A note on f statistics for instrumental variable regessions

The asymptotic distribution of the F statistic calculated from instrumental variable‘two stage least squares residuals is obtained.     

On invariant quadratic unbiased estimation of variance components

The present study deals with three different invarint quadratic unbiased estimators (IQUE) for variance components namely quadratic least squares estimators (QLSE), weighted quadratic least squares estimators (WQLSE) and Mitra type estimators (MTE). The variance and covariances of these three different estimators are presented for unbalanced one-way random model. The relative performances of these estimators are assessed based on different optimality criteria like, D-optimality, T-optimality and M-optimality together with variances of these estimators. As a result, it has been shown that MTE has optimal properties.     

Flexible estimation of serial correlation in nonlinear mixed models

In the conventional linear mixed-effects model, four structures can be distinguished: fixed effects, random effects, measurement error and serial correlation. The latter captures the phenomenon that the correlation structure within a subject depends on the time lag between two measurements. While the general linear mixed model is rather flexible, the need has arisen to further increase flexibility. In addition to work done in the area, we propose the use of spline-based modeling of the serial correlation function, so as to allow for additional flexibility. This approach is applied to data from a pre-clinical experiment in dementia which studied the eating and drinking behavior in mice.     

Standards of Probability Sampling for Legal Evidence

Brief recognition is given to bicentennials of the death of James Stirling (1692–1770) and birth of Ferdinand Rudolph Hassler (1770–1843); to sesquicentennials of the publication of the 3rd definitive edition of Laplace's Théorie analytique des probabilités, and of the births of William Chauvenet (1820–1870) and Isaac Todhunter (1820–1884); to centennials of the births of Louis Bachelier (1870–1946) and Jean Perrin (1870–1942); and to the semicentennial of the initial publication (1920) of Metron, an International Review of Statistics.     

Analysis of bivariate dichotomous data from a stratified two-stage cluster sample

In the health and social sciences, researchers often encounter categorical data for which complexities come from a nested hierarchy and/or cross-classification for the sampling structure. A common feature of these studies is a non-standard data structure with repeated measurements which may have some degree of clustering. In this paper, methodology is presented for the joint estimation of quantities of interest in the context of a stratified two-stage sample with bivariate dichotomous data. These quantities are the mean value π of an observed dichotomous response for a certain condition or time-point and a set of correlation coefficients for intra-cluster association for each condition or time period and for inter-condition correlation within and among clusters. The methodology uses the cluster means and pairwise joint probability parameters from each cluster. They together provide appropriate information across clusters for the estimation of the correlation coefficients.     

AN EXAMINATION OF ESTIMATED RESIDUALS IN A REGRESSION WITH AN INFINITE ORDER PARAMETRIC MODEL

We consider a linear regression with the error term that obeys an autoregressive model of infinite order and estimate parameters of the models. The parameters of the autoregressive model should be estimated based on estimated residuals obtained by means of the method of ordinary least squares, because the errors are unobservable. The consistency of the coefficients, variance and spectral density of the model obeyed by the error term is shown. Further, we estimate the coefficients of the linear regression by means of the method of estimated generalized least squares. We also show the consistency of the estimator.

     

Nonlinear voxel-based modelling of the haemodynamic response in fMRI

A common assumption for data analysis in functional magnetic resonance imaging is that the response signal can be modelled as the convolution of a haemodynamic response (HDR) kernel with a stimulus reference function. Early approaches modelled spatially constant HDR kernels, but more recently spatially varying models have been proposed. However, convolution limits the flexibility of these models and their ability to capture spatial variation. Here, a range of (nonlinear) parametric curves are fitted by least squares minimisation directly to individual voxel HDRs (i.e., without using convolution). A ‘constrained gamma curve’ is proposed as an efficient form for fitting the HDR at each individual voxel. This curve allows for spatial variation in the delay of the HDR, but places a global constraint on the temporal spread. The approach of directly fitting individual parameters of HDR shape is demonstrated to lead to an improved fit of response estimates.     

On the power of some tests for examining the stability of regression coefficients

The main objective of the study is to compare four different procedures to test for the stability of regression coefficients. The comparisons are based on a numerical study and are with respect to their abilities to detect various simple forms of parameter instabilities. Besides the power comparisons a special interest is directed towards the choice of “window length” in the tests based on moving sums of squared recursive and ordinary least-squares residuals.     

ESTIMATING PREDATOR-PREY SYSTEMS VIA ORDINARY DIFFERENTIAL EQUATIONS WITH CLOSED ORBITS

This paper considers periodic regression functions, which are solutions to a planar system of differential equations. In particular, it introduces a simple stochastic model which describes the interaction between predator and prey populations. The regression functions are solutions to the classical Lotka‐Volterra system of equations, which admits closed orbits. The proposed method of estimation can be applied whenever pairs of predator‐prey data are available, and the prey is the main source of food of the predator. Canadian mink‐muskrat data are analysed from this new viewpoint. The estimation method is based on the existence of closed trajectories that describe the relationship between the two population sizes, and the paper shows how it can be extended to other systems of differential equations which admit closed orbits (e.g. Hamiltonian systems).     

Asymptotic behavior of the grenander estimator at density flat regions

Over forty years ago, Grenander derived the MLE of a monotone decreasing density f with known mode. Prakasa Rao obtained the asymptotic distribution of this estimator at a fixed point x where f' (x) < 0. Here, we obtain the asymptotic distribution of this estimator at a fixed point x when f is constant and nonzero in some open neighborhood of x. This limiting distribution is expressible as the convolution of a closed-form density and a rescaled standard normal density. Groeneboom (1983) derived the aforementioned closed-form density and we provide an alternative, more direct derivation.