A Lepskiĭ-type stopping rule for the covariance estimation of multi-dimensional Lévy processes

We suppose that a Lévy process is observed at discrete time points. Starting from an asymptotically minimax family of estimators for the continuous part of the Lévy Khinchine characteristics, i.e., the covariance, we derive a data-driven parameter choice for the frequency of estimating the covariance. We investigate a Lepskiĭ-type stopping rule for the adaptive procedure. Consequently, we use a balancing principle for the best possible data-driven parameter. The adaptive estimator achieves almost the optimal rate. Numerical experiments with the proposed selection rule are also presented.

Measuring language ability of students with compensatory multidimensional CAT: A post-hoc simulation study

The computerized adaptive tests (CAT) apply an adaptive process in which the items are tailored to individuals' ability scores. The multidimensional CAT (MCAT) designs differ in terms of different item selection, ability estimation, and termination methods being used. This study aims at investigating the performance of the MCAT designs used to measure the language ability of students and to compare the results of MCAT designs with the outcomes of corresponding paper–pencil tests. For this purpose, items in the English Proficiency Tests (EPT) were used to create a multi-dimensional item pool that consists of 599 items. The performance of the MCAT designs was evaluated and compared based on the reliability coefficients, root means square error (RMSE), test-length, and root means squared difference (RMSD) statistics, respectively. Therefore, 36 different conditions were investigated in total. The results of the post-hoc simulation designs indicate that the MCAT designs with the A-optimality item selection method outperformed MCAT designs with other item selection methods by decreasing the test length and RMSD values without any sacrifice in test reliability. Additionally, the best error variance stopping rule for each MCAT algorithm with A-optimality item selection could be considered as 0.25 with 27.9 average test length and 30 items for the fixed test-length stopping rule for the Bayesian MAP method. Overall, MCAT designs tend to decrease the test length by 60 to 65 percent and provide ability estimations with higher precision compared to the traditional paper–pencil tests with 65 to 75 items. Therefore, it is suggested to use the A-optimality method for item selection and the Bayesian MAP method for ability estimation for the MCAT designs since the MCAT algorithm with these specifications shows better performance than others.

Expected Value of Sample Information to Guide the Design of Group Sequential Clinical Trials

Introduction Adaptive designs allow changes to an ongoing trial based on prespecified early examinations of accrued data. Opportunities are potentially being missed to incorporate health economic considerations into the design of these studies. Methods We describe how to estimate the expected value of sample information for group sequential design adaptive trials. We operationalize this approach in a hypothetical case study using data from a pilot trial. We report the expected value of sample information and expected net benefit of sampling results for 5 design options for the future full-scale trial including the fixed-sample-size design and the group sequential design using either the Pocock stopping rule or the O’Brien-Fleming stopping rule with 2 or 5 analyses. We considered 2 scenarios relating to 1) using the cost-effectiveness model with a traditional approach to the health economic analysis and 2) adjusting the cost-effectiveness analysis to incorporate the bias-adjusted maximum likelihood estimates of trial outcomes to account for the bias that can be generated in adaptive trials. Results The case study demonstrated that the methods developed could be successfully applied in practice. The results showed that the O’Brien-Fleming stopping rule with 2 analyses was the most efficient design with the highest expected net benefit of sampling in the case study. Conclusions Cost-effectiveness considerations are unavoidable in budget-constrained, publicly funded health care systems, and adaptive designs can provide an alternative to costly fixed-sample-size designs. We recommend that when planning a clinical trial, expected value of sample information methods be used to compare possible adaptive and nonadaptive trial designs, with appropriate adjustment, to help justify the choice of design characteristics and ensure the cost-effective use of research funding. Highlights Opportunities are potentially being missed to incorporate health economic considerations into the design of adaptive clinical trials. Existing expected value of sample information analysis methods can be extended to compare possible group sequential and nonadaptive trial designs when planning a clinical trial. We recommend that adjusted analyses be presented to control for the potential impact of the adaptive designs and to maintain the accuracy of the calculations. This approach can help to justify the choice of design characteristics and ensure the cost-effective use of limited research funding.

Optimal Stopping of a Random Sequence with Unknown Distribution

The subject of this paper is the problem of optimal stopping of a sequence of independent and identically distributed random variables with unknown distribution. We propose a stopping rule that is based on relative ranks and study its performance as measured by the maximal relative regret over suitable nonparametric classes of distributions. It is shown that the proposed rule is first-order asymptotically optimal and nearly rate optimal in terms of the rate at which the relative regret converges to zero. We also develop a general method for numerical solution of sequential stopping problems with no distributional information and use it in order to implement the proposed stopping rule. Some numerical experiments illustrating performance of the rule are presented as well.

Cost-effective clinical trial design: Application of a Bayesian sequential model to the ProFHER pragmatic trial

Background/Aims: There is growing interest in the use of adaptive designs to improve the efficiency of clinical trials. We apply a Bayesian decision-theoretic model of a sequential experiment using cost and outcome data from the ProFHER pragmatic trial. We assess the model’s potential for delivering value-based research. Methods: Using parameter values estimated from the ProFHER pragmatic trial, including the costs of carrying out the trial, we establish when the trial could have stopped, had the model’s value-based stopping rule been used. We use a bootstrap analysis and simulation study to assess a range of operating characteristics, which we compare with a fixed sample size design which does not allow for early stopping. Results: We estimate that application of the model could have stopped the ProFHER trial early, reducing the sample size by about 14%, saving about 5% of the research budget and resulting in a technology recommendation which was the same as that of the trial. The bootstrap analysis suggests that the expected sample size would have been 38% lower, saving around 13% of the research budget, with a probability of 0.92 of making the same technology recommendation decision. It also shows a large degree of variability in the trial’s sample size. Conclusions: Benefits to trial cost stewardship may be achieved by monitoring trial data as they accumulate and using a stopping rule which balances the benefit of obtaining more information through continued recruitment with the cost of obtaining that information. We present recommendations for further research investigating the application of value-based sequential designs.

A Model of Position Effects in the Sequential Lineup

What is the effect of placing the suspect in different positions in a sequential lineup? To explore this question, we developed and applied a model called the Independent Sequential Lineup model which analyzes a sequential lineup in terms of both identification position, the position at which the witness identifies a lineup item as the target, and target position, the position at which the target or suspect appears. We conducted a large-scale online eyewitness memory experiment with 7,204 participants each of whom was tested on a 6-item sequential lineup with an explicit stopping rule. The model fit these data well and revealed systematic effects of lineup position on underlying discriminability and response criteria. We also fit the model to data from a similar pair of experiments conducted recently by Wilson, Donnelly, Christenfeld and Wixted (2019; Journal of Memory and Language, 104, 108-125) both with and without application of a stopping rule. In all data sets, if a stopping rule is applied, underlying discriminability was found to be constant, or to increase slightly, across target position. In the absence of a stopping rule, discriminability was found to decrease substantially. We also observed a substantial increase in response criteria following presentation of the target. We discuss the implications of these findings for current theories of recognition memory and current applications of the sequential lineup in different jurisdictions.

Comparative Study of Clustering-Based Outliers Detection Methods in Circular-Circular Regression Model

This paper is a comparative study of several algorithms for detecting multiple outliers in circular-circular regression model based on the clustering algorithms. Three measures of similarity based on the circular distance were used to obtain a cluster tree using the agglomerative hierarchical methods. A stopping rule for the cluster tree based on the mean direction and circular standard deviation of the tree height was used as the cutoff point and classifier to the cluster group that exceeded the stopping rule as potential outliers. The performances of the algorithms have been demonstrated using the simulation studies that consider several outlier scenarios with a certain degree of contamination. Application to real data using wind data and a simulated data set are given for illustrative purposes. Thus, it has been found that Satari’s algorithm (S-SL algorithm) performs well for any values of sample size n and error concentration parameter. The algorithms are good in identifying outliers which are not limited to one or few outliers only, but the presence of multiple outliers at one time.

The representativeness heuristic at work in decision-making: building blocks and individual-level cognitive and behavioral factors

PurposeThis paper aims to develop a conceptual framework on how the representativeness heuristic operates in the decision-making process. Specifically, the authors unbundle representativeness into its building blocks: search rule, stopping rule and decision rule. Furthermore, the focus is placed on how individual-level cognitive and behavioral factors, namely experience, intuition and overconfidence, affect the functioning of this heuristic.Design/methodology/approachFrom a theoretical standpoint, the authors build on dual-process theories and on the adaptive toolbox view from the “fast and frugal heuristics” perspective to develop an integrative conceptual framework that uncovers the mechanisms underlying the representativeness heuristic.FindingsThe authors’ conceptualization suggests that the search rule used in representativeness is based on analogical mapping from previous experience, the stopping rule is the representational stability of the analogs and the decision rule is the choice of the alternative upon which there is a convergence of representations and that exceeds the decision maker's aspiration level. In this framework, intuition may help the decision maker to cross-map potentially competing analogies, while overconfidence affects the search time and costs and alters both the stopping and the decision rule.Originality/valueThe authors develop a conceptual framework on representativeness, as one of the most common, though still poorly investigated, heuristics. The model offers a nuanced perspective that explores the cognitive and behavioral mechanisms that shape the use of representativeness in decision-making. The authors also discuss the theoretical implications of their model and outline future research avenues that may further contribute to enriching their understanding of decision-making processes.

The goal is attainable: the effects of goal gradient and sub-goals on escalation of commitment in a new product evaluation

Purpose The purpose of this study is to investigate whether, in the context of making a go/no-go decision regarding a failing new product, the use of a stopping rule and/or a new decision-maker would reduce the escalation of commitment (EOC). Design/methodology/approach This study uses a classroom experiment design and uses logistic regression and a chi-square test to analyze its data. Findings The findings show that both responsible and non-responsible participants are more likely to perceive the negative performance of a new product as less negative and believe that the goal for the product can be reached when there is a stopping rule and proximal negative feedback indicates a level of performance below but very close to it than when there is no stopping rule. Therefore, they are more likely to continue the failing new product, whether they are responsible for the product or not. However, non-responsible decision-makers are more likely than their responsible counterparts to discontinue the failing new product in the absence of a stopping rule. Research limitations/implications This paper extends the theory of EOC by showing that the use of a stopping rule and/or a new decision-maker may not reduce EOC. Practical implications This paper provides useful guidelines for managers on how to reduce EOC. Originality/value The originality and value of this paper are found in the investigation of a situation in which the use of a stopping rule and/or a new decision-maker may not reduce the EOC.