Estimation of a Conditional Mean in a Linear Regression Model after a Preliminary Test on Regression Coefficient

Consider the two linear regression models of Y_ij on X_ij, namely Y_ij = β_io + β_ij, X_ij + E_ij = 1, 2,…, n_i, i = 1, 2, where E_ij are assumed to be normally distributed with zero mean and common unknown variance σ². The problem of estimating the conditional mean of Y₁ for a given value of X₁ is considered when it is a priori suspected that β₁₀ = β₂₀ and β₁₁ = β₂₁. The preliminary test estimator is proposed. The exact expressions for the bias and the mean square error of the estimator are derived. The relative efficiency of the new estimator to the usual least square estimator based on the first regression alone is computed and is used to determine the appropriate value of the significance level of the preliminary test β₁₀ = β₂₀ and β₁₁ = β₂₁.     

The jackknife estimate of a Kaplan--Meier integral

We derive an explicit formula for the jackknife estimate ofa Kaplan-Meier integral. From this the asymptotic analysis ofthe jackknifed Kaplan-Meier process becomes straightforward.In a small simulation study it is demonstrated that jackknifingmay lead to a considerable reduction of the bias.     

Estimating Ratio of Proportions Using Auxiliary Information

The problem of estimation of ratio of population proportions is considered and a difference-type estimator is proposed using auxiliary information. The bias and mean squared error of the proposed estimator is found and compared to the usual estimator and also to WYNN'S (1976) type estimator. An example is included for illustration.     

A fast algorithm for the exact likelihood of stationary and partially nonstationary vector autoregressive-moving average processes

An expression for the likelihood function of a stationary vectorautoregressive-moving average process is developed. The expressionis very efficient numerically and applies to any stationarybut not necessarily invertible model. In particular, when themultivariate process is autoregressive, the exact likelihoodcan be evaluated with a small number of operations dependingon the order of the autoregressive operator and the processdimension, but not on the size of the observed series. The expressionalso provides an efficient method for the evaluation of theexact likelihood of a partially nonstationary vector autoregressive-movingaverage process, for which the determinant of the autoregressiveoperator has at least one unit root and the remaining rootsare outside the unit circle. This method does not require differencingthe series, so that complications caused by over-differencingthe series, such as noninvertibility and parameter identifiabilityproblems, are avoided. The results for autoregressive modelsare also applied to testing the stationarity and invertibilityof any autoregressive-moving average model with given parametervalues.     

In vivo noninvasive measurement of spatially resolved corneal elasticity in human eyes using Lamb wave optical coherence elastography

Current elastography techniques are limited in application to accurately assess spatially resolved corneal elasticity in vivo for human eyes. The air‐puff optical coherence elastography (OCE) with an eye motion artifacts correction algorithm is developed to distinguish the in vivo cornea vibration from the eye motion and visualize the Lamb wave propagation clearly in healthy subjects. Based on the Lamb wave model, the phase velocity dispersion curve in the high‐frequency is calculated to obtain spatially resolved corneal elasticity accurately with high repeatability. It is found that the corneal elasticity has regional variations and is correlated with intraocular pressure, which suggests that the method has the potential to provide noninvasive measurement of spatially resolved corneal elasticity in clinical practice.     

Sampling Methods for Estimating Breeding Population and Hunting Mortality of Game Birds

In this paper we will summarize some of the important sampling and non-sampling errors with special reference to the mail surveys on migratory game birds and aerial surveys on breeding birds in North America. Where possible, methods for controlling the errors will be indicated.