Design of state estimator for genetic regulatory networks with time-varying delays and randomly occurring uncertainties

In this paper, the design problem of state estimator for genetic regulatory networks with time delays and randomly occurring uncertainties has been addressed by a delay decomposition approach. The norm-bounded uncertainties enter into the genetic regulatory networks (GRNs) in random ways, and such randomly occurring uncertainties (ROUs) obey certain mutually uncorrelated Bernoulli distributed white noise sequences. Under these circumstances, the state estimator is designed to estimate the true concentration of the mRNA and the protein of the uncertain GRNs. Delay-dependent stability criteria are obtained in terms of linear matrix inequalities by constructing a Lyapunov–Krasovskii functional and using some inequality techniques (LMIs). Then, the desired state estimator, which can ensure the estimation error dynamics to be globally asymptotically robustly stochastically stable, is designed from the solutions of LMIs. Finally, a numerical example is provided to demonstrate the feasibility of the proposed estimation schemes.     

Testing Equality of Means and Simultaneous Confidence Intervals in Repeated Measures with Missing Data

In this paper, repeated measures with intraclass correlation model is considered when the observations are missing at random. An exact test for the equality of the mean components and simultaneous confidence intervals (Scheffé and Bonferroni inequality types) are given for linear contrasts of the mean components when the missing observations are of a monotone type. When the missing observations are not of the monotone type, the maximum likelihood estimates are obtained numerically by iterative methods given in Srivastava and Carter (1986). These estimators are then used to obtain asymptotic tests and confidence intervals for the equality of mean components and linear contrasts, respectively. An example is given to illustrate the method.     

An improved algorithm for stoichiometric network analysis: theory and applications

MOTIVATION: Genome scale analysis of the metabolic network of a microorganism is a major challenge in bioinformatics. The combinatorial explosion, which occurs during the construction of elementary fluxes (non-redundant pathways) requires sophisticated and efficient algorithms to tackle the problem. RESULTS: Mathematically, the calculation of elementary fluxes amounts to characterizing the space of solutions to a mixed system of linear equalities, given by the stoichiometry matrix, and linear inequalities, arising from the irreversibility of some or all of the reactions in the network. Previous approaches to this problem have iteratively solved for the equalities while satisfying the inequalities throughout the process. In an extension of previous work, here we consider the complementary approach and derive an algorithm which satisfies the inequalities one by one while staying in the space of solution of the equality constraints. Benchmarks on different subnetworks of the central carbon metabolism of Escherichia coli show that this new approach yields a significant reduction in the execution time of the calculation. This reduction arises since the odds that an intermediate elementary flux already fulfills an additional inequality are larger than when having to satisfy an additional equality constraint.     

Comparing Stochastically Restricted Linear Estimators in a Regression Model

Conditions for superiority of the minimum dispersion estimator over another with respect to the covariance matrix are derived when the vector parameter of a regression model is subject to competing stochastic restrictions. The restrictions may also consist both of a deterministic part and a stochastic part.     

A restricted maximum likelihood estimator for truncated height samples

A restricted maximum likelihood (ML) estimator is presented and evaluated for use with truncated height samples. In the common situation of a small sample truncated at a point not far below the mean, the ordinary ML estimator suffers from high sampling variability. The restricted estimator imposes an a priori value on the standard deviation and freely estimates the mean, exploiting the known empirical stability of the former to obtain less variable estimates of the latter. Simulation results validate the conjecture that restricted ML behaves like restricted ordinary least squares (OLS), whose properties are well established on theoretical grounds. Both estimators display smaller sampling variability when constrained, whether the restrictions are correct or not. The bias induced by incorrect restrictions sets up a decision problem involving a bias-precision tradeoff, which can be evaluated using the mean squared error (MSE) criterion. Simulated MSEs suggest that restricted ML estimation offers important advantages when samples are small and truncation points are high, so long as the true standard deviation is within roughly 0.5 cm of the chosen value.     

Capuchin monkeys (Cebus apella) fail to show inequality aversion in a no-cost situation

Although humans show robust equality concerns across a variety of situations, there is ongoing debate regarding the extent to which any nonhuman species is inequality averse. In the current research, we test nonhuman primates' reactions to conspecifics receiving equal and unequal payoffs using a “no-cost” method in which subjects can respond to inequality without rejecting food. Specifically, we gave capuchin monkeys (Cebus apella) the opportunity to trade with one of two experimenters, each of whom offered the subject an identical reward, but had different histories of trading with the subject and a conspecific partner. An “equal” experimenter had previously given a conspecific the same reward that the subject had received, whereas the other experimenter was either an “advantageous trader” for the subject (giving the conspecific an inferior reward) or a “disadvantageous trader” for the subject (giving the conspecific a superior reward). By offering subjects a choice between experimenters, we removed several competing demands that may have masked the expression of robust equality preferences in previous studies. Even though there was no cost associated with expressing an equality preference, we found no evidence that capuchins differentiated between equal and unequal experimenters.     

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.     

Catch estimation in the presence of declining catch rate due to gear saturation

One strategy for estimating total catch is to employ two separate surveys that independently estimate total fishing effort and catch rate with the estimator for total catch formed by their product. Survey designs for estimating catch rate often involve interviewing the fishermen during their fishing episodes. Such roving designs result in incomplete episode data and characteristically have employed a model in which the catch rate is assumed to be constant over time. This article extends the problem to that of estimating total catch in the presence of a declining catch rate due, e.g., to gear saturation. Using a gill net fishery as an example, a mean-of-ratios type of estimator for the catch rate together with its variance estimator are developed. Their performance is examined using simulations, with special attention given to effects of restrictions on the roving survey window. Finally, data from a Fraser River gill net fishery are used to illustrate the use of the proposed estimator and to compare results with those from an estimator based on a constant catch rate.     

Tests for Order Restrictions in Binary Data

In this article, a general procedure is presented for testing for equality of k independent binary response probabilities against any given ordered alternative. The proposed methodology is based on an estimation procedure developed in Hwang and Peddada (1994, Annals of Statistics 22, 67-93) and can be used for a very broad class of order restrictions. The procedure is illustrated through application to two data sets that correspond to three commonly encountered order restrictions: simple tree order, simple order, and down turn order.     

Regression analysis when covariates are regression parameters of a random effects model for observed longitudinal measurements

We consider regression analysis when covariate variables are the underlying regression coefficients of another linear mixed model. A naive approach is to use each subject's repeated measurements, which are assumed to follow a linear mixed model, and obtain subject-specific estimated coefficients to replace the covariate variables. However, directly replacing the unobserved covariates in the primary regression by these estimated coefficients may result in a significantly biased estimator. The aforementioned problem can be evaluated as a generalization of the classical additive error model where repeated measures are considered as replicates. To correct for these biases, we investigate a pseudo-expected estimating equation (EEE) estimator, a regression calibration (RC) estimator, and a refined version of the RC estimator. For linear regression, the first two estimators are identical under certain conditions. However, when the primary regression model is a nonlinear model, the RC estimator is usually biased. We thus consider a refined regression calibration estimator whose performance is close to that of the pseudo-EEE estimator but does not require numerical integration. The RC estimator is also extended to the proportional hazards regression model. In addition to the distribution theory, we evaluate the methods through simulation studies. The methods are applied to analyze a real dataset from a child growth study.     

Penalized estimating equations

Penalty models--such as the ridge estimator, the Stein estimator, the bridge estimator, and the Lasso-have been proposed to deal with collinearity in regressions. The Lasso, for instance, has been applied to linear models, logistic regressions, Cox proportional hazard models, and neural networks. This article considers the bridge penalty model with penalty sigma(j)/beta(j)/gamma for estimating equations in general and applies this penalty model to the generalized estimating equations (GEE) in longitudinal studies. The lack of joint likelihood in the GEE is overcome by the penalized estimating equations, in which no joint likelihood is required. The asymptotic results for the penalty estimator are provided. It is demonstrated, with a simulation and an application, that the penalized GEE potentially improves the performance of the GEE estimator, and enjoys the same properties as linear penalty models.     

The Inequality Footprints of Nations: A Novel Approach to Quantitative Accounting of Income Inequality

In this study we use economic input-output analysis to calculate the inequality footprint of nations. An inequality footprint shows the link that each country''s domestic economic activity has to income distribution elsewhere in the world. To this end we use employment and household income accounts for 187 countries and an historical time series dating back to 1990. Our results show that in 2010, most developed countries had an inequality footprint that was higher than their within-country inequality, meaning that in order to support domestic lifestyles, these countries source imports from more unequal economies. Amongst exceptions are the United States and United Kingdom, which placed them on a par with many developing countries. Russia has a high within-country inequality nevertheless it has the lowest inequality footprint in the world, which is because of its trade connections with the Commonwealth of Independent States and Europe. Our findings show that the commodities that are inequality-intensive, such as electronic components, chemicals, fertilizers, minerals, and agricultural products often originate in developing countries characterized by high levels of inequality. Consumption of these commodities may implicate within-country inequality in both developing and developed countries.     

Sameness and difference in government equality talk

Abstract

This article discusses two sets of policy documents produced in the UK which form part of the ‘equality and diversity agenda' as it was articulated by the Labour government and which led to formulation of the 2006 and 2010 Equality Acts. These documents are critically examined in order to identify the underlying definitions and discourses of equality and diversity that they deploy. What definitions of ‘equality’ and ‘diversity’ provide the legitimating discursive structure within which debates about human rights, inequality and discrimination take place? What does this tell us about the understanding of the relationship of sameness and difference to equality, and the relationship between different differences in government equality talk? I argue that, in both cases, gestures towards recognizing the central importance of difference and towards a more intersectional approach to those differences are ultimately subverted by the liberal terms within which these challenges are understood.     

A Class of Ratio-Cum-Product-Type Estimator

The problem of estimating the population mean using an auxiliary information has been dealt with in literature quite extensively. Ratio, product, linear regression and ratio-type estimators are well known. A class of ratio-cum-product-type estimator is proposed in this paper. Its bias and variance to the first order of approximation are obtained. For an appropriate weight ‘a’ and good range of α-values, it is found that the proposed estimator is superior than a set of estimators (i.e., sample mean, usual ratio and product estimators, SRIVASTAVA's (1967) estimator, CHAKRABARTY's (1979) estimator and a product-type estimator) which are, in fact, the particular cases of it. At optimum value of α, the proposed estimator is as efficient as linear regression estimator.     

Relative index of inequality: definition, estimation, and inference

The relative index of inequality (RII) is a commonly used measure of the extent to which the occurrence of an outcome such as chronic illness or early death varies with socioeconomic status or some other background variable. The standard RII estimator applies only to linear variation in incidence rates. In this paper a general definition of the RII is introduced, alternative approaches to point estimation are considered, and a parametric bootstrap method is suggested for the construction of approximate confidence intervals. Estimation based on cubic splines fitted by maximum penalized likelihood is developed in some detail, and the proposed approach handles naturally the commonly needed adjustment for a 'standardizing' covariate such as age. Death rates in a large longitudinal study in England and Wales from 1996-2000 are analyzed in order to illustrate the various methods. A small simulation study explores the relative merits of different estimators. The approach based on cubic splines is found to reduce bias substantially, at the expense of some increase in variance, when variation in incidence rates is nonlinear.     

Some comments on anderson and pospahala's correction of bias in line transect sampling

ANDERSON and POSPAHALA (1970) investigated the estimation of wildlife population size using the belt or line transect sampling method and devised a correction for bias, thus leading to an estimator with interesting characteristics. This work was given a uniform mathematical framework in BURNHAM and ANDERSON (1976). In this paper we show that the ANDERSON-POSPAHALA estimator is optimal in the sense of being the (unique) best linear unbiased estimator within the class of estimators which are linear combinations of cell frequencies, provided certain assumptions are met.     

Additive partial linear models with measurement errors

We consider statistical inference for additive partial linearmodels when the linear covariate is measured with error. Wepropose attenuation-to-correction and simulation-extrapolation,simex, estimators of the parameter of interest. It is shownthat the first resulting estimator is asymptotically normaland requires no undersmoothing. This is an advantage of ourestimator over existing backfitting-based estimators for semiparametricadditive models which require undersmoothing of the nonparametriccomponent in order for the estimator of the parametric componentto be root-n consistent. This feature stems from a decreaseof the bias of the resulting estimator, which is appropriatelyderived using a profile procedure. A similar characteristicin semiparametric partially linear models was obtained by Wanget al. (2005). We also discuss the asymptotics of the proposedsimex approach. Finite-sample performance of the proposed estimatorsis assessed by simulation experiments. The proposed methodsare applied to a dataset from a semen study.     

A Class of Ratio Cum Product-Type Estimator in Double Sampling

A class of ratio cum product-type estimator is proposed in case of double sampling in the present paper. Its bias and variance to the first order of approximation are obtained. For an appropriate weight ‘a’ and a good range of α-values, it is found that the proposed estimator is more efficient than the set of estimator viz., simple mean estimator, usual ratio and product estimators, SRIVASTAVA 's estimator (1967), CHAKARBARTY 's estimator and product-type estimator, which are in fact the particular cases of it. The proposed estimator is as efficient as linear regression estimator in double sampling at optimum value of α.     

Estimating average annual percent change for disease rates without assuming constant change

The annual percent change (APC) is often used to measure trends in disease and mortality rates, and a common estimator of this parameter uses a linear model on the log of the age-standardized rates. Under the assumption of linearity on the log scale, which is equivalent to a constant change assumption, APC can be equivalently defined in three ways as transformations of either (1) the slope of the line that runs through the log of each rate, (2) the ratio of the last rate to the first rate in the series, or (3) the geometric mean of the proportional changes in the rates over the series. When the constant change assumption fails then the first definition cannot be applied as is, while the second and third definitions unambiguously define the same parameter regardless of whether the assumption holds. We call this parameter the percent change annualized (PCA) and propose two new estimators of it. The first, the two-point estimator, uses only the first and last rates, assuming nothing about the rates in between. This estimator requires fewer assumptions and is asymptotically unbiased as the size of the population gets large, but has more variability since it uses no information from the middle rates. The second estimator is an adaptive one and equals the linear model estimator with a high probability when the rates are not significantly different from linear on the log scale, but includes fewer points if there are significant departures from that linearity. For the two-point estimator we can use confidence intervals previously developed for ratios of directly standardized rates. For the adaptive estimator, we show through simulation that the bootstrap confidence intervals give appropriate coverage.     

The Geography of Gender Inequality

Reducing gender inequality is a major policy concern worldwide, and one of the Sustainable Development Goals. However, our understanding of the magnitude and spatial distribution of gender inequality results either from limited-scale case studies or from national-level statistics. Here, we produce the first high resolution map of gender inequality by analyzing over 689,000 households in 47 countries. Across these countries, we find that male-headed households have, on average, 13% more asset wealth and 303% more land for agriculture than do female-headed households. However, this aggregate global result masks a high degree of spatial heterogeneity, with bands of both high inequality and high equality apparent in countries and regions of the world. Further, areas where inequality is highest when measured by land ownership generally are not the same areas that have high inequality as measured by asset wealth. Our metrics of gender inequality in land and wealth are not strongly correlated with existing metrics of poverty, development, and income inequality, and therefore provide new information to increase the understanding of one critical dimension of poverty across the globe.