Simultaneous Statistical Inference Research Articles

Modeling Model Misspecification in Structural Equation Models

Structural equation models constrain mean vectors and covariance matrices and are frequently applied in the social sciences. Frequently, the structural equation model is misspecified to some extent. In many cases, researchers nevertheless intend to work with a misspecified target model of interest. In this article, a simultaneous statistical inference for sampling errors and model misspecification errors is discussed. A modified formula for the variance matrix of the parameter estimate is obtained by imposing a stochastic model for model errors and applying M-estimation theory. The presence of model errors is quantified in increased standard errors in parameter estimates. The proposed inference is illustrated with several analytical examples and an empirical application.

Simultaneous statistical inference in dynamic factor models: Chi-square approximation and model-based bootstrap

Statistical inference methodology in dynamic factor models (DFMs) is extended to the multiple testing context based on a central limit theorem for empirical Fourier transforms of multivariate time series. This theoretical result allows for employing a vector of Wald-type test statistics which asymptotically follows a multivariate chi-square distribution under the global null hypothesis when the observation horizon tends to infinity. Multiplicity-adjusted asymptotic multiple test procedures based on Wald statistics are compared with a model-based bootstrap procedure proposed in recent previous work. Monte Carlo simulations demonstrate that both the asymptotic multiple chi-square test with an appropriate multiplicity adjustment and the bootstrap-based multiple test procedure keep the family-wise error rate approximately at the predefined significance level. The estimation algorithm as well as the implementation of the testing procedures are described in detail and a real-life application is performed on European commodity data.

High-throughput arrays identify distinct genetic profiles associated with lymph node involvement in rectal cancer.

Preoperative clinical diagnosis of lymph node involvement guides treatment decisions for rectal cancer. Unfortunately, clinical staging still suffers from a lack of accuracy. The aim of this study was to evaluate objective genetic differences in primary rectal cancers with and without associated lymph node metastasis. cDNA microarrays were generated from fresh-frozen tumors. Normalized data underwent global unsupervised hierarchical clustering analysis, and discriminating genes were mapped. Top discriminating genes were compared between stage II and III rectal cancers by use of an empirical Bayes 2 group t test with the Statistical Analysis of Microarrays and the Reproducibility-Optimized Test Statistic software separately to guide data reduction and deal with the difficulties of simultaneous statistical inference. Ingenuity Pathways Analysis software was used to analyze discriminating genes in terms of function and biological processes. Fifty-five patients with stage II and 22 patients with stage III rectal adenocarcinomas not treated with chemoradiation were included. Two major unsupervised clusters emerged representing stage II and III cancers. In 1 cluster, 11 of 12 patients (92%) had stage III cancer; in the other cluster, 54 of 65 patients (83%) had stage II (p < 0.001). Five significantly differentially expressed genes characterized the stage III cluster: interleukin-8, 3-hydroxy-3-methylglutaryl coenzyme A synthase, carbonic anhydrase, ubiquitin, and cystatin (all p < 0.05). Of the 12 patients with differential expression of the 5 marker genes, only one had stage II cancer. Fifty-four of 55 stage II patients clustered with alternative expression patterns of the predictor genes. Differentially expressed genes are related to cancer-associated processes, pathways, and networks. The identified gene signatures have not yet been validated in independent patient populations. Distinct gene expression signatures from primary rectal adenocarcinomas can help differentiate the presence or absence of lymph node metastases. These data are informative, and validation of this gene signature may provide a novel approach for more appropriate individualized treatment selection.

Advanced Distribution Theory for SiZer

SiZer is a powerful method for exploratory data analysis. In this article approximations to the distributions underlying the simultaneous statistical inference are investigated, and large improvements are made in the approximation using extreme value theory. This results in improved size, and also in an improved global inference version of SiZer. The main points are illustrated with real data and simulated examples.

Systematic Approach for Validating Traffic Simulation Models

Modeling processes and model testing processes are discussed as parts of the model life cycle, and the tasks of these processes and their relations are highlighted. Of particular interest is the model validation process, which ensures that the model closely simulates what the real system does. A collection of validation techniques is presented to facilitate a systematic check of model performance from various perspectives. Under the qualitative category, a few graphical techniques are presented to help a visual examination of the differences between the simulation and the observation. Under the quantitative category, several statistical measures are discussed to quantify the goodness of fit; to achieve a higher level of confidence about model performance, a simultaneous statistical inference technique is proposed that tests both model accuracy and precision. As an illustrative example, these validation techniques are comprehensively applied to test an enhanced macroscopic simulation model, KWaves, in a systematic manner.

Calculation of critical values for Dunnett and Tamhane's step-up multiple test procedure

Dunnett and Tamhane (1992, J. Amer. Statist. Assoc. 87, 162–170; 1993, Statist. Probab. Lett. 16 (1), 55–58; 1995, Biometrics 51, 217–227) proposed a step-up testing procedure for comparing k treatments with a control and showed that it is often more powerful than its competitors, the single-step (Dunnett, 1955, J. Amer. Statist. Assoc. 50, 1096–1121) and the step-down (Miller, 1966, Simultaneous Statistical Inference, McGraw-Hill, New York; Dunnett and Tamhane, 1991, Statist Med. 10 (6), 939–947) procedures. However, the applications of the step-up procedure may be hindered by the lengthy time for computing the required critical values, especially when the design of experiment is unbalanced or the value of k is large. In this paper we propose some more efficient approaches to the computation of the critical values to make the step-up test more applicable.

Control-Variate Models of Common Random Numbers for Multiple Comparisons with the Best

Using common random numbers (CRN) in simulation experiment design is known to reduce the variance of estimators of differences in system performance. However, when more than two systems are compared, exact simultaneous statistical inference in conjunction with CRN is typically impossible. We introduce control-variate models of CRN that permit exact statistical inference, specifically multiple comparisons with the best. These models explain the effect of CRN via a linear regression of the simulation output on “control variates” that are functions of the simulation inputs. We establish theoretically, and illustrate empirically, that the control-variate models lead to sharper statistical inference in the sense that the probability of detecting differences in systems' performance is increased.

One-sided monte carlo tolerance limit factors in the case of the random effects one-way layout-an algorithm for application in statistical quality control

Assuming the statistical model of the random effects one-way layout under the usual conditions (normality and independence) and considering a realization of this model, the present paper treats the problem of the computation of one-sided tolerance limits for the corresponding defining random variable on the basis of the Monte Carlo method. Since subpopulations occurring in this scope can be considered as batches and since the model under consideration is sometimes called ‘cluster sampling model’, it is obvious that the present problem has important applications in the field of statistical quality control.—The Monte Carlo approach together with its realization by a computer program for the determination of such tolerance limit factors proved elementary and effective. In particular, in the important cases of limited sampling information (costs), this approach led to more realistic values in comparison, with other approaches. An additional problem occurring in connection with simultaneous statistical inference was solved by means of the Bonferroni inequality. Finally, the paper contains a computer program (FORTRAN 77) the applicability and use of which is shown by numerical examples.

Book Reviews

Book Reviews

A problem of multiple significance tests

Journal of Research in Science TeachingVolume 21, Issue 1 p. 105-106 Comments and CriticismFree Access A problem of multiple significance tests Ron Good, Ron Good Science Education, Florida State University, Tallahassee, Florida 32306Search for more papers by this author Ron Good, Ron Good Science Education, Florida State University, Tallahassee, Florida 32306Search for more papers by this author First published: January 1984 https://doi.org/10.1002/tea.3660210112Citations: 3AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL No abstract is available for this article. References Lindman, H. Analysis of variance in complex experimental designs. San Francisco: W. H. Freeman, 1974. Miller, R. Simultaneous statistical inference. New York: McGraw-Hill, 1966. Citing Literature Volume21, Issue1January 1984Pages 105-106 ReferencesRelatedInformation

Pattern analysis as simultaneous statistical inference.

Pattern analysis as simultaneous statistical inference.

Pattern analysis as simultaneous statistical inference.

Pattern analysis as simultaneous statistical inference.

Simultaneous inference in epidemiological studies.

Some difficulties encountered in using and interpreting significance tests in both exploratory and hypothesis testing epidemiological studies are discussed. Special consideration is given to the problems of simultaneous statistical inference--how are inferences to be modified when many significance tests are performed on the same set of data? Although some partial solutions are available, greater emphasis on estimation methods and less use of and reliance on significance testing in epidemiological studies is more appropriate.

On sequentially rejective subset selection procedures

A technique for selection procedures, called sequential rejection, is investigated. It is shown that this technique is posssible to apply to certain selection goals of the or nothing type, i.e. selecting a subset containing all good populations or selecting a subset containing no bad population. The analogy with existing sequential techniques in the general theory of simultaneous statistical inference is pointed out.

Simultaneous Statistical Inference on Interactions in Two-Way Analysis of Variance

Abstract Three statistics for testing additivity and making detailed inferences on interactions in a two-way setup are considered. The first method uses the well-known sum of squares for testing and yields Scheffe bounds for all contrasts; the second introduces a maximum characteristic root statistic and Roy bounds, but is restricted to product-type contrasts; the last is limited to tetrad differences and its statistic is the maximum of all such differences. Bounds on percentage points for this maximum are provided in the appendix. Uses of the three methods in inferring various types of interaction contrasts are discussed and illustrated.

Simultaneous Statistical Inference on Interactions in Two-Way Analysis of Variance

Abstract Three statistics for testing additivity and making detailed inferences on interactions in a two-way setup are considered. The first method uses the well-known sum of squares for testing and yields Scheffé bounds for all contrasts; the second introduces a maximum characteristic root statistic and Roy bounds, but is restricted to product-type contrasts; the last is limited to tetrad differences and its statistic is the maximum of all such differences. Bounds on percentage points for this maximum are provided in the appendix. Uses of the three methods in inferring various types of interaction contrasts are discussed and illustrated.