Block empirical likelihood for longitudinal partially linear regression models

The authors propose a block empirical likelihood procedure to accommodate the within‐group correlation in longitudinal partially linear regression models. This leads them to prove a nonparametric version of the Wilks theorem. In comparison with normal approximations, their method does not require a consistent estimator for the asymptotic covariance matrix, which makes it easier to conduct inference on the parametric component of the model. An application to a longitudinal study on fluctuations of progesterone level in a menstrual cycle is used to illustrate the procedure developed here.     

Parameter Estimation for a Discretely Observed Integrated Diffusion Process

Abstract.  We consider the estimation of unknown parameters in the drift and diffusion coefficients of a one-dimensional ergodic diffusion X when the observation is a discrete sampling of the integral of X at times i Δ , i  =  1 ,…, n . Assuming that the sampling interval tends to 0 while the total length time interval tends to infinity, we first prove limit theorems for functionals associated with our observations. We apply these results to obtain a contrast function. The associated minimum contrast estimators are shown to be consistent and asymptotically Gaussian with different rates for drift and diffusion coefficient parameters.     

Direct Inference, Probability, and a Conceptual Gulf in Risk Communication

Differences in the conceptual frameworks of scientists and nonscientists may create barriers to risk communication. This article examines two such conceptual problems. First, the logic of "direct inference" from group statistics to probabilities about specific individuals suggests that individuals might be acting rationally in refusing to apply to themselves the conclusions of regulatory risk assessments. Second, while regulators and risk assessment scientists often use an "objectivist" or "relative frequency" interpretation of probability statements, members of the public are more likely to adopt a "subjectivist" or "degree of confidence" interpretation when estimating their personal risks, and either misunderstand or significantly discount the relevance of risk assessment conclusions. If these analyses of inference and probability are correct, there may be a conceptual gulf at the center of risk communication that cannot be bridged by additional data about the magnitude of group risk. Suggestions are made for empirical studies that might help regulators deal with this conceptual gulf.     

The fiducial argument and hacking's principle of irrelevance

In a searching analysis of the fiducial argument Hacking (1965) proposed the Principle of Irrelevance as a condition under which the argument is valid. His statement of the Principle was essentially non-mathematical and this paper presents a mathematical development of the Principle. The relationship with likelihood inference is explored and some of the proposed counter-examples to fiducial theory are considered. It is shown that even with the Principle of Irrelevance examples of non-uniqueness of fiducial distributions exist.     

SPLINE SMOOTHER AS A DYNAMIC LINEAR MODEL

The paper shows how a finite dimensional representation of a cubic smoothing spline can be put in the framework of a dynamic linear model. The formulation provides an updating scheme when observations do not occur sequentially in time or space.     

Dependent masking and system life data analysis: Bayesian inference for two-component systems

Data from field operations of a system is often used to estimate the reliability of components. Under ideal circumstances, this system field data contains the time to failure along with information on the exact component responsible for the system failure. However, in many cases, the exact component causing the failure of the system cannot be identified, and is considered to be masked. Previously developed models for estimation of component reliability from masked system life data have been based upon the assumption that masking occurs independently of the true cause of system failure. In this paper we develop a Bayesian methodology for estimating component reliabilities from masked system life data when the probability of masking is dependent upon the true cause of system failure. The Bayesian approach is illustrated for the case of a two-component system of exponentially distributed components.     

Confidence Intervals for Scale

This paper explains the approach to parameter estimation based on the idea of simultaneous models. Instead of using a single shape—as for example the normal distribution—a simultaneous model uses a finite number of distinct shapes F, G, etc. Such simultaneous systems are tools in gauging the finite sample behavior of estimators. And they can be applied in the design of an estimator with prescribed desirable properties. The problem considered in this paper is interval estimation for a scale parameter. We discuss among other things the computation of optimal estimators in simultaneous models and study more closely the case of protecting against heavy-tailed error distributions.     

Conditional inference for subject-specific and marginal agreement: Two families of agreement measures

A two-stage procedure is described for assessing subject-specific and marginal agreement for data from a test-retest reliability study of a binary classification procedure. Subject-specific agreement is parametrized through the log odds ratio, while marginal agreement is reflected by the log ratio of the off-diagonal Poisson means. A family of agreement measures in the interval [-1, 1] is presented for both types of agreement. The conditioning argument described facilitates exact inference. The proposed methodology is demonstrated by way of an example involving hypothetical data chosen for illustrative purposes, and data from a National Health Survey Study (Rogot and Goldberg 1966).     

The interpretation of maximum-likelihood estimation

Maximum-likelihood estimation is interpreted as a procedure for generating approximate pivotal quantities, that is, functions u(X;θ) of the data X and parameter θ that have distributions not involving θ. Further, these pivotals should be efficient in the sense of reproducing approximately the likelihood function of θ based on X, and they should be approximately linear in θ. To this end the effect of replacing θ by a parameter ϕ = ϕ(θ) is examined. The relationship of maximum-likelihood estimation interpreted in this way to conditional inference is discussed. Examples illustrating this use of maximum-likelihood estimation on small samples are given.     

Some aspects of modern population mathematics

The purpose of this paper is to survey a number of the technical tools and models that have found use in the study of human and other populations, and to indicate some problems of current interest. These tools and models are varied: integral equations, nonlinear oscillations, differential geometry, dynamical systems, nonlinear operations, bifurcation theory, semigroup theory, martingale theory, Markov processes, diffusion processes, branching processes, ergodic theory, prediction theory and state-space models. A fairly extensive bibliography is provided. Also an Appendix has been added describing the analysis of a classical entomological data set.