Showing papers on "Confidence interval published in 1976"
TL;DR: In this paper, the problems of model classification and parameter estimation are examined, with the objective of establishing the statistical reliability of inferences drawn from X-ray observations, and a procedure based on minimizing the chi/sup 2/ statistic is recommended; it provides a rejection criterion at any desired significance level.
Abstract: The problems of model classification and parameter estimation are examined, with the objective of establishing the statistical reliability of inferences drawn from X-ray observations. For testing the validities of classes of models, the procedure based on minimizing the chi/sup 2/ statistic is recommended; it provides a rejection criterion at any desired significance level. Once a class of models has been accepted, a related procedure based on the increase of chi/sup 2/ gives a confidence region for the values of the model's adjustable parameters. The procedure allows the confidence level to be chosen exactly, even for highly nonlinear models. Numerical experiments confirm the validity of the prescribed technique.The chi/sup 2//sub min/+1 error estimation method is evaluated and found unsuitable when several parameter ranges are to be derived, because it substantially underestimates their joint errors. The ratio of variances method, while formally correct, gives parameter confidence regions which are more variable than necessary. (AIP)
700 citations
TL;DR: This modification has the effect of decreasing the "effective" length of the confidence interval, on which the decision concerning bioequivalence is based, while increasing the confidence coefficient.
Abstract: The conventional method of setting confidence intervals for the difference of the means of two normal populations gives an interval which is not, in general, symmetrical about zero. A modification of the conventional method which leads to symmetry about zero is discussed and is recommended as particularly appropriate for use in bioequivalence trials. This modification has the effect of decreasing the "effective" length of the confidence interval, on which the decision concerning bioequivalence is based, while increasing the confidence coefficient.
309 citations
TL;DR: In this paper, the authors present a method for computing predictions, prediction error variances, and confidence intervals, which can be implemented with any regression program, and demonstrate that a regression estimated for an augmented data set, obtained by combining n sample points with r forecast points, and including r dummy variables (each equalling one only for the corresponding forecast point), will yield r dummy variable coefficients and variances which equal the corresponding prediction errors and prediction error variance.
157 citations
TL;DR: In this paper, a variety of 95-percent confidence interval procedures have been examined in some detail using Monte Carlo techniques on simulated samples of sizes 10 and 20 from a spectrum of distributions ranging from the Gaussian to the long-tailed Cauchy.
Abstract: A variety of 95-percent confidence interval procedures have been examined in some detail using Monte Carlo techniques. These estimators were tried on simulated samples of sizes 10 and 20 from a spectrum of distributions ranging from the Gaussian to the long-tailed Cauchy. The robustness of an estimator is measured by both the closeness of its level to the 5-percent goal (robustness of validity) and its expected length as compared to its competitors (robustness of efficiency). Results include some quite robust procedures including some of the point M-estimators from the Princeton Robustness Study.
146 citations
TL;DR: The ten-year mortality in a single-plant population of 6678 male rubber workers is examined, in terms of the association of specific causes of death with a history of having worked in certain categories of jobs within the rubber industry, to identify the work-environment agents responsible for the associations reported here.
Abstract: This study has examined the ten-year mortality in a single-plant population of 6678 male rubber workers, in terms of the association of specific causes of death with a history of having worked in certain categories of jobs within the rubber industry. The work-histories of individual study subjects were analyzed, in detail, for all workers dying of selected causes of death. Comparison was made with the work-histories of a 22% age-stratified random sample of the total population. Age-adjusted exposure ratios (Tables 3 and 4) were calculated for all nine case groups in all 16 work areas, using differing exposure criteria (i.e. duration and calendar period). These ratios provide an approximation of the increased mortality risk associated with particular work areas. The risk ratios (with their associated confidence intervals), in Table 5, provide more rigorous estimates of these instances of increased mortality risk. For each cause of death studied, there were statistically significant associations with several work areas. For the cancers, the strongest associations tended to be with work areas at the front end of the production line (especially compounding and mixing), where the likelihood of contact with dusts, chemical ingredients, and vapors containing the early reaction byproducts, is high. The reclaim operation and the synthetic plant were each associated with several cancers (respiratory and bladder, and stomach and lymphato-hematopoietic cancers, respectively). The lymphatic leukemias were associated with solvent-exposure areas, especially inspection, finishing, and repair. Ischemic heart disease deaths, at ages 40-54, were strongly associated with having worked in extrusion and tread cementing, and in the synthetic plant. Deaths from diabetes mellitus were strongly associated with the janitoring-trucking category, and with jobs in the inspection, finishing and repair area. These observed associations, calculated after controlling for the variables sex and age, were apparently not due to confounding by smoking and race differences between work areas. The role of selective transfer of sick individuals (into, say janitoring or trucking) warrants further investigation. However, this mechanism is unlikely to be involved in the great majority of the observed associations. Another possible source of spurious inferences of increased risk would be correlation, within work-histories, between two job categories, one of which actually involved increased risk, while the other did not. Such associations could occur if certain job sequency trends existed within this working population. (Preliminary analyses indicate that this likelihood is not great; however, further analysis is planned.) Detailed study of specific environmental agents, historically and cross-sectionally, is currently underway, in an attempt to identify the work-environment agents responsible for the associations reported here.
144 citations
TL;DR: A study of the relathonship between alcohol consumption and nonfatal myocardial infarction indicated absence of any major overall association, but there was some evidence of a lower rate in subjects consuming six or more drinks per day.
Abstract: A study of the relathonship between alcohol consumption and nonfatal myocardial infarction, involving 399 cases and 2486 reference subjects, indicated absence of any major overall association (rate ratio point estimate of 0.9 with 95% confidence limits of 0.6 and 1.2), but there was some evidence of a lower rate in subjects consuming six or more drinks per day (rate ratio point estimate of 0.6 with 95% confidence limits of 0.3 and 1.1). Confounding by several potential confounders was controlled by stratification according to a confounder-summarizing score.
132 citations
TL;DR: The probability density and confidence intervals for the maximum entropy (or regression) method (MEM) of spectral estimation are derived using a Wishart model for the estimated covariance and asymptotic expressions are derived which are the same as those of Akaike.
Abstract: The probability density and confidence intervals for the maximum entropy (or regression) method (MEM) of spectral estimation are derived using a Wishart model for the estimated covariance. It is found that the density for the estimated transfer function of the regression filter may be interpreted as a generalization of the student's t distribution. Asymptotic expressions are derived which are the same as those of Akaike. These expressions allow a direct comparison between the performance of the maximum entropy (regression) and maximum likelihood methods under these asymptotic conditions. Confidence intervals are calculated for an example consisting of several closely space tones in a background of white noise. These intervals are compared with those for the maximum likelihood method (MLM). It is demonstrated that, although the MEM has higher peak to background ratios than the MLM, the confidence intervals are correspondingly larger. Generalizations are introduced for frequency wavenumber spectral estimation and for the joint density at different frequencies.
72 citations
TL;DR: In this article, confidence sequences are constructed for the unknown parameters of the binomial, Poisson, uniform, gamma, and other distributions by making use of generalized likelihood ratio martingales, i.e., sequences of confidence regions which contain the true parameter for every sample size simultaneously at a prescribed level of confidence.
Abstract: This paper is concerned with confidence sequences, i.e., sequences of confidence regions which contain the true parameter for every sample size simultaneously at a prescribed level of confidence. By making use of generalized likelihood ratio martingales, confidence sequences are constructed for the unknown parameters of the binomial, Poisson, uniform, gamma and other distributions. It is proved that for the exponential family of distributions, the method of using generalized likelihood ratio martingales leads to a sequence of intervals which have the desirable property of eventually shrinking to the population parameter. The problem of nuisance parameters is considered, and in this connection, boundary crossing probabilities are obtained for the sequence of Student's $t$-statistics, and a limit theorem relating to the boundary crossing probabilities for the Wiener process is proved.
67 citations
TL;DR: In this article, the authors discuss testing hypotheses and interval estimation for the mean of the first passage time distribution in Brownian motion with positive drift (inverse Gaussian distribution) and derive the optimum test procedures and confidence intervals for both one-sided and two-sided cases.
Abstract: In this paper we discuss testing hypotheses and interval estimation for the mean of the first passage time distribution in Brownian motion with positive drift (inverse Gaussian distribution). Optimum test procedures and confidence intervals for both one-sided and two-sided cases are derived in their exact forms, which utilize the percentage points of standard normal and Student's t distributions. In thecase of an hypothesis with a two-sided alternative, it is shown that a uniformly most powerful (UMP) unbiased test is simply a two-tailed normal test if the nuisance parameter is known, and a two-tailed Student's t test if it is unknown.
40 citations
TL;DR: In this paper, for the rth and sth order statistics in a sample of size n (1 ≤ r < s ≤ n), upper and lower bounds and an exact expression for the confidence coefficient are derived.
Abstract: Wilks [6] introduced distribution-free confidence intervals based on order statistics for quantile intervals. For the rth and sth order statistics in a sample of size n (1 ≤ r < s ≤ n), upper and lower bounds and an exact expression for the confidence coefficient are derived. Numerical examples comparing the bounds and the exact solution are provided. A connection with distribution-free tolerance intervals is indicated.
35 citations
TL;DR: In this paper, a 95 % confidence interval of 0-5629 + 0-0006 is obtained for the limit of mean random packing density, which is slightly but significantly higher than the value conjectured by Palasti.
Abstract: The twoand three-dimensional random packing problems in Pal'asti's (1960) sense are studied by means of Monte Carlo simulations and extrapolation techniques. In the twodimensional case, a 95 % confidence interval of 0-5629 + 0-0006 is obtained for the limit of mean random packing density. This estimate is slightly but significantly higher than the value conjectured by Palasti, c2 0-5589. For the three-dimensional case, we calculate only a lower bound of the limiting density and give a 95 % confidence interval of 0-4148 + 0-0025, which is also fairly near to the conjectured value (C3 0.4178).
TL;DR: In this paper, a comparison of conditional confidence interval procedures for estimating the parameters in the power law model, and for estimating mean life at a given future stress level, is made based on asymptotic properties of the maximum likelihood estimates.
Abstract: SUMMARY Estimation and prediction procedures are discussed for the inverse power law model, when the time to failure follows an exponential distribution. In the context of accelerated life test experiments, procedures are given for estimating the parameters in the power law model, and for estimating mean life at a given future stress level. The procedures given are conditional confidence interval procedures, obtained by conditioning on ancillary statistics. A comparison is made of these procedures and procedures based on asymptotic properties of the maximum likelihood estimates. IN studies concerning the length of life of certain types of manufactured items, it is often wished to consider the relationship between length of life and one or more concomitant variables. Thus, for example, in an experiment to study the lifetimes of a certain type of electrical insulation, the relationship between length of life and environmental temperature was studied (Nelson, 1970). Sometimes the main problem of interest involves determining the effect of environmental factors (concomitant variables) on the life distribution of the items in question, and in incorporating this into a useful statistical model. In other situations, the general form of the model may be considered determined, and it may be wished to estimate various parameters in the model. The estimated relationship between length of life and the concomitant variables allows the prediction of item life under specified environmental condi- tions. This latter situation commonly arises in accelerated life testing where, on the basis of tests run at "accelerated" test conditions, it is desired to predict item life under standard operating conditions. This paper deals with the second type of problem: we discuss estimation and prediction procedures for a model which is commonly used in reliability and life testing work, the so-called inverse power law model, with exponential time to fail data. This model has been discussed a number of times in the statistical literature, and a number of estimation procedures have been proposed for it, mainly based on large sample theory. Our purpose here is to describe confi- dence interval estimation procedures for this model, and to illustrate their use. The procedures do not involve the use of any asymptotic approximations and so all distributions given are exact for any sample size. Before describing the model, we remark that an excellent survey of work on the inverse power law model and its application in accelerated life testing is given by Nelson (1970), who discusses the more general situation in which the time to failure follows the two-parameter Weibull distribution. We consider the inverse power law in the following form: let the lifetime of an item under environmental condition i have an exponential distribution with mean Oi. In this model the environmental conditions are specified by means of a single covariate vi (which we will call the "stress"), and the relationship Oi = c/vg? is assumed, where c,p are (unknown) constants.
TL;DR: In this paper, a two-stage procedure is developed which provides a confidence interval for μ[k] with fixed width, where k denotes the largest of the means of the independent and normally distributed populations.
Abstract: Suppose that we are given k(≥1) independent and normally distributed populations π1, …, πk , where πi has unknown mean μ i and unknown variance σi 2 (i = 1, …, k). Let μ[k] denote the largest of the means μ1, …, μk . A two-stage procedure is developed which provides a confidence interval for μ[k] with fixed width. Tables needed to apply the procedure are provided.
TL;DR: In this paper, confidence regions are constructed for linear combinations of fixed effects and realized or sample values of random effects, where the ratios of the variance components can be regarded as known, and the prescribed long run frequency of coverage when there is repeated sampling of the random effects as well as the residual effects.
Abstract: Confidence regions are constructed for linear combinations of fixed effects and realized or sample values of random effects. These regions can be used in instances where the ratios of the variance components can be regarded as known. They have the prescribed long-run frequency of coverage when there is repeated sampling of the random effects as well as the residual effects. They have smaller expected volume than confidence regions obtained by proceeding as though the random effects are fixed effects.
TL;DR: In this paper, a single-sample procedure is proposed for obtaining asymptotically optimum confidence intervals for the largest mean of k normal populations with common unknown variance, and a single sample procedure is used to obtain the confidence intervals.
Abstract: A single-sample procedure is proposed for obtaining asymptotically optimum confidence intervals for the largest mean of k normal populations with common unknown variance.
TL;DR: In this article, the distribution-free outer confidence interval for the quantile interval introduced by Wilks is investigated and some bounds for the probability of correct coverage of the interval are derived.
Abstract: This paper investigates the distribution-free outer confidence interval for the quantile interval introduced by Wilks. Besides exact expressions and a recurrence formula some bounds are derived for the probability of correct coverage of the quantile interval which improve bounds known up to now, and which are tested in several examples. Asymptotic approximations are discussed and applications of the developed methods to other statistics based on order statistics are indicated.
TL;DR: It is shown that distribution-free confidence intervals can be placed about the resubstitution estimate of the probability of error of any linear discrimination procedure.
Abstract: It is shown that distribution-free confidence intervals can be placed about the resubstitution estimate of the probability of error of any linear discrimination procedure.
TL;DR: The authors compared the decisions of student subjects where one set of subjects was provided both a confidence interval statement about the variability of a population and several observations from prior periods and the other set was provided solely with the observations.
Abstract: reports. However, the results failed to show any significant differences, and they are offered simply as a note to guide others now interested in this topic. In the experiment, we compared the decisions of student subjects where one set of subjects was provided both a confidence interval statement about the variability of a population and several observations from prior periods and the other set was provided solely with the observations. (For reasons described below the task was not set in an accounting environment.) No significant differences were found between the two disclosure conditions. The presence of a formal confidence interval statement did not yield significant differences in the subject's decision, regardless of whether the variability in the attribute reported on was set at a high or low level. The only manipulation that produced a significant result was when the size of the variance in the attribute was changed from low to high in the experiment.
TL;DR: In this article, it is shown that a statistic due to Morrison is to be preferred, unless there is a large variance difference, and the usual procedure is to treat the individual differences as a random sample and then to calculate a confidence interval or to perform a test of significance by means of a one-sample t test.
Abstract: SUMMARY Several procedures have been suggested for estimating the mean difference from correlated data with missing observations on one response. By Monte Carlo studies it is shown that a statistic due to Morrison is to be preferred, unless there is a large variance difference. An often-used experimental design is one in which observations are obtained from the same sampling units under two different conditions, the purpose being the estimation or testing of the mean difference. The usual procedure is to treat the individual differences as a random sample and then to calculate a confidence interval or to perform a test of significance by means of a one-sample t test.
TL;DR: In this article, the variability of nitrate-nitrogen concentrations in soil water in samples taken at 09-m intervals from the 45- to 119m depth from four holes per site.
Abstract: Data from a study of 56 field sites were used to examine the variability of nitrate-nitrogen concentrations in the unsaturated zone underneath the root zone The specific data were nitrate-nitrogen concentrations in soil water in samples taken at 09-m intervals from the 45- to 119-m depth from four holes per site Analyses of variance of these data provided estimates of variances that were used to predict the depth sampling interval and the number of holes required for site means to be within confidence limits of 10, 20, and 30% Calculations were based on sampling intervals of 09, 06, and 03 m providing 9, 13, and 26 samples per hole, respectively Relationships developed between number of sites, number of holes required, sampling interval, and confidence limits were used to test selected sampling plans for degree of precision in comparison with the actual sampling procedure A cost analysis of the field study indicated that it would cost three to four times more than the field study to use a sampling plan which would reasonably ensure that 75% of the sites' true means fall within 20% of the measured means at a confidence level of 95%
TL;DR: In this paper, Steinhorst and Bowden [5] used the theory of Roy's maximum root test statistics to set confidence bands for, of the normal population with mean and variance σ2, k being the pth quantile of the standard normal distribution, I fixed or specified but unknown and p known.
Abstract: Given the general linear regression model , where y is N X 1, X of full rank is N X (q + 1), is (q + 1) X 1, and e is N(0, σ2I), Steinhorst and Bowden [5], using the theory of Roy's maximum root test statistics, set confidence bands for , of the normal population with mean and variance σ2, k being the pth quantile of the standard normal distribution, I fixed or specified but unknown and p known. However, narrower bands may be obtained using the exact test statistic, Student's t. The bands lead to confidence intervals for a known fixed I for which a given component of y, say, , is the pth quantile of the distribution of that component of y, or, conversely, confidence intervals for yp for fixed I.
TL;DR: Reliability tended to be reduced when precaviation (initial) lesions were included in the DMFS count, but there was little difference between the reliability coefficients for each of four different surface-types.
Abstract: The reliability of caries data obtained during three clinical trials is presented. Each of the three trials, conducted by different examiners, lasted 3 years and involved children aged 12 to 15 years. Reliability was quantified in terms of reliability coefficient and error variance, which allowed the effect of error upon the efficiency of each study to be measured. Reliability tended to be reduced when precavitation (initial) lesions were included in the DMFS count, but there was little difference between the reliability coefficients for each of four different surface-types. Error was more important in 3-year incremental rather than prevalence data, but nevertheless had a rather small influence upon sample size estimation or confidence limits of percent caries reductions.
TL;DR: In this paper, the authors reviewed the existing results for the maximum likelihood estimation of the parameters of a 2-parameter Weibull life distribution for the case where the data are censored by failures due to an arbitrary number of independent 2parameter failure modes, and showed that sudden death endurance test results can be analyzed as a special case of competing-mode censoring.
Abstract: Existing results are reviewed for the maximum likelihood (ML) estimation of the parameters of a 2-parameter Weibull life distribution for the case where the data are censored by failures due to an arbitrary number of independent 2-parameter Weibull failure modes. For the case where all distributions have a common but unknown shape parameter the joint ML estimators are derived for i) a general percentile of the j-th distribution, ii) the common shape parameter, and iii) the proportion of failures due to failure mode j. Exact interval estimates of the common shape parameter are constructable in terms of the ML estimates obtained by using i) the data without regard to failure mode, and ii) existing tables of the percentage points of a certain pivotal function. Exact interval estimates for a general percentile of failure-mode-j distribution are calculable when the failure proportion due to failure-mode-j is known; otherwise a joint s-confidence region for the percentile and failure proportion is calculable. It is shown that sudden death endurance test results can be analyzed as a special case of competing-mode censoring. Tabular values for the construction of interval estimates for the 10-th percentile of the failure-mode-j distribution are given for 17 combinations of sample size (from 5 to 30) and number of failures.
TL;DR: This study analyzes the degree of confidence that can be placed in cost predictions for airframes from standard cost models and develops statistical theory to test the independence of component models and to estimate predictive statistics for aggregated cost estimates.
Abstract: Past experience of cost overruns in weapon system acquisition programs has underscored the variation between cost estimates and actual expenses. This study analyzes the degree of confidence that can be placed in cost predictions for airframes from standard cost models. Each airframe cost observation is partitioned into six components based on phases of the development or production cycle, e.g., flight test costs and manufacturing labor wages. Confidence measures are then compared for alternative model forms and for the use of a single regression on total costs versus the aggregation of regressions on component costs. We develop statistical theory to test the independence of component models and to estimate predictive statistics for aggregated cost estimates. Component regression errors are found to be significantly correlated, thereby increasing the width of confidence intervals. To assume error independence for the sake of simplifying the confidence assessment is thus misleading.
TL;DR: In this article, the authors derived simultaneous confidence intervals for all or certain subsets of the parameters of a balanced incomplete random model based on the mean squares of the analysis of variance.
Abstract: Inferences concerning the variance ratios of a random linear model are important in genetics and other areas of scientific investigation. For example, in genetics, the heritability parameters are functions of the variance ratios of a random model. This paper derives simultaneous confidence intervals for all or certain subsets of the parameters of a balanced incomplete random model. This procedure is based on the mean squares of the analysis of variance, and the mean squares are linear functions of a set of minimal sufficient statistics for estimating the parameters of the model. The procedure is demonstrated for a layout of six treatments, ten blocks, and five observations per block.
TL;DR: In this paper, the problem of construction of simultaneous confidence intervals among probabilities of success on the basis of matched samples has been studied for contrasts among several binomial populations, each with the same number, say J, of classes.
Abstract: It is well known (see, e.g., Scheffe (1959)) that if confidence intervals are desired for several treatment comparisons of interest, especially after a preliminary test of significance, then the appropriate technique is to consider simultaneous confidence intervals with a certain joint confidence coefficient. Goodman (1964) derived such simultaneous confidence intervals for contrasts among several multinomial populations, each with the same number, say J, of classes. The special case involving simultaneous confidence intervals for contrasts among several binomial populations on the basis of independent samples follows simply by taking J=2. This paper now deals with the problem of construction of simultaneous confidence intervals among probabilities of ‘success’ on the basis of matched samples.
TL;DR: Based on a random sample from the normal cumulative distribution function with unknown parameters μ and σ, one-sided confidence contours for ϕ(x; μ, σ), −∞
Abstract: Based on a random sample from the normal cumulative distribution function ϕ(x; μ, σ) with unknown parameters μ and σ, one-sided confidence contours for ϕ(x; μ, σ), −∞
TL;DR: The reliability and validity coefficients were computed for a 60-item four-choice test of English vocabulary in which examinees were asked to mark on a three-level scale the degree of confidence with respect to a word as mentioned in this paper.
Abstract: The reliability and validity coefficients were computed for a 60-item four-choice test of English vocabulary in which examinees were asked to mark on a three-level scale the degree of confidence wi...
TL;DR: In this paper, four methods of approximating confidence limits for the single negative binomial parameter, P, are outlined and an empirical study is presented and some remarks on prediction intervals are also included.
Abstract: Four methods of approximating confidence limits for the single negative binomial parameter, P, are outlined and an empirical study is presented. Some remarks on prediction intervals are also included.
TL;DR: In this paper, distribution-free tolerance intervals for stochastically ordered distributions with order statistics in samples of the same size from each of the distributions were defined for determining such intervals.
Abstract: Consider $k$ stochastically ordered distributions with $F_{(1)} \leqq\cdots\leqq F_{(k)}$. The present paper deals with distribution-free tolerance intervals for $F_{(j)}$ based on order statistics in samples of same size from each of the $k$ distributions. Two criteria are defined for determining such intervals. These two criteria are extensions of $\beta$-expectation tolerance intervals and $\beta$-content tolerance intervals with confidence coefficient $\gamma$ used in the single population literature. A tolerance interval for the lifetime distribution of a series system is considered as an example.