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Modeling of variation propagation in multistation assembly processes is crucial in predicting product dimensional quality and general performance of manufacturing systems. Based on the state space modeling, this paper develops a variation propagation model, which can be applied for analysis of various tolerances such as size tolerance, bonus tolerance, floating tolerance, etc. The nonstationary tolerance/variation (varying variance) caused by bonus tolerance and floating tolerance is properly handled by the proposed method. Thus, by using the developed variation propagation model, the variations on key product characteristics (KPCs) can be accurately predicted. This enables broad applications of the proposed method in actual manufacturing processes. The results of the case study also validated the proposed model. [DOI: 10.1115/1.4000094]

A state space representation for smoothing spline ANOVA (SS ANOVA) that addresses the problems of heavy computational burden of the process is presented. Such a representation not only leads to high computational efficiency, but also allows the algorithm to be implemented in an online setting.

Values of a dependent variable are created with linear construction formulae, with or without a product team to study as to whether ANOVA is fit to detect interaction in a fixed 2 * 2 design. The results recommend abandoning the fixed ANOVA model for the study of interaction effects and using a regression model to assess level values of each variable instead.

The objective was to compare the performance of a recently derived, new method of estimating variances and covariances with any mixed linear mode] and any pattern of missing data with that of restricted maximum likelihood. For each of 96 combinations of six three-herd x four-sire unbalanced designs of 39 offspring each, four heritability values, two ratios of sire variance to interaction variance, and two distributions (multivariate normal and multivariate [chi square], 3 df), 15,000 vectors (n = 39) were generated. Least squares Lehmann-Scheffe (LSLS) estimators of sire variance, interaction variance, and heritability were compared to those of REML with the performance measures of percentage of estimates (of the 15,000) that were positive, mean square error, variance, percentage of estimates within [+ or -] 50% of the parameter, bias, maximum value, skewness, and kurtosis. The LSLS method vastly outperformed REML in almost all 96 combinations. Averaged over the 48 combinations with multivariate normal data, the average percentage that REML estimators of heritability performed relative to those of LSLS for the first five of the above listed eight performance measures was -100%. The number of times LSLS was better than REML was 235 out of 240. The analogous values for the 48 combinations with multivariate [chi square], 3df data were -90% and 230 out of 240. The REML maximum values were always larger than the LSLS values. The LSLS skewness and kurtosis values were about the same as those for REML, with the exception of LSLS heritability kurtosis values, which were notably less than those for REML. The explicit expectations of the LSLS estimators showed that the LSLS estimators were surprisingly unbiased given the paucity of data. Explicit coefficients for calculating mean square errors, variances, and biases squared of the LSLS estimators of the three variances were obtained for each design. The LSLS advantage was not quite so large with the multivariate [chi square], 3-df data as with the multivariate normal data. Results with a symmetric multinomial distribution were the same as with the multivariate normal. The overall result was that the LSLS estimators produced substantially more non-zero estimates than REML estimators and these more abundant positive estimates were substantially grouped closer to their respective parameters. Results justify efforts to make the LSLS procedure computationally available. Key Words: Estimation, Heritability, Least Squares, Linear Models, Variance Components

This paper studies properties of tests for long memory for general fourth order stationary sequences. We propose a rescaled variance test based on V/S statistic which is shown to have a simpler asymptotic distribution and to achieve a somewhat better balance of size and power than Lo's (Econometrica 59 (1991) 1279) modified R/S test and the KPSS test of Kwiatkowski et al. (J. Econometrics 54 (1992) 159). We investigate theoretical performance of R/S, KPSS and V/S tests under short memory hypotheses and long memory alternatives, providing a Monte Carlo study and a brief empirical example. Assumptions of the same type are used in both short and long memory cases, covering all persistent dependence scenarios. We show that the results naturally apply and the assumptions are well adjusted to linear sequences (levels) and to squares of linear ARCH sequences (volatility). Keywords: Long memory; Modified R/S statistic; KPSS statistic; WS statistic; Linear process; LARCH model

Value-at-risk analysis is not better than mean-variance analysis for investment selection.

This note deals with the problem of estimating the variance of an undermodeled model. Undermodeling means that the model class used is not flexible enough to describe the underlying system. The proposed solution to the problem is an algorithm that is based on the bootstrap. A simulation example shows that the variance estimates based on the proposed algorithm are in very good agreement with Monte Carlo simulations. Index Terms--Bootstrap, identification, model uncertainty, simulation-based methods, undermodeling.

Social scientists often use agreement among multiple coders to check the reliability and validity of the analytic process. High degrees of intercoder agreement indicate that multiple coders are applying the codes in the same manner and are thus acting as 'reliable' measurement instruments. Coders who independently mark the same text for a theme provide evidence that a theme has external 'validity' and is not just a figment of the investigator's imagination. In this article, I extend the use of multiple coders. I use data taken from clinicians' descriptions of personal illness experiences to demonstrate how agreement and disagreement among coders can be used to measure core and peripheral features of abstract constructs and themes. I then show how such measures of multicoder agreement can be used to identify typical or exemplary examples from the corpus of text. Key words: validity measures, reliability measures, intercoder agreement, text analysis, qualitative research methods

The statistical method known as total variance is examined, focusing on its use to improve the ability to estimate frequency stability. A comparison of the total variance method to the standard unbiased estimator is presented.

The treatment effects of different randomized clinical trials are compared using an approach that combines the one-sided and two-sided test methods. A one-way layout is considered along with a confidence interval procedure to compare the treatment effects. The confidence interval procedure maintains the sensitivity of a one-sided studentized range test in detecting ordered differences while providing two-sided finite confidence intervals in case the sample averages are all far apart., 1. INTRODUCTION Consider the balanced one-way layout [X.sub.ij] = [[[Mu].sub.i] + [[Epsilon].sub.ij] for 1 [less than or equal to] i [less than or equal to] k and 1 [less than [...]

A high degree of leptokurtosis is present in all statistical distribution of exchange rate returns. Conditional variance is low for European Monetary System (EMS) currencies during entry to the exchange rate mechanism (ERM), while non-EMS currencies reveal highly erratic volatility. These findings are shown in an analytical study of five European currencies using the student's t autoregressive (STAR) model with dynamic heteroskedasticity. This model is based on the probabilistic attributes of the data and provides sufficient representation of the study.

An adjusted balanced repeated replication (BRR) method is derived to analyze the increased variance in survey data due to imputation. The adjusted BRR method is obtained by adjusting imputed values for each replication. It is shown that under certain conditions, the method provides consistent variance estimators for functions of estimated totals and sample quantiles. Application of the method to data from the National Immunization Program Record Check Study is discussed., 1. INTRODUCTION A sampled unit often fails to provide information on some items in a survey, which is referred to as item nonresponse. Imputation is commonly applied to compensate for [...]

The Monte Carlo (MC) method exhibits generality and insensitivity to the number of stochastic variables, but is expensive for accurate yield estimation of electronic circuits. In the literature, several variance reduction techniques have been described, e.g., stratified sampling. In this contribution the theoretical aspects of the partitioning scheme of the tolerance region in stratified sampling is presented. Furthermore, a theorem about the efficiency of this estimator over the primitive MC (PMC) estimator versus sample size is given. To the best of our knowledge, this problem was not previously studied in parametric yield estimation. In this method we suppose that the components of parameter disturbance space are independent or can be transformed to an independent basis. The application of this approach to a numerical example (Rosenbrock's curved-valley function) and a circuit example (Sallen-Key low-pass filter) are given. Index Terms - Monte Carlo method, optimal stratified sampling, parametric yield estimation.

Epsilon-efficiency algorithms solve problems of choosing a set of portfolio. Computational efficiency of epsilon-dominated algorithms are performed using other algorithms with a given number of iterations and mean-variance preference structures. The approach is shown to generate alternative and acceptable sets of portfolio with no restrictions on the number of iterations to be performed.

The mean absolute deviation (MAD) model introduced by Konno and Yamazaki (1992) as an alternative to the Markowitz mean-variance (MV) portfolio selection model is examined. The new model turns the portfolio selection problem from a quadratic problem to a linear problem by substituting the variance in the MV objective function with the mean absolute deviation. Konno and Yamazaki claim that their model possesses all the favorable attributes of the MV model and offers additional advantages. They contend that the model does not require the covariance matrix of asset returns; that MAD portfolios have less assets and, therefore, lesser transaction costs in portfolio revisions; and that linear problems are easier to solve than quadratic problems. It is shown that the MAD model entails higher estimation risk than the MV model because it ignores the covariance matrix.

To illustrate the limitations of commonly used methods of handling missing data when using traditional analysis of variance (ANOVA) models and highlight the relative advantages of random-effects regression models, multiple analytic strategies were applied to follow-up data from a clinical trial. Traditional ANOVA and random-effects models produced similar results when underlying assumptions were met and data were complete. However, analyses based on subsamples, to which investigators would have been limited with traditional models, would have led to different conclusions about treatment effects over time than analyses based on intention-to-treat samples using random-effects regression models. These findings underscore the advantages of models that use all data collected and the importance of complete data collection to minimize sample bias.

A method of displaying the relationships between the various factors in experimental designs is described. Emphasis is placed on identifying crossed and nested factors and the experimental units for each factor. The resulting factor relationship diagram (FRD) is useful in establishing the correct model, such as analysis of variance (ANOVA), for analysis. The method is illustrated with a randomized block design and two split-plot designs. Some common pitfalls of these designs are discussed. KEY WORDS: ANOVA; Factor relationship diagram; Pseudoreplication; Randomized block design; Split-plot design., 1. INTRODUCTION Conversion of study descriptions into proper mathematical models for data analysis is an important statistical task. This conversion requires identifying the independent variables in the study, how they [...]

The optimal experimental design theory is applied to cases involving the development of a parametric structure for variance. Particular consideration is given for D-optimal design applications to heteroscedastic models. It is shown that such designs exhibits an exponential link that generates a log variance linear model. Although the link offers a simple information matrix, variance inference inconsistency makes such information rarely useful for model analysis., 1. INTRODUCTION In this article we expand the optimum experimental design theory to models in which there is a parametric structure in the variance. All of the substantial literature on [...]

This article addresses advantages of performing transformations that eliminate interactions in both moderated regression and analysis of variance models, when these transformations also result in homoscedasticity, and when the transformed scores attain at least the same level of measurement as the raw scores. It is shown that these transformations are in fact what have been called subgroup variance equating transformations (SVET), though equality of subgroup variances is a side effect of eliminating interactions and heteroscedasticity. Moderated regression analyses of these transformed data have the following advantages over comparable analyses of raw data: (a) greater tenability of the assumptions of analysis of variance (and moderated regression) models, (b) potentially much greater sensitivity of main effects significance tests, and (c) simpler (more parsimonious) interpretations. (Reprinted by permission of the publisher.)

Changes in variance, or volatility, over time can be modelled using the approach based on autoregressive conditional heteroscedasticity (ARCH). However, the generalizations to multivariate series can be difficult to estimate and interpret. Another approach is to model variance as an unobserved stochastic process. Although it is not easy to obtain the exact likelihood function for such stochastic variance models, they tie in closely with developments in finance theory and have certain statistical attractions. This article sets up a multivariate model, discusses its statistical treatment and shows how it can be modified to capture common movements in volatility in a very natural way. The model is then fitted to daily observations on exchange rates.

College basketball fans often speculate on the extent and nature of the home-court advantage. In this article, it is shown how questions about the size of the home-court advantage and about team-to-team differences in the home-court advantage can be addressed by fitting three different linear models to the outcomes of college basketball games. This approach was applied to data from the 1991-1992 college basketball season. The advantage of playing at home (in relation to playing on a neutral court) was estimated to be 4.68 [+ or -] 0.28 points. The effect of team-to-team differences in the home-court advantage was found to be relatively small. KEY WORDS: Analysis of variance: College basketball: Least squares; Prediction; Ranking., 1. INTRODUCTION College basketball has become one of America's most popular spectator sports. Of the colleges and universities that belong to the National Collegiate Athletic Association (NCAA), approximately 300 field [...]

If panel data are not available but repeated cross-sections are, the parameters in a regression model with fixed individual effects can be estimated consistently using the cohort approach proposed by Deaton (1985). In this paper we show that Deaton's estimator is inconsistent if the number of time periods is small, even if the number of cohorts tends to infinity. Moreover, we propose an alternative estimator which does not suffer from a bias due to a small number of sampling periods and we introduce a new class of estimators, containing both estimators mentioned above. We discuss minimum mean squared error estimation within this class. Our results show that it may be optimal to eliminate only part of the measurement error in the cohort averages, since the implied bias is offset by a smaller variance.

Empirical applications of the variance ratio (VR) test frequently employ multiple VR estimates to examine the random walk hypothesis against stationary alternatives. Failing to control the joint test size for these estimates results in very large Type I errors. This manuscript extends the Lo and MacKinlay (1988) methodology and provides a simple modification for testing multiple variance ratios. Monte Carlo results indicate that the size of our test is close to its nominal size and that it is as reliable as the Dickey-Fuller (D-F) and the Phillips-Perron (P-P) unit root tests. For a stationary AR(1) alternative, our test is comparable to both the D-F and the P-P tests and seems to be more powerful than these tests against two unit root alternatives, an ARIMA(1,1,1) and an ARIMA(1,1,0).

This paper examines the bias in the OLS estimators when the regressors have measurement errors correlated in a particular manner. When a variable is decomposed into two components but only one of them is observed with error, the induced measurement error in the other component is identical but has the opposite sign. This specific correlation pattern enables us to assess the direction of the bias in the OLS estimators from observed data. In the standard EIV case this would require knowledge of the relative variances of the measurement errors. Examples of this type of decomposition in applied work are presented.

A study was done to examine an extension of earlier research on optimal solution development for serial replacement problems. The study focuses on the allowance for correlation in replacement schedules. Results show that correlation exhibits predictive power in describing the impact of external environments to rewards. In addition, a heuristic function may be developed with a margin of 8-11% greater than most other solution approaches.

The general linear model (GLM) is applied in the adjustment for spatial autocorrelation using a spatial autoregressive formula. Approximation of the agricultural data derived from Puerto Rican sources is through latent Jacobian spatial correlation. Results indicate that the application of a two-way analysis of variance model is of particular application to a GLM with spatial autocorrelation.

This paper considers forecasting the conditional mean and variance from a single-equation dynamic model with autocorrelated disturbances following an ARMA process, and innovations with time-dependent conditional heteroskedasticity as represented by a linear GARCH process. Expressions for the minimum MSE predictor and the conditional MSE are presented. We also derive the formula for all the theoretical moments of the prediction error distribution from a general dynamic model with GARCH(1,1) innovations. These results are then used in the construction of ex ante prediction confidence intervals by means of the Cornish-Fisher asymptotic expansion. An empirical example relating to the uncertainty of the expected depreciation of foreign exchange rates illustrates the usefulness of the results.

The Type I and II error properties of the t test were evaluated by means of a Monte Carlo study that sampled 8 real distribution shapes identified by Micceri (1986, 1989) as being representative of types encountered in psychology and education research. Results showed the independent-samples t test to be reasonably robust to Type I error when (a) sample sizes are equal, (b) sample sizes are fairly large, and (c) tests are two-tailed rather than one-tailed. Nonrobust results were obtained primarily under distributions with extreme skew. The t test was robust to Type II error under these nonnormal distributions, but researchers should not overlook robust nonparametric competitors that are often more powerful than the t test when it underlying assumptions are violated.

Split-plot experimental designs are common in studies of the effects of air pollutants on crop yields. Nonlinear functions such as the Weibull function have been used extensively to model the effect of ozone ([O.sub.3]) exposure on yield of several crop species. The usual nonlinear regression model, which assumes independent errors, is not appropriate for data from nested or split-plot designs in which there is more than one source of random variation. The nonlinear model with variance components combines a nonlinear model for the mean with additive random effects to describe the covariance structure. We propose an estimated generalized least squares (EGLS) method of estimating the parameters for this model. This method is demonstrated and compared with results from ordinary nonlinear least squares for data from the National Crop Loss Assessment Network (NCLAN) program regarding the effects of [O.sub.3] on soybean [Glycine mar (L.) Merr.]. In this example, all methods give similar point estimates of the parameters of the Weibull function. The advantage of estimated generalized least squares is that it produces proper estimates of the variances of the parameters, estimated yields, and relative yield losses, which take the covariance structure into account. Model selection, hypothesis testing, and construction of confidence intervals are also demonstrated. A computer program that fits the nonlinear model with variance components by the EGLS method is available from the authors., A statistical procedure for estimating the parameters in nested or split-plot designs used to assess the effects of air pollutants on crop yields was developed. The method is called the estimated generalized least squares (EGLS) method, and it estimates the parameters in a nonlinear model with variance components. Using the EGLS procedure, more precise estimates of the variances of the parameters, yield and yield losses are possible. Furthermore, application of EGLS is possible even with unbalanced data.

The invariance properties of some well known asymptotic tests are studied. Three types of invariance are considered: invariance to the representation of the null hypothesis, invariance to one-to-one transformations of the parameter space (reparameterizations), and invariance to one-to-one transformations of the model variables such as changes in measurement units. Tests that are not invariant include the Wald test and generalized versions of it, a widely used variant of the Lagrange multiplier test, Neyman's C([infinity]) test, and a generalized version of the latter. For all these tests, we show that simply changing measurement units can lead to vastly different answers even when equivalent null hypotheses are tested. This problem is illustrated by considering regression models with Box-Cox transformations on the variables. We observe, in particular, that various consistent estimators of the information matrix lead to test procedures with different invariance properties. General sufficient conditions are then established, under which the generalized C([infinity]) test becomes invariant to reformulations of the null hypothesis and/or to one-to-one transformations of the parameter space as well as to transformations of the variables. In many practical cases where Wald-type tests lack invariance, we find that special formulations of the generalized C([infinity]) test are invariant and hardly more costly to compute than Wald tests. This computational simplicity stands in contrast with other invariant tests such as the likelihood ratio test. We conclude that noninvariant asymptotic tests should be avoided or used with great care. Further, in many situations, the suggested implementation of the generalized C([infinity]) test often yields an attractive substitute to the Wald test (which is not invariant) and to other invariant tests (which are more costly to perform).

In this paper we consider the relative efficiency of rotating-panel designs in analysis-of-variance models. Throughout we assume that the parameter of interest is a linear combination of period means in the analysis-of-variance model. Results from spectral theory are used to obtain manageable expressions for the variance of the BLUE of this parameter. Relative efficiencies of the BLUE for rotating panels with rotation periods are presented, e.g., for the period means themselves, of differences, or of averages of means. Moreover we present bounds on the relative efficiency which are valid irrespective of the parameter of interest. The analysis shows that the gains from choosing an optimal rotation design can be quite substantial, evenif the cost of a reinterview equals the cost of a first observation. In many cases either the smaller or the highest possible rotation period is optimal. The analysis is illustrated with an empirical example concerning monthly consumer expenditures on food and clothing.

A sample of 76 white, middle-class couples from a rural midwestern county was used to examine the effects of method variance on models linking family economic pressure, marital quality, and expressions of hostility and warmth. Reports of hostility and warmth were obtained from three sources: self-report, spouse's report, and observer ratings from videotapes of family interactions. Using observer reports of hostility and warmth yielded results consistent with previous literature linking economic pressure to marital quality indirectly through interactional processes such as hostility. When the models were based on information obtained from self-reports or spouses' reports, however, it was difficult empirically to separate the interactional processes of hostility and warmth from the distinct concept of marital quality.

A nonnull model for rank statistics based on Kendall's tau has received quite a bit of attention in the ranking literature lately. In this article, we analyze this model with an eye towards applying it to situations in which nonparametric statistics such as Kendall's tau, the Mann-Whitney/Wilcoxon U, the Jonckheere-Terpstra statistic, the Kruskal-Wallis statistic, and Friedman's statistic for randomized blocks designs are often used. The data for the basic model are a pair of vectors of length n, where both are permutations of the first n integers or one is a fixed and arbitrary design vector and the other a permutation. The model is Mallow's [empty se] model, a one-parameter exponential family with natural statistic the number of discordant pairs between the two vectors. This model originated with Mann and has appeared in many articles since. We extend the model to cases in which there may be ties in the observations and to analysis of variance problems (in which there are several parameters). The first four sections describe the models and verify the asymptotic normality of the statistics and the maximum likelihood estimators of the parameters, as well as the asymptotic chi-squared nature of the likelihood ratio statistics under the null hypotheses. In Section 5 we compare the model to some other typical models. Section 6 contains examples, including analysis of the 1970 Draft Lottery data, and a 2 x 2 x 2 analysis of variance design. KEY WORDS: Discordant pairs; Exponential family; Kendall's tau; Permutations., 1. INTRODUCTION There is an increasing literature dealing with nonnull models for rank statistics: Mann (1945); Mallows (1957); Barton, David, and Mallows (1958); Feigin and Cohen (1978); Schulman (1979); Silverberg [...]

Link and others have derived formulas for the moments of certain discrete probability distributions using various finite-difference operators. In this article, we establish a method of obtaining moments of certain discrete distributions that makes use of differential operators. The derivations are elegant and more compact than derivations using standard methods. Students in a first-year mathematical statistics course are typically more acquainted with differential operators than with difference operators. Contrasted with difference operators, this familiarity affords a better opportunity to introduce the connection between operator mathematics and probability in such courses. However, we propose that both operators be employed: differential operators to introduce the connection and difference operators to broaden the students' exposure and prepare them for such courses as time series analysis. KEY WORDS: Expectation; Variance.

In the two-sample means test, the need for a preliminary variance test and the special emphasis given to the equal variance assumption are questioned. The conclusions can be easily used in the classroom to teach the two sample means test. KEY WORDS: Size; Power; Preliminary variance test.

A simple and more intuitive explanation of the bias of the ratio and the regression estimators of finite population is provided. The finite population is represented by certain regression fits, and the leading term of bias is described in terms of familiar concepts. We show that the asymptotic] bias of the ratio estimator is due to intercept of a linear regression fit, whereas for the regression estimator, it is due to the coefficient of the quadratic term of a quadratic regression fit. We also give some variance formulas written in terms of easily interpretable quantities of the linear regression fit.

We discuss the nature of possibilistic uncertainty. Two approaches to the determination of the equivalent value for a possibilistically uncertain variable are introduced. These approaches are then generalized to yield a parameterized class of functions for obtaining the equivalent value of a possibilistic variable. A novel aspect of this class is that it is parameterized by a weak ordering. A discussion to try to understand the semantics of this parameterizing ordering is included. A method is suggested for obtaining the weak ordering directly from a scalar value. We briefly look at the issue of variance in possibilistic uncertainty. Index Terms--Decision making, fuzzy sets, information aggregation, possibility theory, uncertainty.

This paper describes, analyzes and evaluates an algorithm for estimating portfolio loss probabilities using Monte Carlo simulation. Obtaining accurate estimates of such loss probabilities is essential to calculating value-at-risk, which is a quantile of the loss distribution. The method employs a quadratic ('delta-gamma') approximation to the change in portfolio value to guide the selection of effective variance reduction techniques; specifically importance sampling and stratified sampling. If the approximation is exact, then the importance sampling is shown to be asymptotically optimal. Numerical results indicate that an appropriate combination of importance sampling and stratified sampling can result in large variance reductions when estimating the probability of large portfolio losses., 1. Introduction An important concept for quantifying and managing portfolio risk is value-at-risk (VAR) (Jorion 1997, Wilson 1999). VAR is defined as a quantile of the loss in portfolio value [...]

Variance components in the context of Generalizability Theory are useful indices for attributing the amount of variance to a particular facet or object of measurement. The mean difference effect size [...]