Multivariate sequential analysis with linear boundaries

Let $\{S_n=(X_n,W_n)\}_{n\ge0}$ be a random walk with $X_n\in \mathbb{R}$ and $W_n\in \mathbb{R}^m$. Let $\tau=\tau_a=\inf\{n:X_n>a\}$. The main results presented are two term asymptotic expansions for the joint distribution of $S_{\tau}$ and $\tau$ and the marginal distribution of $h(S_{\tau}/a,\tau/a)$ in the limit $a\to\infty$. These results are used to study the distribution of $t$-statistics in sequential experiments with sample size $\tau$, and to remove bias from confidence intervals based on Anscombe's theorem.Comment: Published at http://dx.doi.org/10.1214/074921706000000608 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Nonanticipating estimation applied to sequential analysis and changepoint detection

Suppose a process yields independent observations whose distributions belong to a family parameterized by \theta\in\Theta. When the process is in control, the observations are i.i.d. with a known parameter value \theta_0. When the process is out of control, the parameter changes. We apply an idea of Robbins and Siegmund [Proc. Sixth Berkeley Symp. Math. Statist. Probab. 4 (1972) 37-41] to construct a class of sequential tests and detection schemes whereby the unknown post-change parameters are estimated. This approach is especially useful in situations where the parametric space is intricate and mixture-type rules are operationally or conceptually difficult to formulate. We exemplify our approach by applying it to the problem of detecting a change in the shape parameter of a Gamma distribution, in both a univariate and a multivariate setting.Comment: Published at http://dx.doi.org/10.1214/009053605000000183 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

An idiographic approach to the fluctuation of appraisals and coping during a trapshooting competition

Events occurring during competition can impact athletes differently and influence their cognitive states and emotional states. Therefore, appraisal and coping processes are individual and can be understood better using an idiographic approach. The purpose of this study is two-fold: 1) to describe the nature of the fluctuation of emotional states and coping processes during the competition and 2) to propose an idiographic and ecologically valid method of study of these processes through the use of verbal protocols and sequential analysis. One master world-class elite (58 years old and 28 years of competitive experience) and one master 4th-category regional level trapshooter (59 years old and 30 of experience) participated in this study. Participants completed an affect grid after each shot during two competitions of the national trapshooting championship. Each competition was composed of 6 sets of 25 shots. After each set, participants provided verbal reports using a delayed verbal protocol procedure. This procedure consisted of identifying critical moments within the competition, and reporting thoughts and feelings immediately before and after each critical moment. Verbal reports were transcribed verbatim and coded according to Lazarus’ cognitive-motivational-relational theory of emotion. Units of information were submitted to event sequential analysis to determine the probability of occurrence of paired-events. The elite level athlete reported a stable pattern of pleasure and arousal levels, while the non-elite athlete reported greater fluctuation of emotional states. It was found great inter- and intra-individual variability depending on the context, but patterns of appraisal and coping were identified through sequential analysis

Depression, Relationship Quality, and Couples’ Demand/Withdraw and Demand/Submit Sequential Interactions

This study investigated the associations among depression, relationship quality, and demand/withdraw and demand/submit behavior in couples’ conflict interactions. Two 10-min conflict interactions were coded for each couple (N = 97) using Structural Analysis of Social Behavior (SASB; Benjamin, 1979a, 1987, 2000a). Depression was assessed categorically (via the presence of depressive disorders) and dimensionally (via symptom reports). Results revealed that relationship quality was negatively associated with demanding behavior, as well as receiving submissive or withdrawing behavior from one’s partner. Relationship quality was positively associated with withdrawal. Demanding behavior was positively associated with women’s depression symptoms but negatively associated with men’s depression symptoms. Sequential analysis revealed couples’ behavior was highly stable across time. Initiation of demand/withdraw and demand/submit sequences were negatively associated with partners’ relationship adjustment. Female demand/male withdraw was positively associated with men’s depression diagnosis. Results underscore the importance of sequential analysis when investigating associations among depression, relationship quality, and couples’ interpersonal behavior

SEQUENTIAL ANALYSIS OF AGRICULTURAL EXPERIMENTS

Interim monitoring of accumulating data has been widely used in clinical trials, but it has not received the same attention in agricultural experimentation. The methodology, however, can be a useful tool in agronomic trials designed to find better production techniques or optimal animal treatments at low cost, plus the possible economic advantages resulting from correct early decisions. These sequential procedures for testing hypothesis with available data in successive periods of time dictate termination of the experiment when a significant difference is detected, or otherwise continuation of the experiment to the end of the stipulated time or until all the planned sample size is realized. The statistical cost of repeated testing of part of the same data is a reduction in the significance levels a to the time-related significance levels αj (αj\u3cα). We apply three methods for this type of analysis, which we illustrate with two examples involving respectively, comparisons of two proportions and two means from normally distributed random variables with unknown variances. The examples show the usefulness and limitations of the proposed methods and also that there can be no absolute rule for choosing the best method of analysis in a particular case. The optimal strategy depends on the specifics of the trial and the investigator\u27s criterion to choose the αj

Robust Sequential Analysis for Special Capacities

Huber type robustness will be considered for some extensions of Wald\u27s Sequential Probability Ratio Test, including Wald\u27s three decision problem and the Kiefer-Weiss formulation. The results of Huber (1965, 1968), Huber and Strassen (1973), Rieder (1977) and Osterreicher (1978) will be extended to derive a least favorable tuple in the multiple decision problem. And then the asymptotically least favorable KieferWeiss procedure together with its asymptotic relative efficiency for the s-contamination and the total variation models will be discusse