Showing papers in "Technometrics in 1980"
TL;DR: In this paper, the exact likelihood function of a stationary autoregressive moving average (ARMA) time series based on Akaike's Markovian representation and using Kalman recursive estimation is reviewed.
Abstract: The method of calculating the exact likelihood function of a stationary autoregressive moving average (ARMA) time series based on Akaike's Markovian representation and using Kalman recursive estimation is reviewed. This state space approach involves matrices and vectors with dimensions equal to Max (p, q + 1) where p is the order of the autoregression and q is the order of the moving average, rather than matrices with dimensions equal to the number of observations. A key to the calculation of the exact likelihood function is the proper calculation of the initial state covariance matrix. The inclusion of observational error into the model is discussed as is the extension to missing observations. The use of a nonlinear optimization program gives the maximum likelihood estimates of the parameters and allows for model identification based on Akaike's Information Criterion (AIC). An example is presented fitting models to western United States drought data.
576 citations
537 citations
TL;DR: In this article, the concept of aberration is proposed as a way of selecting the best designs from those with maximum resolution, and algorithms are presented for constructing these minimum aberration designs.
Abstract: For studying k variables in N runs, all 2 k–p designs of maximum resolution are not equally good. In this paper the concept of aberration is proposed as a way of selecting the best designs from those with maximum resolution. Algorithms are presented for constructing these minimum aberration designs.
420 citations
TL;DR: An empirical comparison of existing algorithms for the computer generation of exact D-optimal experimental designs is carried out and a modification of the Fedorov algorithm is given and shown to effect substantial decreases in the computer time required for design generation.
Abstract: An empirical comparison of existing algorithms for the computer generation of exact D-optimal experimental designs is carried out. Among algorithms considered were those due to Wyrnn, Mitchell, Fedorov, and Van Schalkwyk. A procedure for rounding off approximate designs as suggested by Kiefer is also evaluated. A modification of the Fedorov algorithm is given and shown to effect substantial decreases in the computer time required for design generation.
368 citations
TL;DR: In this paper, a method of determining whether all the parameters meet their respective standards is proposed, which consists of testing each parameter individually and deciding that the product is acceptable only if each parameter passes its test.
Abstract: The quality of a product might be determined by several parameters, each of which must meet certain standards before the product is acceptable. In this article, a method of determining whether all the parameters meet their respective standards is proposed. The method consists of testing each parameter individually and deciding that the product is acceptable only if each parameter passes its test. This simple method has some optimal properties including attaining exactly a prespecified consumer's risk and uniformly minimizing the producer's risk. These results are obtained from more general hypothesis-testing results concerning null hypotheses consisting of the unions of sets.
345 citations
TL;DR: In this paper, the influence of individual or groups of cases on a regression problem is assessed based on an empirical influence function, and an example using data from the Florida Area Cumulus Experiments (FACE) on cloud seeding is presented.
Abstract: Traditionally, most of the effort in fitting full rank linear regression models has centered on the study of the presence, strength and form of relationships between the measured variables. As is now well known, least squares regression computations can be strongly influenced by a few cases, and a fitted model may more accurately reflect unusual features of those cases than the overall relationships between the variables. It is of interest, therefore, for an analyst to be able to find influential cases and, based on them, make decisions concerning their usefulness in a problem at hand. Based on an empirical influence function, we discuss methodologies for assessing the influence of individual or groups of cases on a regression problem. We conclude with an example using data from the Florida Area Cumulus Experiments (FACE) on cloud seeding.
326 citations
TL;DR: In this paper, a three-stage iterative procedure for building space-time models is presented, which fall into the general class of STARIMA models and are characterized by autoregressive and moving average terms lagged in both time and space.
Abstract: A three-stage iterative procedure for building space-time models is presented. These models fall into the general class of STARIMA models and are characterized by autoregressive and moving average terms lagged in both time and space. This model class collapses into the ARIMA model class in the absence of spatial correlation. The theoretical properties of STARIMA models are presented and the model building procedure is described and illustrated by a substantive example.
323 citations
TL;DR: In this article, the authors present simple criteria which can be used to select which of the three members of the Johnson System of distributions should be used for fitting a set of data.
Abstract: This paper presents simple criteria which can be used to select which of the three members of the Johnson System of distributions should be used for fitting a set of data. The paper also presents elementary formulas for estimating the parameters for each of the members of the family. Thus, many obstacles to the use of the Johnson System are resolved.
251 citations
TL;DR: The IDB distribution as mentioned in this paper is motivated by mixtures of a set of IFR distributions but can also be given a competing risk interpretation, and the asymptotic gain from classifying failures into two categories is illustrated.
Abstract: A distribution with one scale and two shape parameters is studied. The distribution can describe increasing (I), decreasing (D), constant and bathtub-shaped (B) failure rates. This motivates the working name, IDB distribution. The IDB distribution is motivated by mixtures of a set of IFR distributions but can also be given a competing risk interpretation. For mixed distributions a more general result on the initial slope of the failure rate is given. Asymptotic results for the ML estimation of survival probabilities are given, and when possible compared with ML estimation based on the Weibull, Rayleigh and exponential distributions. Also, the asymptotic gain from classifying failures into two categories is illustrated. One application to real data is given.
244 citations
TL;DR: The EM algorithm provides a simple and easily programmed iterative solution for the ML estimates of the parameters in the models to identify outliers in single sample or regression problems, based on mixture models.
Abstract: Maximum likelihood (ML) methods are described for the identification of outliers in single sample or regression problems, based on mixture models. The EM algorithm provides a simple and easily programmed iterative solution for the ML estimates of the parameters in the models. The procedure is illustrated on three examples.
237 citations
TL;DR: In this paper, the authors show that the expected value of R 2 is substantially inflated above its value without selection, especially when the number of observations is less than a small number of predictor variables, and the extent of this increase was investigated by a Monte Carlo simulation.
Abstract: When subset selection is used in regression the expected value of R 2 is substantially inflated above its value without selection, especially when the number of observations is less than the number of predictor variables. The extent of this increase was investigated by a Monte Carlo simulation. Tables are given with average values and percentage points of R 2 for the null case of independence between the response variable and the predictor variables. Approximation formulas are provided to supplement the coverage in the tables.
TL;DR: In this article, the problem of obtaining confidence intervals or tests of significance for the parameters or other characteristics of the generalized gamma distribution is addressed, and procedures are given whereby confidence intervals for parameters, quantiles or the reliability (survivor) function of the distribution can be obtained.
Abstract: This paper is concerned with the problem of obtaining confidence intervals or tests of significance for the parameters or other characteristics of the generalized gamma distribution. Procedures are given whereby confidence intervals for the parameters, quantiles or the reliability (survivor) function of the distribution can be obtained, when the generalized gamma index parameter is known. Their application in studying robustness and model-dependence in lifetime distributions is also discussed.
TL;DR: In this paper, the effect of system size and shape on the theoretical space-time autocorrelation function for first order STARMA models is described and an initial estimation for the STAR(11 and STMA(11) models is presented.
Abstract: The effect of system size and shape on the theoretical space-time autocorrelation function is described for first order STARMA models. Figures and tables are presented to assist in identification considerations which include model interpretation, patterns of the theoretical spacetime autocorrelation and partial autocorrelation functions, and initial estimation for the STAR(11) and STMA(11) models.
TL;DR: In this paper, the authors give variable sampling plans for items whose failure times are distributed as either extreme-value variates or Weibull variates (the logarithms of which are from an extreme value distribution).
Abstract: In this paper, we give variables sampling plans for items whose failure times are distributed as either extreme-value variates or Weibull variates (the logarithms of which are from an extreme-value distribution). Tables applying to acceptance regions and operating characteristics for sample size n, ranging from 3 to 18, are given. The tables allow for Type II censoring, with censoring number r ranging from 3 to n. In order to fix the maximum time on test, the sampling plan also allows for Type I censoring. Acceptance/rejection is based upon a statistic incorporating best linear invariant estimates, or, alternatively, maximum likelihood estimates of the location and scale parameters of the underlying extreme value distribution. The operating characteristics are computed using an approximation discussed by Fertig and Mann (1980).
TL;DR: In this paper, a family of computer search methods for finding optimum designs, that generalize and improve upon Mitchell's exchange and DETMAK algorithms, were developed, with an emphasis on time and space-saving considerations that permit us to handle larger problems, or to run each search "try" for the optimum more rapidly, than was previously possible.
Abstract: We develop a family of computer search methods for finding optimum designs, that generalize and improve upon Mitchell's exchange and DETMAK algorithms. Our emphasis is on time- and space-saving considerations that permit us to handle larger problems, or to run each search “try” for the optimum more rapidly, than was previously possible. This last means that more tries can be attempted for a given total cost, with consequent greater chance of finding an optimum or near-optimum design. Indeed, we have found a number of new optimum or improved designs using these methods. For k = 6 to 12 parameters and with n observations and k ≤ n ≤ 2k, our methods are typically 15 to 50 times faster than DETMAX (more as n and k increase), with comparable success rates. Numerical studies in linear and quadratic regression examples treat also the effect of amount of initial randomization on the success of a try.
TL;DR: Different approaches based on minimum mean squared error, cross-validation and pseudo-Bayesian techniques are compared, particularly from the points of view of reliability and ease of computation.
Abstract: Kernel estimates of discrete probabilities are considered, with emphasis on computation of the smoothing parameters. Different approaches based on minimum mean squared error, cross-validation and pseudo-Bayesian techniques are compared, particularly from the points of view of reliability and ease of computation. The advantages of a fractional allocation procedure and of computing the bandwidths marginally for each variable are pointed out. Multicategory variables and incomplete data can be coped with. The relationship between the kernel method and other smoothing techniques for categorical data is discussed.
TL;DR: In this article, a detailed study of three sets of large sample simultaneous confidence intervals for the probabilities of a multinomial distribution, all three making use of the Bonferroni inequality, is presented.
Abstract: The paper outlines a detailed study of three sets of large sample simultaneous confidence intervals for the probabilities of a multinomial distribution, all three making use of the Bonferroni inequality. One of them, originally proposed by Goodman, is based on the assumption that each cell frequency ni is, marginally, normally distributed, while the other two require the normality of transformations of ni —an angular transformation in one case and a square root in the other. It is shown that all three sets of intervals should be used with a correction for continuity; their coverage probabilities are investigated, and it is seen that the two sets based on transformations of ni produce shorter intervals than Goodman's when ni is small. There is little to choose between these two except that one of them is a little simpler to use than the other.
TL;DR: In this paper, conditional inference procedures are discussed for the shape parameter and for the current system reliability for a time truncated Weibull process. And approximate confidence limits for the scale parameter are also developed.
Abstract: Conditional inference procedures are discussed for the shape parameter and for the current system reliability for a time truncated Weibull process. These tests are shown to be uniformly most powerful unbiased. Approximate confidence limits for the scale parameter are also developed.
TL;DR: In this paper, normal-gamma distributions are employed as prior distributions for the regression parameters of the model and, as a result, the posterior distribution of regression parameters are mixtures of t distributions.
Abstract: This paper is a generalization of earlier studies by Ferreira (1975) and Holbert and Broemeling (1977), who used improper prior distributions in order to make informal Bayesian inferences for the shift point and other parameters of a changing linear model. In this study, normal-gamma distributions are employed as prior distributions for the regression parameters of the model and, as a result, the posterior distribution of the regression parameters are mixtures of t distributions, while a mixture of gamma distributions is the posterior distribution of the precision parameter. Point and interval estimators of the regression parameters and the residual precision are based on the appropriate marginal and conditional posterior distributions and are illustrated with data generated from a known model.
TL;DR: In this article, a general model for which the simpler rate models are special cases is developed, and a means for generating the conditional distributions needed for the tests is presented to assess the adequacy of the simpler models.
Abstract: The Weibull and log linear rate models are frequently used in the statistical analysis of a Poisson series of events. By developing a general model for which the simpler rate models are special cases it becomes possible to use optimal conditional tests to assess the adequacy of the simpler models. A means is presented for generating the conditional distributions needed for the tests.
TL;DR: In this paper, a Bayesian analysis of shape, scale, and mean of the two-parameter gamma distribution is presented, with a focus on conjugate and non-informative priors.
Abstract: This paper presents a Bayesian analysis of shape, scale, and mean of the two-parameter gamma distribution. Attention is given to conjugate and “non-informative” priors, to simplifications of the numerical analysis of posterior distributions, and to comparison of Bayesian and classical inferences.
TL;DR: In this article, it is shown that application of procedures such as Larsen's that assume stationarity to a non-stationary sequence of concentrations can produce seriously erroneous results, and two methods for using air quality data to estimate the distributional properties of maxima of nonstationary sequences of concentrations are illustrated.
Abstract: A procedure for using air quality data to estimate the mean value of the maximum concentration in a year-long sequence of lognormally distributed air pollutant concentrations has been described by Larsen. This procedure and analogous procedures for non-lognormal concentrations implicitly assume that sequences of pollutant concentrations are stationary. However, air pollutant concentrations often vary systematically in response to seasonal and other factors and, therefore, are nonstationary. In this paper it is shown that application of procedures, such as Larsen's, that assume stationarity to a nonstationary sequence of concentrations can produce seriously erroneous results. Two methods for using air quality data to estimate the distributional properties of maxima of nonstationary sequences of concentrations are illustrated. One method involves identifying a nonstationary stochastic process that explains the data and computing the probability distributions of maxima of sequences generated by this stochast...
TL;DR: In this article, the use of moving sums of squares of recursive residuals (MOSUM-SQs) in addition to MOSUMs is demonstrated for testing the constancy of a limited series of T independent observations normally distributed with equal variance.
Abstract: The use of moving sums of squares of recursive residuals (MOSUM-SQs) in addition to MOSUMs (Bauer and Hackl, 1978) is demonstrated for testing the constancy of a limited series of T independent observations normally distributed with equal variance. The cases of known and unknown process level as well as process variance are treated separately and conservative probability limits are derived. An assessment of the power in the cases of sudden changes of the process level and/or variance is based on a simulation study. The combined use of MOSUMs and MOSUM-SQs for the interpretation of the nature of the nonconstancy is discussed and demonstrated in an example. Finally, the application of the moving sum techniques in the situation of a continuing series of observations is discussed.
TL;DR: In this paper, the relationship between the mixed hazard rate h(t) and the mixing density g(λ) is discussed. And the relationship of the mixed exponential hazard rate to the intensity function of some generalized stochastic point processes is discussed, together with their Muth global classification measures.
Abstract: Various properties of the mixed exponential hazard rate and reliability are discussed. Particular attention is given to the relationship between the mixed hazard rate h(t) and the mixing density g(λ). Characteristic functions are derived and expressions relating integral transforms (Laplace, Fourier and Mellin) to the mixed exponential family are presented. A complex contour integration is used to invert a given mixed R(t) and recover the mixing density g(λ). Several generalized mixed reliability functions and the corresponding mixing densities are provided together with their Muth global classification measures. The relationship of the mixed exponential hazard rate to the intensity function of some generalized stochastic point processes is discussed. Results for a mixed Weibull density are also included.
TL;DR: In this article, the standard jackknife and two linear jackknife methods based on a single fit were compared in the context of nonlinear regression fitting, where emphasis was on determination of confidence regions for parameters.
Abstract: The standard jackknife and two linear jackknife methods based on a single fit are compared in the context of nonlinear regression fitting. Emphasis is on determination of confidence regions for parameters, where we find that the standard jackknife may be inferior.
TL;DR: In this article, a method of reducing Bukac's quartic equations to a quadratic equation is presented, which leads to an explicit solution for the S B parameters, using the method of moments.
Abstract: The S B distributions were defined by Johnson (1949). Tables for fitting the four S B parameters by the method of moments have been provided by Johnson and Kitchen (1971a, b). Bukac (1972) showed that a choice of four symmetrical and equidistant standard normal deviates simplified the solution to allow a direct solution of a quartic equation for the S B parameters. This paper presents a method of reducing Bukac's quartic equations to a quadratic equation which leads to an explicit solution for the S B parameters.
TL;DR: In this article, the authors used multiresponse data for estimating the parameters in a model, and showed that conversion of the organic material in shale to oil was better explained when an intermediate product was included in the reaction network.
Abstract: In the chemical and petrochemical industries kinetic models are useful for describing the physical and chemical steps that occur in commercial processes. Often kinetic models involve several responses. Box and Draper (1965) have demonstrated that using multiresponse data for estimating the parameters in a model results in confidence regions for the parameters that are smaller than those obtained when the responses are considered individually, and they have developed a procedure for the multiresponse estimation of common parameters. Using multiresponse data also provides a better understanding of the reaction mechanism and makes possible a more comprehensive assessment of the correctness of the proposed model. Data from an oil shale pyrolysis experiment was used to fit and critique a sequence of models. These showed that conversion of the organic material in shale to oil was better explained when an intermediate product was included in the reaction network, and multiresponse techniques were employed. This ...
TL;DR: The application of optimal experimental design theory to models for dynamic systems is surveyed and applications are split roughly into those involving choice of input functions and those in which sampling rates also are selected.
Abstract: The application of optimal experimental design theory to models for dynamic systems is surveyed. Preliminary sections briefly discuss the models used and the main points of statistical optimal design theory. Then the ways in which the latter carry over to dynamic models are described. These applications are split roughly into those involving choice of input functions and those in which sampling rates also are selected.