A Linear City Model with Asymmetric Consumer Distribution

The article analyzes a linear-city model where the consumer distribution can be asymmetric, which is important because in real markets this distribution is often asymmetric. The model yields equilibrium price differences, even though the firms’ costs are equal and their locations are symmetric (at the two endpoints of the city). The equilibrium price difference is proportional to the transportation cost parameter and does not depend on the good''s cost. The firms'' markups are also proportional to the transportation cost. The two firms’ prices will be equal in equilibrium if and only if half of the consumers are located to the left of the city’s midpoint, even if other characteristics of the consumer distribution are highly asymmetric. An extension analyzes what happens when the firms have different costs and how the two sources of asymmetry – the consumer distribution and the cost per unit – interact together. The model can be useful as a tool for further development by other researchers interested in applying this simple yet flexible framework for the analysis of various topics.     

选择回归方程自变量的条件数法及其在RK手术中的应用

选择合适的自变量是确定线性回归模型的首要问题,本文以消除自变量之间的复共线性为目标,介绍了一种选择回归方程自变量的条件数法,并在ＲＫ手术的结果预测问题中采用了这一方法。     

A MINE Alternative to D-Optimal Designs for the Linear Model

Doing large-scale genomics experiments can be expensive, and so experimenters want to get the most information out of each experiment. To this end the Maximally Informative Next Experiment (MINE) criterion for experimental design was developed. Here we explore this idea in a simplified context, the linear model. Four variations of the MINE method for the linear model were created: MINE-like, MINE, MINE with random orthonormal basis, and MINE with random rotation. Each method varies in how it maximizes the MINE criterion. Theorem 1 establishes sufficient conditions for the maximization of the MINE criterion under the linear model. Theorem 2 establishes when the MINE criterion is equivalent to the classic design criterion of D-optimality. By simulation under the linear model, we establish that the MINE with random orthonormal basis and MINE with random rotation are faster to discover the true linear relation with regression coefficients and observations when . We also establish in simulations with , , and 1000 replicates that these two variations of MINE also display a lower false positive rate than the MINE-like method and additionally, for a majority of the experiments, for the MINE method.     

The Estimation of Skewness and Kurtosis of Random Effects in the Linear Model

Generalising the ANOVA method of estimating variance components in mixed linear models a simple procedure is presented to estimate skewness and kurtosis of the distributions of the random effects of the model. For the model II of a one-way classification this procedure is demonstrated explicitly.     

Linear Model of Colon Cancer Initiation

Cancer results if regulatory mechanisms of cell birth and death are disrupted. Colorectal tumorigenesis is initiated by somatic or inherited mutations in the APC tumor suppressor gene pathway. Several additional genetic hits in other tumor suppressor genes and oncogenes drive the progression from polyps to malignant, invasive cancer. The majority of colorectal cancers present chromosomal instability, CIN, which is caused by mutations in genes that are required to maintain chromosomal stability. A major question in cancer genetics is whether CIN is an early event and thus a driving force of tumor progression. We present a new mathematical model of colon cancer initiation assuming a linear flow from stem cells to differentiated cells to apoptosis. We study the consequences of mutations in different cell types and calculate the conditions for CIN to precede APC inactivation. We find that early emergence of CIN is very likely in colorectal tumorigenesis.     

A Note on Comparing Stochastically Restricted Linear Estimators in a Regression Model

In his recent paper Liski (1989) derived conditions for superiority of the minimum dispersion estimator over another with respect to the covariance matrix when the parameter vector of a regression model is subject to competing stochastic restrictions. The aim of this note is to provide another necessary and sufficient condition which admits an easier interpretation of superiority related to the covariance matrix criterion.     

A Method to Quantify FRET Stoichiometry with Phasor Plot Analysis and Acceptor Lifetime Ingrowth

FRET is widely used for the study of protein-protein interactions in biological samples. However, it is difficult to quantify both the FRET efficiency (E) and the affinity (K_d) of the molecular interaction from intermolecular FRET signals in samples of unknown stoichiometry. Here, we present a method for the simultaneous quantification of the complete set of interaction parameters, including fractions of bound donors and acceptors, local protein concentrations, and dissociation constants, in each image pixel. The method makes use of fluorescence lifetime information from both donor and acceptor molecules and takes advantage of the linear properties of the phasor plot approach. We demonstrate the capability of our method in vitro in a microfluidic device and also in cells, via the determination of the binding affinity between tagged versions of glutathione and glutathione S-transferase, and via the determination of competitor concentration. The potential of the method is explored with simulations.     

Generalized Linear Model for Mapping Discrete Trait Loci Implemented with LASSO Algorithm

Generalized estimating equation (GEE) algorithm under a heterogeneous residual variance model is an extension of the iteratively reweighted least squares (IRLS) method for continuous traits to discrete traits. In contrast to mixture model-based expectation–maximization (EM) algorithm, the GEE algorithm can well detect quantitative trait locus (QTL), especially large effect QTLs located in large marker intervals in the manner of high computing speed. Based on a single QTL model, however, the GEE algorithm has very limited statistical power to detect multiple QTLs because of ignoring other linked QTLs. In this study, the fast least absolute shrinkage and selection operator (LASSO) is derived for generalized linear model (GLM) with all possible link functions. Under a heterogeneous residual variance model, the LASSO for GLM is used to iteratively estimate the non-zero genetic effects of those loci over entire genome. The iteratively reweighted LASSO is therefore extended to mapping QTL for discrete traits, such as ordinal, binary, and Poisson traits. The simulated and real data analyses are conducted to demonstrate the efficiency of the proposed method to simultaneously identify multiple QTLs for binary and Poisson traits as examples.     

On Admissible Estimators in a Linear Model

Let Y be observable random vector such that EY=Xβ and D(Y)=ρ²V. Linear estimation of a parameter p′β under the squared loss is considered. RAO, 1976 and 1979, obtained a necessary and sufficient condition for admissibility of an estimator t′Y in the case X=I. This result will be extended for arbitrary X. AMS 1970 subject classifications. Primary 62J05; secondary 62C15.     

Long-Range Correlation in Synchronization and Syncopation Tapping: A Linear Phase Correction Model

We propose in this paper a model for accounting for the increase in long-range correlations observed in asynchrony series in syncopation tapping, as compared with synchronization tapping. Our model is an extension of the linear phase correction model for synchronization tapping. We suppose that the timekeeper represents a fractal source in the system, and that a process of estimation of the half-period of the metronome, obeying a random-walk dynamics, combines with the linear phase correction process. Comparing experimental and simulated series, we show that our model allows accounting for the experimentally observed pattern of serial dependence. This model complete previous modeling solutions proposed for self-paced and synchronization tapping, for a unifying framework of event-based timing.     

Stationary Probabilities and Asymptotic Behaviour of a non-Markovian Model with Linear Transition Rule

Explicit and recursive formulae are obtained for the n-step stochastic kernel, and its stationarity and asymptotic behaviour is examined for a special class of non-Markovian models with a linear transition rule occuring in learning theory, adaption theory, control theory, and biological research.     

Experiments with Three-Treatment Three-Period Crossover Design: Analysis Through the General Linear Model

In this paper we consider balanced three-treatment three-period crossover designs. Using a strategy similar to that applied in the analysis of split-plot experiments we describe both the within and the between sample units models, as well as the corresponding Analysis of Variance. We illustrate these procedures with a numerical example and discuss their implementation through computer programs designed for the analysis of the general linear model.     

Linear Rank Tests Derived from a Superpopulation Model

A superpopulation model generates the probabilities of a Bernouilli random variable. The ranks of the involved variables are considered as survey weights. The distribution f each linear rank statistic is derived under the null hypothesis for the two sample problem and for the case k2 when a simple random sampling or stratified sampling is used. The growth of a population of insects and the behavior of patients with imsomnia are studied using these procedures.     

Information in Observation Under the Correlated Linear Model

In this paper we propose a measure of information in a set of observations under a given design and the linear model with the observations being correlated. We then compare the different sets of observations with respect to the information measure in the situations where the underlying designs are nested and split-plot. AMS 1970 Subject Classification: Secondary 62J05, 62J10, 62K05, 62K10, 62K15, 62K99.     

Analysis of a Generalized Linear Mixed Model: A Case Study and Simulation Results

A class of generalized linear mixed models can be obtained by introducing random effects in the linear predictor of a generalized linear model, e.g. a split plot model for binary data or count data. Maximum likelihood estimation, for normally distributed random effects, involves high-dimensional numerical integration, with severe limitations on the number and structure of the additional random effects. An alternative estimation procedure based on an extension of the iterative re-weighted least squares procedure for generalized linear models will be illustrated on a practical data set involving carcass classification of cattle. The data is analysed as overdispersed binomial proportions with fixed and random effects and associated components of variance on the logit scale. Estimates are obtained with standard software for normal data mixed models. Numerical restrictions pertain to the size of matrices to be inverted. This can be dealt with by absorption techniques familiar from e.g. mixed models in animal breeding. The final model fitted to the classification data includes four components of variance and a multiplicative overdispersion factor. Basically the estimation procedure is a combination of iterated least squares procedures and no full distributional assumptions are needed. A simulation study based on the classification data is presented. This includes a study of procedures for constructing confidence intervals and significance tests for fixed effects and components of variance. The simulation results increase confidence in the usefulness of the estimation procedure.