Retrospective Change Point Detection: From Parametric to Distribution Free Policies

The literature displays change point detection problems in the context of one of the key issues that belong to testing statistical hypotheses. The main focus in this article is to review recent retrospective change point policies and propose new relevant procedures. Commonly, applied quality control purposes have declared statements of the change point problems. Various biostatistical and engineering applications cause consideration of an extended form of the change point problem. In this article, we consider parametric and distribution free generalized change point detection policies, attending to different contexts of optimality and robustness of the procedures. We conducted a broad Monte Carlo study to compare various parametric and nonparametric tests, also investigating a sensitivity of the change point detection policies with respect to assumptions required for correct executions of the procedures. An example based on real biomarker measurements is provided to judge our conclusions.     

Optimal stimulation level theory, exploratory consumer behaviour and product adoption: an analysis of underlying structures across product categories

Research of the last decades focused on answering several questions in view of optimum stimulation theory. Which variables do influence general explorative tendencies such as risk taking, variety seeking, or curiosity-motivated behaviour and how do the general explorative tendencies effect the willingness to choose new or familiar products on a repurchase occasion? The approach of this research is the attempt to analyse a wide range of variables, which have successfully been tested to influence innovative behaviour, within one simultaneous model. This research is applied across different product-categories. It is confirming the nomological validity of OSL-theory including some contextual variables by attesting a principal consistency between all (six) models that have been established throughout the range of several examined product categories. The parameters between inherent factors do not contradict when comparing the single models with each other, parameter values do only differ slightly according to category-specific peculiarities. As a consequence of these results, an overall fairly good picture is drawn of what is behind the keenness for innovations of early adopters in general (regardless of the product category).     

Stratified Double Sampling with Continuous Outcomes: Design and Analysis

We provide a method for estimating the sample mean of a continuous outcome in a stratified population using a double sampling scheme. The stratified sample mean is a weighted average of stratum specific means. It is assumed that the fallible and true outcome data are related by a simple linear regression model in each stratum. The optimal stratified double sampling plan, i.e. , the double sampling plan that minimizes the cost of sampling for fixed variances, or alternatively, minimizes the variance for fixed costs, is found and compared to a standard sampling plan. The design parameters are the total sample size and the number of doubly sampled units in each stratum. We show that the optimal double sampling plan is a function of the between-strata and within-strata cost and variance ratios. The efficiency gains, relative to standard sampling plans, under broad set of conditions, are considerable.     

RCBDs with a control

The randomized complete block designs, RCBDs, are among the most popular of block designs for comparing a set of experimental treatments. The question of this design's effectiveness when one of the treatments is a control is examined here. Optimality ranges are established for the RBCD in terms of the strength of interest in control comparisons. It is found that if the control treatment is of secondary interest, the RCBD, when not best, is typically near best. This is not so when comparisons with the control are of greater interest than those among the other treatments.     

Designs for two-colour microarray experiments

Summary.  Designs for two-colour microarray experiments can be viewed as block designs with two treatments per block. Explicit formulae for the A- and D-criteria are given for the case that the number of blocks is equal to the number of treatments. These show that the A- and D-optimality criteria conflict badly if there are 10 or more treatments. A similar analysis shows that designs with one or two extra blocks perform very much better, but again there is a conflict between the two optimality criteria for moderately large numbers of treatments. It is shown that this problem can be avoided by slightly increasing the number of blocks. The two colours that are used in each block effectively turn the block design into a row–column design. There is no need to use a design in which every treatment has each colour equally often: rather, an efficient row–column design should be used. For odd replication, it is recommended that the row–column design should be based on a bipartite graph, and it is proved that the optimal such design corresponds to an optimal block design for half the number of treatments. Efficient row–column designs are given for replications 3–6. It is shown how to adapt them for experiments in which some treatments have replication only 2.     

Optimal design for the Bradley–Terry paired comparison model

Paired comparisons are a popular tool for questionnaires in psychological marketing research. The quality of the statistical analysis of the responses heavily depends on the design, i.e. the choice of the alternatives in the comparisons. In this paper we show that the structure of locally optimal designs changes substantially with the parameters in the underlying utility. This fact is illustrated by elementary examples, where the optimal designs can be completely characterized. As an alternative maximin efficient designs are proposed which perform well for all parameter settings. Research supported by grant Ho 1286 of the German Research Council (Deutsche Forschungsgemeinschaft).     

Response-adaptive randomization for survival trials: the parametric approach

Summary.  Few references deal with response-adaptive randomization procedures for survival outcomes and those that do either dichotomize the outcomes or use a non-parametric approach. In this paper, the optimal allocation approach and a parametric response-adaptive randomization procedure are used under exponential and Weibull distributions. The optimal allocation proportions are derived for both distributions and the doubly adaptive biased coin design is applied to target the optimal allocations. The asymptotic variance of the procedure is obtained for the exponential distribution. The effect of intrinsic delay of survival outcomes is treated. These findings are based on rigorous theory but are also verified by simulation. It is shown that using a doubly adaptive biased coin design to target the optimal allocation proportion results in more patients being randomized to the better performing treatment without loss of power. We illustrate our procedure by redesigning a clinical trial.     

关联理论看幽默及对中国相声的话语分析

以语用学中Speber和Wilson所提出的关联理论为框架,从认知角度来解释幽默话语。指出理解幽默话语是人们通过对已知信息推理的不断修改与重考而找到最佳关联——幽默的真谛。同时因读者在理解时付出更多努力而获得补偿——开怀一笑。并以此为基础对传统幽默——中国相声进行分析研究,指出其幽默根源在于错误推理的表面合理性,即说话者选择的最佳关联与听话者心中的最佳关联产生鲜明的对照和冲突,旨在探求关联性和幽默之间的关系,以期待对言语幽默有更好的理解和欣赏。     

Scaling bias in pooled exponential random graph models

Researchers often use pooled exponential random graph models (ERGM) to analyze samples of networks. However, pooled ERGM—here, understood to include both meta-regression and combined estimation on a stacked adjacency matrix—may be biased if there is heterogeneity in the latent error variance (‘scaling’) of each lower-level model. This study explores the implications of scaling for pooled ERGM analysis. We illustrate that scaling can produce bias in pooled ERGM coefficients that is more severe than in single-network ERGM and we introduce two methods for reducing this bias. Simulations suggest that scaling bias can be large enough to alter conclusions about pooled ERGM coefficient size, significance, and direction, but can be substantially reduced by estimating the marginal effect within a block diagonal or random effects meta-regression framework. We illustrate each method in an empirical example using Add Health data on 15 in-school friendship networks. Results from the application illustrate that many substantive conclusions vary depending on choice of pooling method and interpretational quantity.