Results concerning the generalized partially linear single-index model

The central topic of this article is the estimation of parameters of the generalized partially linear single-index model (GPLSIM). Two numerical optimization procedures are presented and an S-plus program based on these procedures is compared to a program by Wand in a simulation setting. The results from these simulations indicate that the estimates for the new procedures are as good, if not better, than Wand's. Also, this program is much more flexible than Wand's since it can handle more general models. Other simulations are also conducted. The first compares the effects of using linear interpolation versus spline interpolation in an optimization procedure. The results indicate that by using spline interpolation one gets more stable estimates at a cost of increased computational time. A second simulation was conducted to assess the performance of a method for estimating the variance of alpha. A third set of simulations is carried out to determine the best criterion for testing that one of the elements of alpha is equal to zero. The GPLSIM is applied to a water quality data set and the results indicate an interesting relationship between gastrointestinal illness and turbidity (cloudiness) of drinking water.     

Books on probability ideas are reviewed

In this paper, semiparametric methods are applied to estimate multivariate volatility functions, using a residual approach as in [J. Fan and Q. Yao, Efficient estimation of conditional variance functions in stochastic regression, Biometrika 85 (1998), pp. 645–660; F.A. Ziegelmann, Nonparametric estimation of volatility functions: The local exponential estimator, Econometric Theory 18 (2002), pp. 985–991; F.A. Ziegelmann, A local linear least-absolute-deviations estimator of volatility, Comm. Statist. Simulation Comput. 37 (2008), pp. 1543–1564], among others. Our main goal here is two-fold: (1) describe and implement a number of semiparametric models, such as additive, single-index and (adaptive) functional-coefficient, in volatility estimation, all motivated as alternatives to deal with the curse of dimensionality present in fully nonparametric models; and (2) propose the use of a variation of the traditional cross-validation method to deal with model choice in the class of adaptive functional-coefficient models, choosing simultaneously the bandwidth, the number of covariates in the model and also the single-index smoothing variable. The modified cross-validation algorithm is able to tackle the computational burden caused by the model complexity, providing an important tool in semiparametric volatility estimation. We briefly discuss model identifiability when estimating volatility as well as nonnegativity of the resulting estimators. Furthermore, Monte Carlo simulations for several underlying generating models are implemented and applications to real data are provided.     

On partial linear additive isotonic regression

In this paper we discuss semiparametric additive isotonic regression models. We discuss the efficiency bound of the model and the least squares estimator under this model. We show that the ordinary least square estimator studied by Huang (2002) and Cheng (2009) for the semiparametric isotonic regression achieves the efficiency bound for the regular estimator when the true parameter belongs to the interior of the parameter space. We also show that the result by Cheng (2009) can be generalized to the case that the covariates are dependent on each other.     

Complex Latent Variable Modeling in Educational Assessment

Bayesian item response theory models have been widely used in different research fields. They support measuring constructs and modeling relationships between constructs, while accounting for complex test situations (e.g., complex sampling designs, missing data, heterogenous population). Advantages of this flexible modeling framework together with powerful simulation-based estimation techniques are discussed. Furthermore, it is shown how the Bayes factor can be used to test relevant hypotheses in assessment using the College Basic Academic Subjects Examination (CBASE) data.     

Local estimation for varying-coefficient models with longitudinal data

Varying-coefficient models are very useful for longitudinal data analysis. In this paper, we focus on varying-coefficient models for longitudinal data. We develop a new estimation procedure using Cholesky decomposition and profile least squares techniques. Asymptotic normality for the proposed estimators of varying-coefficient functions has been established. Monte Carlo simulation studies show excellent finite-sample performance. We illustrate our methods with a real data example.     

Attributing Outcomes to Social Policy Interventions – ‘Gold Standard’ or ‘Fool's Gold’ in Public Policy and Management?

In recent years there has been increased interest in outcome‐based social policy‐making and management. The UK has been in the forefront of this movement but similar movements have been identified internationally. This interest in outcome‐based decision‐making has been given particular impetus through the ‘results’‐based movement in evaluation and performance management since the 1980s, which has increased in scope over time, slowly changing its emphasis from cost reduction and measuring outputs to measuring outcomes. This change has been widely welcomed by policymakers, practitioners and academics. However, there is evidence that the reality is often rather less than the rhetoric. Moreover, the ‘attribution problem’ of attributing changes in outcomes to specific social policies has remained a major issue. The conceptual solution of constructing ‘cause‐and‐effect’ models, imported from the policy evaluation field, has only recently become common for operationalising these models. This article outlines the evolution of interest in outcome‐based social policy‐making up to recent times and the growing realization of the importance of the attribution problem. It then outlines both how the ‘cause‐and‐effect’ policy modelling approach can partially tackle the attribution problem, but also its inherent limitations. Lastly, the article uses several case studies in current UK social policy‐making to demonstrate the potential importance of the reasoning embedded within cause‐and‐effect models but also the dangers in policy‐making which adopts this approach without understanding its conceptual basis or in fields where it is inappropriate, given the current state of our knowledge of social policy systems.     

Statistical estimation of internal available bandwidth

This paper presents a method for using end-to-end available bandwidth measurements in order to estimate available bandwidth on individual internal links. The basic approach is to use a power transform on the observed end-to-end measurements, model the result as a mixture of spatially correlated exponential random variables, carryout estimation by moment methods, then transform back to the original variables to get estimates and confidence intervals for the expected available bandwidth on each link. Because spatial dependence leads to certain parameter confounding, only upper bounds can be found reliably. Simulations with ns2 show that the method can work well and that the assumptions are approximately valid in the examples.     

Assessing the performance of variational methods for mixed logistic regression models

We present a variational estimation method for the mixed logistic regression model. The method is based on a lower bound approximation of the logistic function [Jaakkola, J.S. and Jordan, M.I., 2000, Bayesian parameter estimation via variational methods. Statistics & Computing, 10, 25–37.]. Based on the approximation, an EM algorithm can be derived that results in a considerable simplification of the maximization problem in that it does not require the numerical evaluation of integrals over the random effects. We assess the performance of the variational method for the mixed logistic regression model in a simulation study and an empirical data example, and compare it to Laplace's method. The results indicate that the variational method is a viable choice for estimating the fixed effects of the mixed logistic regression model under the condition that the number of outcomes within each cluster is sufficiently high.     

Adaptation of the jackknifed ridge methods to the linear mixed models

The purpose of this article is to obtain the jackknifed ridge predictors in the linear mixed models and to examine the superiorities, the linear combinations of the jackknifed ridge predictors over the ridge, principal components regression, r?k class and Henderson's predictors in terms of bias, covariance matrix and mean square error criteria. Numerical analyses are considered to illustrate the findings and a simulation study is conducted to see the performance of the jackknifed ridge predictors.