirmed the interpretation of the geophysical results. The combination of a non‐invasive geophysical investigation together with selective invasive control has enabled the full subsurface characterization of this site.

Estimation of Variance Components and Heritabilities of Growth Characteristics in Morkaraman Lambs Using Different Statistical Methods

Bilgin, O.C., Esenbuga, N., Macit, M. and Karaoglu, M. 2004. Estimation of variance components and heritabilities of growth characteristics in Morkaraman lambs using different statistical methods. J. Appl. Anim. Res., 26: 83–88. Henderson's method 3, maximum likelihood (ML), restricted maximum likelihood (REML) and minimum variance quadratic unbiased estimation (MIVQUE) methods were used to estimate variance components and to predict heritabilities of birth weight, weaning weight and daily weight gain until weaning in Morkaraman lambs. The different variance components methods gave similar results. The moderately-high estimate of heritability for weaning weight, demonstrates an opportunity for improvement of this trait through genetic selection.

Calculation of ionic surface excess concentrations in the diffuse double layer at low field strengths for a restricted primitive model electrolyte

Analytical expressions have been derived for the ionic surface excesses of a restricted primitive-model z–z electrolyte near a charged wall, by combination of a thermodynamic result with a recently derived equation for the surface potential as a function of salt concentration and surface charge density within the context of the Fawcett–Henderson method. This approximate result accounts for the finite size of ions and applies in the limit of low field strengths at the surface, corresponding to absolute surface charge densities not exceeding ca. 10 μC cm −2 and concentrations of at least 0.1 M. The theoretical expression has been tested via comparison with predictions based on Gouy–Chapman theory and data obtained with Monte Carlo simulations, and has been found to show a superior performance at high concentrations and large ion sizes in the case of 1–1 electrolytes and, to a lesser extent, 2–2 electrolytes.

Random balanced resampling: A new method for estimating variance components in unbalanced designs

Variance components in factorial designs with balanced data are commonly estimated by equating mean squares to expected mean squares. For unbalanced data, the usual extensions of this approach are the Henderson methods, which require formulas that are rather involved. Alternatively, maximum likelihood estimation based on normality has been proposed. Although the algorithm for maximum likelihood is computationally complex, programs exist in some statistical packages. This article introduces a simpler method, that of creating a balanced data set by resampling from the original one. Revised formulas for expected mean squares are presented for the two-way case; they are easily generalized to larger factorial designs. The results of a number of simulation studies indicate that, in certain types of designs, the proposed method has performance advantages over both the Henderson Method I and maximum likelihood estimators.