Random coefficient regression models have received considerable attention, especially from econometricians. Previous work has assumed that the coefficients have normal distributions. The variances of the coefficients have, in previous papers, been estimated by maximum likelihood or by least squares methodology applied to the squared residuals from a preliminary (unweighted) fit. Maximum likelih...

When design decisions are informed by consumer choice models, uncertainty in choice model predictions creates uncertainty for the designer. We investigate the variation and accuracy of market share predictions by characterizing fit and forecast accuracy of discrete choice models for the US light duty new vehicle market. Specifically, we estimate multinomial logit models for 9000 utility functio...

tion (DMS-08-06199). We are grateful to two referees and an Associate Editor for their constructive comments and careful reading. Summary The proposed functional varying coefficient model provides a versatile and flexible analysis tool for relating longitudinal responses to longitudinal predictors. Specifically , this approach provides a novel representation of varying coefficient functions thr...

This paper describes a recursive method for estimating random coefficient models. Starting with a trial value for the moments of the distribution of coefficients in the population, draws are taken and then weighted to represent draws from the conditional distribution for each sampled agent (i.e., conditional on the agent’s observed dependent variable.) The moments of the weighted draws are calc...

Abstract. We analyze the statistical properties of nonparametrically estimated functions in a functional-coefficient model if the data has a unit root. We show that the estimated function converges at a faster rate than under the stationary case. However, the estimator has a mixed normal distribution so that point-wise confidence intervals are calculated using the usual normal distribution theo...

Recently there has been considerable work on stochastic time-varying coefficient models as vehicles for modelling structural change in the macroeconomy with a focus on the estimation of the unobserved sample path of time series of coefficient processes. The dominant estimation methods, in this context, are various filters, such as the Kalman filter, that are applicable when the models are cast ...

This work is concerned with nonlinear time series models and, in particular, with nonparametric models for the dynamics of the mean of the time series. We build on the functional-coefficient autoregressive (FAR) model of Chen and Tsay (1993) which is a generalization of the autoregressive (AR) model where the coefficients are varying and are given by functions of the lagged values of the series...

Random Coefficient AutoRegressive (RCAR) models are obtained by introducing random coefficients to an AR or more generally ARMA model. These models have second order properties similar to that of ARCH and GARCH models. In this article, a Bayesian approach to estimate the first order RCAR models is considered. A couple of Bayesian testing criteria for the unit-root hypothesis are proposed: one i...

In this paper we consider the problem of testing for a general parametric form against a nonparametric alternative for a coefficient function in a varying coefficient multivariate regression model. We propose a test statistic and derive its asymptotic null and alternative distributions. We analyze the asymptotic power of the test in shrinking neighborhoods of the null hypothesis, and show that ...

We propose a possible statistical model for both contextual analysis and slopes as outcomes analysis. These techniques have been used in multilevel analysis for quite some time, but a precise specification of the regression models has not been given before. We formalize them by proposing a random coefficient regression model, and we investigate its statistical properties in some detail. Various...