Identifying Preferences for Conditional Cooperation Using Individual Beliefs

The relationship between contributions and elicited beliefs in a repeated two-person public good experiment is modeled with the help of a parsimounious random-utility function that allows for conditionally cooperative, opportunistic, and altruistic patterns of behavior. Under standard assumptions, a latent-class mixed logit specification with three sub-populations is shown to capture well heterogeneity in individual contribution levels over time, while also accomodating for different degrees of heteroscedasticity. The estimation results are consistent with the conjecture that the majority of players in public goods games are strongly conditional cooperators, with smaller fractions of the population leaning to opportunistic or altruistic behavior.     

Nonparametric Predictive Inference for Ordinal Data

Nonparametric predictive inference (NPI) is a powerful frequentist statistical framework based only on an exchangeability assumption for future and past observations, made possible by the use of lower and upper probabilities. In this article, NPI is presented for ordinal data, which are categorical data with an ordering of the categories. The method uses a latent variable representation of the observations and categories on the real line. Lower and upper probabilities for events involving the next observation are presented, and briefly compared to NPI for non ordered categorical data. As application, the comparison of multiple groups of ordinal data is presented.     

Optimal Simultaneous Confidence Bands in Multiple Linear Regression with Predictor Variables Constrained in an Ellipsoidal Region

A simultaneous confidence band provides useful information on the plausible range of an unknown regression model function, just as a confidence interval gives the plausible range of an unknown parameter. For a multiple linear regression model, confidence bands of different shapes, such as the hyperbolic band and the constant width band, can be constructed and the predictor variable region over which a confidence band is constructed can take various forms. One interesting but unsolved problem is to find the optimal (shape) confidence band over an ellipsoidal region χ_E under the Minimum Volume Confidence Set (MVCS) criterion of Liu and Hayter (2007 Liu, W., Hayter, A.J. (2007). Minimum area confidence set optimality for confidence bands in simple linear regression. J. Amer. Statist. Assoc. 102:181–190.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) and Liu et al. (2009 Liu, W., Bretz, F., Hayter, A.J., Wynn, H.P. (2009). Assessing non-superiority, non-inferiority or equivalence when comparing two regression models over a restricted covariate region. Biometrics 65:1279–1287.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). This problem is challenging as it involves optimization over an unknown function that determines the shape of the confidence band over χ_E. As a step towards solving this difficult problem, in this paper, we introduce a family of confidence bands over χ_E, called the inner-hyperbolic bands, which includes the hyperbolic and constant-width bands as special cases. We then search for the optimal confidence band within this family under the MVCS criterion. The conclusion from this study is that the hyperbolic band is not optimal even within this family of inner-hyperbolic bands and so cannot be the overall optimal band. On the other hand, the constant width band can be optimal within the family of inner-hyperbolic bands when the region χ_E is small and so might be the overall optimal band.     

An Improved Procedure of Estimating the Finite Population Mean Using Auxiliary Information in the Presence of Random Non Response

This article deals with the problem of estimation of the finite population mean using auxiliary information in the presence of random non response. Three different situations where random non response occurs either in study variate, or in auxiliary variate, or in both the variates, have been discussed. The asymptotically optimum estimators (AOEs) for each strategy are also identified. Expressions of biases and mean squared errors of the proposed estimators have been derived up to the first degree of approximation. Proposed estimators have been compared with the usual unbiased estimator, ratio estimator, and product estimator in the presence of random non response. Empirical studies are also carried out to show the performance of the proposed estimators over other estimators.     

Generalized Estimating Equations for Symmetric Distributions Observed with Admixture

A semiparametric two-component mixture model is considered, in which the distribution of one (primary) component is unknown and assumed symmetric. The distribution of the other component (admixture) is known. Generalized estimating equations are constructed for the estimation of the mixture proportion and the location parameter of the primary component. Asymptotic normality of the estimates is demonstrated and the lower bound for the asymptotic covariance matrix is obtained. An adaptive estimation technique is proposed to obtain the estimates with nearly optimal asymptotic variances.     

Bayesian shrinkage estimates for regression coefficients in m populations

For a linear regression model over m populations with separate regression coefficients but a common error variance, a Bayesian model is employed to obtain regression coefficient estimates which are shrunk toward an overall value. The formulation uses Normal priors on the coefficients and diffuse priors on the grand mean vectors, the error variance, and the between-to-error variance ratios. The posterior density of the parameters which were given diffuse priors is obtained. From this the posterior means and variances of regression coefficients and the predictive mean and variance of a future observation are obtained directly by numerical integration in the balanced case, and with the aid of series expansions in the approximately balanced case. An example is presented and worked out for the case of one predictor variable. The method is an extension of Box & Tiao's Bayesian estimation of means in the balanced one-way random effects model.     

Bayesian Estimation of the Regression Model with Autocorrelated Errors Under Contamination

In this article, the Bayesian analysis of the regression model with errors terms generated by a first-order autoregressive model is considered. Our aim is to study the effect of two kinds of contamination of this model via the posterior distribution of the regression parameter.     

On an application of the diffusion approximation of the generalized birth and death process for stochastic population projection

Assuming that both birth and death rates are density and time dependent, a diffusion approximation of the generalized birth and death process has been considered in this paper to obtain a suitable stochastic population model describing the population size and its moments. A simple method of estimating the parameters of the model Is discussed. The predictions of the expected size of the population, and the variance are made and compared with the corresponding census figures as well as with another deterministic projection series made for the corresponding period.     

Estimating the mean of the selected uniform population

Let π_i(i=1,2,…K) be independent U(0,?_i) populations. Let Y_i denote the largest observation based on a random sample of size n from the i-th population. for selecting the best populaton, that is the one associated with the largest ?_i, we consider the natural selection rule, according to which the population corresponding to the largest Y_i is selected. In this paper, the estimation of M. the mean of the selected population is considered. The natural estimator is positively biased. The UMVUE (uniformly minimum variance unbiased estimator) of M is derived using the (U,V)-method of Robbins (1987) and its asymptotic distribution is found. We obtain a minimax estimator of M for K≤4 and a class of admissible estimators among those of the form cY_max. For the case K = 2, the UMVUE is improved using the Brewster-Zidek (1974) Technique with respect to the squared error loss function L₁ and the scale-invariant loss function L₂. For the case K = 2, the MSE'S of all the estimators are compared for selected values of n and ρ=?₁/(?₁+?₂).     

The Gaussian Mixture Dynamic Conditional Correlation Model: Parameter Estimation,Value at Risk Calculation,and Portfolio Selection

A multivariate generalized autoregressive conditional heteroscedasticity model with dynamic conditional correlations is proposed, in which the individual conditional volatilities follow exponential generalized autoregressive conditional heteroscedasticity models and the standardized innovations follow a mixture of Gaussian distributions. Inference on the model parameters and prediction of future volatilities are addressed by both maximum likelihood and Bayesian estimation methods. Estimation of the Value at Risk of a given portfolio and selection of optimal portfolios under the proposed specification are addressed. The good performance of the proposed methodology is illustrated via Monte Carlo experiments and the analysis of the daily closing prices of the Dow Jones and NASDAQ indexes.