A note on robustness of D-optimal block designs for two-colour microarray experiments

Two-colour microarray experiments form an important tool in gene expression analysis. Due to the high risk of missing observations in microarray experiments, it is fundamental to concentrate not only on optimal designs but also on designs which are robust against missing observations. As an extension of Latif et al. (2009), we define the optimal breakdown number for a collection of designs to describe the robustness, and we calculate the breakdown number for various D-optimal block designs. We show that, for certain values of the numbers of treatments and arrays, the designs which are D-optimal have the highest breakdown number. Our calculations use methods from graph theory.     

Evaluation of a method for setting confidence intervals on the common mean of two normal populations

Let X₁, , X₂, …, X be distributed N(µ, σ² _x), let Y₁, Y₂, …, Y"_n be distributed N(µ, σ² _y), and let X , X , … X_m, Y₁, Y₂, …, Y_n be mutually independent. In this paper a method for setting confidence intervals on the common mean µ is proposed and evaluated.     

Bayesian,MLE, and GMM Estimation of a Spot Rate Model

ABSTRACT

We develop Markov chain Monte Carlo algorithms for estimating the parameters of the short-term interest rate model. Using Monte Carlo experiments we compare the Bayes estimators with the maximum likelihood and generalized method of moments estimators. We estimate the model using the Japanese overnight call rate data.     

Optimal orthogonal block designs for four-mixture components in two blocks based on F-squares for Becker's models and K-model

Orthogonal block designs in mixture experiments have been extensively studied by various authors. Aggarwal et al. [M.L. Aggarwal, P. Singh, V. Sarin, and B. Husain, Mixture designs in orthogonal blocks using F-squares, METRON – Int. J. Statist. LXVII(2) (2009), pp. 105–128] considered the case of components assuming the same volume fractions and obtained mixture designs in orthogonal blocks using F-squares. In this paper, we have used the class of designs presented by Aggarwal et al. and have obtained D-, A- and E-optimal orthogonal block designs for four components in two blocks for Becker's mixture models and K-model, respectively. Orthogonality conditions for the considered models are also given.     

Measuring and framing support for universal basic income

We execute an original survey experiment to examine the extent and determinants of support for a nascent policy issue, universal basic income (UBI), in the American public. We explore the effects of how UBI is framed (either in the context of values or the context of policy), finding three key results. First, UBI is primarily a Democratic and liberal policy. Second, negative arguments against UBI move support for UBI more than positive arguments. Third, and surprisingly, respondents are equally affected by both policy-driven and value-driven arguments about UBI. In conclusion, an increase in messaging about UBI is likely to widen existing partisan differences in UBI support. These differences are unlikely to be won over by policy or values arguments.     

Are Groups More (or Less) Consistent Than Individuals?

There is now overwhelming experimental evidence that individuals systematically violate the axioms of Expected Utility theory. In reality, however, many economic decisions are taken by, or on behalf of, groups whose members have a joint stake in those decisions. This paper reports on an experiment in which pairs of individuals are tested for Common-Ratio inconsistencies. We find that the agreed choices of subject-pairs follow a pattern of inconsistency very close to that of individuals' choices. We also look for evidence that group participation increases the consistency of the individuals themselves. With one solitary exception, we find none.     

Pretrial Bargaining in the Face of a Random Court Decision: Evidence from Laboratory Games

If negotiation over ownership of an asset is unsuccessful, agents go to court to determine possession. Experiments examine how the presence of a stochastic court decision affects pretrial bargaining behavior. Two players have private information over the value of an asset, owned by one player. If there is no acceptable trade price, a random court decision assigns ownership. The impact of a second stage court decision on bargaining outcomes and the efficiency of trades is measured. Courts reduce the total earnings of players and the frequency of efficient trades. Relative earnings and bargaining behavior depend on which agent proposes the trade price.     

Remove unwanted variation retrieves unknown experimental designs

Remove unwanted variation (RUV) is an estimation and normalization system in which the underlying correlation structure of a multivariate dataset is estimated from negative control measurements, typically gene expression values, which are assumed to stay constant across experimental conditions. In this paper we derive the weight matrix which is estimated and incorporated into the generalized least squares estimates of RUV-inverse, and show that this weight matrix estimates the average covariance matrix across negative control measurements. RUV-inverse can thus be viewed as an estimation method adjusting for an unknown experimental design. We show that for a balanced incomplete block design (BIBD), RUV-inverse recovers intra- and interblock estimates of the relevant parameters and combines them as a weighted sum just like the best linear unbiased estimator (BLUE), except that the weights are globally estimated from the negative control measurements instead of being individually optimized to each measurement as in the classical, single measurement BIBD BLUE.     

A graphical evaluation of logistic ridge estimator in mixture experiments

In comparison to other experimental studies, multicollinearity appears frequently in mixture experiments, a special study area of response surface methodology, due to the constraints on the components composing the mixture. In the analysis of mixture experiments by using a special generalized linear model, logistic regression model, multicollinearity causes precision problems in the maximum-likelihood logistic regression estimate. Therefore, effects due to multicollinearity can be reduced to a certain extent by using alternative approaches. One of these approaches is to use biased estimators for the estimation of the coefficients. In this paper, we suggest the use of logistic ridge regression (RR) estimator in the cases where there is multicollinearity during the analysis of mixture experiments using logistic regression. Also, for the selection of the biasing parameter, we use fraction of design space plots for evaluating the effect of the logistic RR estimator with respect to the scaled mean squared error of prediction. The suggested graphical approaches are illustrated on the tumor incidence data set.