A note on shrinkage factors in two stage testimation

We obtain a simple and natural testimator which has locally, at the parametric point corresponding to the prior knowledge, a smaller mean squared error than any other two stage testimator of a location or a scale parameter of an arbitrary distribution.     

Experimentation order in factorial designs: new findings

Under some very reasonable hypotheses, it becomes evident that randomizing the run order of a factorial experiment does not always neutralize the effect of undesirable factors. Yet, these factors do have an influence on the response, depending on the order in which the experiments are conducted. On the other hand, changing the factor levels is many times costly; therefore it is not reasonable to leave to chance the number of changes necessary. For this reason, run orders that offer the minimum number of factor level changes and at the same time minimize the possible influence of undesirable factors on the experimentation have been sought. Sequences which are known to produce the desired properties in designs with 8 and 16 experiments can be found in the literature. In this paper, we provide the best possible sequences for designs with 32 experiments, as well as sequences that offer excellent properties for designs with 64 and 128 experiments. The method used to find them is based on a mixture of algorithmic searches and an augmentation of smaller designs.     

Estimation of parameters in a generalized GMANOVA model based on an outer product analogy and least squares

This paper investigates estimation of parameters in a combination of the multivariate linear model and growth curve model, called a generalized GMANOVA model. Making analogy between the outer product of data vectors and covariance yields an approach to directly do least squares to covariance. An outer product least squares estimator of covariance (COPLS estimator) is obtained and its distribution is presented if a normal assumption is imposed on the error matrix. Based on the COPLS estimator, two-stage generalized least squares estimators of the regression coefficients are derived. In addition, asymptotic normalities of these estimators are investigated. Simulation studies have shown that the COPLS estimator and two-stage GLS estimators are alternative competitors with more efficiency in the sense of sample mean, standard deviations and mean of the variance estimates to the existing ML estimator in finite samples. An example of application is also illustrated.     

A Consistent Variance Estimator for 2SLS When Instruments Identify Different LATEs

Under treatment effect heterogeneity, an instrument identifies the instrument-specific local average treatment effect (LATE). With multiple instruments, two-stage least squares (2SLS) estimand is a weighted average of different LATEs. What is often overlooked in the literature is that the postulated moment condition evaluated at the 2SLS estimand does not hold unless those LATEs are the same. If so, the conventional heteroscedasticity-robust variance estimator would be inconsistent, and 2SLS standard errors based on such estimators would be incorrect. I derive the correct asymptotic distribution, and propose a consistent asymptotic variance estimator by using the result of Hall and Inoue (2003 Hall, A.R., and Inoue, A. (2003), “The Large Sample Behaviour of the Generalized Method of Moments Estimator in Misspecified Models,” Journal of Econometrics, 114, 361–394.[Crossref], [Web of Science ®] , [Google Scholar], Journal of Econometrics) on misspecified moment condition models. This can be used to correctly calculate the standard errors regardless of whether there is more than one LATE or not.     

A Two-stage Binary Optional Randomized Response Model

Social desirability bias (SDB) is the tendency in respondents to answer questions untruthfully in the hope of giving good impression to others. SDB occurs when the survey question is highly sensitive or personal. The Randomized Response Technique (RRT) is one of several methods to get around SDB in face-to-face interview surveys involving sensitive questions. In this article, we first review some of the existing binary response RRT models. Then, we propose a new model—Two-Stage Binary Optional RRT model. Much of the focus is on estimating π, the prevalence of sensitive characteristic, and ω, the sensitivity level of the underlying question. We discuss the asymptotic properties of our estimators and present some simulation results. It turns out that the proposed Two-Stage Binary Optional RRT model is more effective than the Optional RRT model proposed by Gupta (2001).     

A smoothed Q‐learning algorithm for estimating optimal dynamic treatment regimes

In this paper, we propose a smoothed Q‐learning algorithm for estimating optimal dynamic treatment regimes. In contrast to the Q‐learning algorithm in which nonregular inference is involved, we show that, under assumptions adopted in this paper, the proposed smoothed Q‐learning estimator is asymptotically normally distributed even when the Q‐learning estimator is not and its asymptotic variance can be consistently estimated. As a result, inference based on the smoothed Q‐learning estimator is standard. We derive the optimal smoothing parameter and propose a data‐driven method for estimating it. The finite sample properties of the smoothed Q‐learning estimator are studied and compared with several existing estimators including the Q‐learning estimator via an extensive simulation study. We illustrate the new method by analyzing data from the Clinical Antipsychotic Trials of Intervention Effectiveness–Alzheimer's Disease (CATIE‐AD) study.     

Conditionally unbiased estimation in the normal setting with unknown variances

To efficiently and completely correct for selection bias in adaptive two-stage trials, uniformly minimum variance conditionally unbiased estimators (UMVCUEs) have been derived for trial designs with normally distributed data. However, a common assumption is that the variances are known exactly, which is unlikely to be the case in practice. We extend the work of Cohen and Sackrowitz (Statistics & Probability Letters, 8(3):273-278, 1989), who proposed an UMVCUE for the best performing candidate in the normal setting with a common unknown variance. Our extension allows for multiple selected candidates, as well as unequal stage one and two sample sizes.     

Large sample test criteria on Toeplitz covariance structure

In the analysis of stationary stochastic process, one has to deal with covariance matrix of Toeplitz (or Laurent) structure. Such structure has a feature that not only the elements on the principal diagonal but also those lying on each of the parallel sub-diagonals are equal as well. The present investigation is on the problem of large sample testing of the Toeplitz pattern of the population covariance matrix. Apart from usual application of likelihood ratio and Rao’s efficient score criteria, some heuristic two-stage tests are suggested. The results of Monte Carlo experiment are reported for the size of the proposed tests.     

Split-plot designs with mirror image pairs as sub-plots

In this article we investigate two-level split-plot designs where the sub-plots consist of only two mirror image trials. Assuming third and higher order interactions negligible, we show that these designs divide the estimated effects into two orthogonal sub-spaces, separating sub-plot main effects and sub-plot by whole-plot interactions from the rest. Further we show how to construct split-plot designs of projectivity P≥3. We also introduce a new class of split-plot designs with mirror image pairs constructed from non-geometric Plackett-Burman designs. The design properties of such designs are very appealing with effects of major interest free from full aliasing assuming that 3rd and higher order interactions are negligible.     

Estimating reference ranges from stratified two-stage samples

We present methodology for estimating age-specific reference ranges by using data from two-stage samples. On the basis of the information obtained in the first stage, the initial sample is stratified and random subsamples are drawn from each stratum, where the selection probabilities in this second-stage sampling may be different across strata in the population. The variable for which the reference ranges are to be established is measured at the second phase. The approach involves maximum likelihood estimation of the parameters of the age-specific distributions and separate estimation of the population stratum probabilities. These are combined to yield estimates of the quantiles of interest. The issue of variance estimation for the estimated quantiles is also addressed. The methodology is applied to the estimation of reference ranges for a cognitive test score in a study of non-demented older Japanese-Americans.