Showing papers on "Confidence interval published in 1975"
TL;DR: In this paper, the authors investigated the likelihood ratio method for confidence interval estimation of survival or life-time probabilities for censored data, which depends on a constrained product-limit estimator for the survival function.
Abstract: The likelihood ratio method for confidence interval estimation of survival or life-time probabilities is investigated for censored data. This approach depends on a constrained product-limit estimator for the survival function. The likelihood method is compared with two alternative methods based on normal approximations to the product-limit estimator for several cases of uncensored and randomly censored samples. The methods are generalized for the ratio of two survival probabilities.
303 citations
TL;DR: In this article, a type of hybrid retrospective design for epidemiologic studies within defined populations is considered, which requires exposure information for the complete population of cases and for a random sample of the original population at risk (PAR).
Abstract: A type of hybrid retrospective design for epidemiologic studies within defined populations is considered. The design requires “exposure” information for the complete population of cases and for a random sample of the original population at risk (PAR). Assuming that the only stochastic feature occurs with the random sampling of the PAR, confidence intervals for incidence rates and relative risk (R) are developed in conjunction with PAR sample size requirements. Analysis by stratification is discussed and a numerical example included.
111 citations
TL;DR: In this paper, the regenerative method for estimating parameters in a simulation requires the simulator to estimate the ratio of two means, and five point estimates and four confidence intervals for this ratio have been computed for three stochastic simulations.
Abstract: The regenerative method for estimating parameters in a simulation requires the simulator to estimate the ratio of two means. Five point estimates and four confidence intervals for this ratio have been computed for three stochastic simulations. The jackknife method appears to be the most promising for both point and interval estimation.
103 citations
TL;DR: Approximate parametric prediction intervals are obtained for an unobserved random variable when the amount of data on which to base the estimation is large as discussed by the authors, and applications include the construction of approximate confidence intervals in empirical Bayes estimation.
Abstract: Approximate parametric prediction intervals are obtained for an unobserved random variable when the amount of data on which to base the estimation is large. Applications include the construction of approximate confidence intervals in empirical Bayes estimation.
79 citations
TL;DR: In the statistical analysis of the values of luteinizing hormone, follicle-stimulating hormone, estradiol, and progesterone obtained from normal menstrual cycles, a depature from normality was noted and the distributions were not normal (Gaussian) but log-normal.
77 citations
TL;DR: There was no evidence from this study that consumption of above average amounts of saccharin had led to bladder cancer in diabetics, and the proporation of current smokers among diabetic was significantly less than among non-diabetics.
Abstract: The frequency with which diabetes mellitus was mentioned on the death certificates of 18,733 patients dying from bladder cancer has been compared with that of 19,709 patients dying from other cancers (excluding cancer of the lung and pancreas). The estimated relative risk of bladder cancer in diabetics was 0-98 with 95% confidence limits 0-70-1-38. There was no increase in risk of bladder cancer in patients with diabetes of long duration. Diabetics were shown by questionnaire to consume substantially more saccharin than non-diabetics, and the duration of regular saccharin use by diabetics was highly correlated with the duration of diabetes. There was therefore no evidence from this study that consumption of above average amounts of saccharin had led to bladder cancer in diabetics. The proporation of current smokers among diabetics was significantly less than among non-diabetics, and this may account for a low relative risk of lung cancer in the former (0-72).
73 citations
TL;DR: Although the standard deviation is the most widely used measure of the precision of quantitative methods, there is a need to re-examine the conditions necessary to obtain a meaningful estimate of this quantity.
Abstract: Although the standard deviation is the most widely used measure of the precision of quantitative methods, there is a need to re-examine the conditions necessary to obtain a meaningful estimate of this quantity. The importance of the material to be sampled, the sample size, the calculation of confidence intervals, and the segregation of outliers are discussed.
65 citations
TL;DR: This paper obtained Edgeworth or Gram-Charlier expansions for the t ratio of instrumental variable and k-class estimators, and used them to give approximations to the confidence intervals obtained from these t ratios.
Abstract: This paper obtains Edgeworth or Gram-Charlier expansions for the t ratio of instrumental variable and k-class estimators, and uses them to give approximations to the confidence intervals obtained from these t ratios. These confidence intervals for large sample size are more accurate than the usual asymptotic confidence interval. Charlier expansions is applied to the t ratio of 2SLS and non-stochastic k-class estimators. Previous general theorems in this field, with the exception of those given by Chambers [2], such as those in [3] have assumed that the statistic has moments of appropriate orders. The theorem proved here assumes only that it can be expressed as a function of other variables with moments of all orders with appropriate properties in some neighborhood of the origin. It can be applied to a wide range of
64 citations
TL;DR: In this article, the authors used the alternate method of moments to determine confidence limits for several common probability distributions, and showed that the assumption of normality of the distribution of design events is valid for quite small samples.
Abstract: Frequency analysis is commonly used in hydrology to define flood plains, design hydraulic structures, and aid in watershed planning and management. Although design event magnitudes may be determined analytically by using probability distributions, the analytical determination of confidence limits for the design event is not easy. Using the alternate method of moments to determine confidence limits involves an assumption of normality of the distribution of design events. It is shown by data generation that this assumption is valid for quite small samples. Tables are given to compute confidence limits in this manner for several common probability distributions.
59 citations
37 citations
TL;DR: In this article, a Stein-type two-stage procedure is presented and some of its properties are investigated, and it is shown that the procedure is generally more efficient than Chapman's [1] solution.
Abstract: We consider the problem of constructing a fixed-width confidence interval for the difference between the means of two normal populations with unknown variances. A Stein-type two-stage procedure is presented and some of its properties are investigated. It is shown that the procedure is generally more efficient than Chapman's [1] solution.
TL;DR: A new method is presented which enables intervals with almost the desired level of confidence to be easily computed from the initial samples on which W is based.
Abstract: In this study we are concerned with the construction of confidence intervals for the conditional probability of misallocation associated with Anderson's classification statistics, W. The available methods of computing confidence intervals for the conditional probability are not satisfactory in practice, mainly because the intervals obtained are fairly inaccurate. A new method is presented which enables intervals with almost the desired level of confidence to be easily computed from the initial samples on which W is based.
TL;DR: In this paper, some families of distributions are presented for which certain Neyman confidence intervals have very poor conditional properties, and more than one example is presented in order to show that the theory of confidence intervals cannot easily step around the difficulties presented to it.
Abstract: SUMMARY Some families of distributions are presented for which certain Neyman confidence intervals have very poor conditional properties. In each case there is a 50 % Neyman confidence interval I(x) for a parameter 0 and a subset A of the sample space such that the conditional probability that I(X) covers 0 given that X belongs to A is less than 0-2 for all 0 and the conditional probability that I(X) covers 0 given that X is not in A is at least 0-8 for all 0. The families of distributions are somewhat alike. More than one example is presented in order to show that the theory of confidence intervals cannot easily step around the difficulties presented to it.
TL;DR: In this article, conditional confidence intervals are obtained for the parameters of a double exponential distribution by finding the conditional distributions of the pivotal quantities (a)/ and /b given the ancillary statistics for a and b where a is the location parameter, b is the scale parameter, and (â and are the maximlrm likelihood estimators).
Abstract: Conditional confidence intervals are obtained for the parameters of a double exponential distribution. The intervals are produced by finding the conditional distributions of the pivotal quantities (â – a)/ and /b given the ancillary statistics for a and b where a is the location parameter, b is the scale parameter, and (â and are the maximlrm likelihood estimators. Conditional and unconditional confidence intervals are compared in an example.
TL;DR: A time-sharing program written in BASIC language has been developed to compute exact confidence limits for the odds ratio parameter in a 2 x 2 table based upon a recent redefinition of the exact p-value aimed at avoidance of conservatism in the classical procedure.
Abstract: A time-sharing program written in BASIC language has been developed to compute exact confidence limits for the odds ratio parameter in a 2 × 2 table. The program offers the user a choice between the classical exact limits and limits based upon a recent redefinition of the exact p -value aimed at avoidance of conservatism in the classical procedure. The user selects the degree of confidence desired during a run of the program, which then computes the exact limits and p -value.
TL;DR: In this paper, the accuracy of the finite population correlation is examined and a procedure based on a computer program for hypergeometric probabilities is described for obtaining exact confidence limits and exact confidence level.
Abstract: This article examines the accuracy of the finite population correlation ordinarily applied to binomial confidence limits, suggests a more accurate FPC and describes a procedure, based on a computer program for hypergeometric probabilities, for obtaining exact confidence limits and exact confidence level.
TL;DR: In this article, a random sample from the Weibull population with unknown shape and scale parameters, one-and two-sided confidence bands on the entire cumulative distribution function, and simultaneous confidence intervals for the interval probabilities under the distribution are constructed using Kolmogorov-Smirnov type statistics.
Abstract: Based on a random sample from the Weibull population with unknown shape and scale parameters, one- and two-sided confidence bands on the entire cumulative distribution function, and simultaneous confidence intervals for the interval probabilities under the distribution are constructed using Kolmogorov-Smirnov type statistics. Small sample and asymptotic percentiles of the relevant statistics are provided.
TL;DR: In this article, a method for computing Bayes confidence limits for the reliability of a redundant system of N subsystems, each having an exponential distribution of life with reliabilities, for given mission times is presented.
Abstract: A method is presented for computing Bayes confidence limits for the reliability R = 1 – Π i = 1 N (1 – Ri ) of a redundant system of N subsystems each having exponential distribution of life with reliabilities Ri = exp (– λ iti ) for given mission times ti . The failure rates are unknown and must be estimated from test data (life samples). The results provide a useful generalization of a previously published treatment in which test conditions were restricted to a single life sample for each subsystem. The present result places no such restriction on the test data. Exact confidence limits are obtained from the posterior distribution of system reliability which is developed in terms of an expansion in shifted Chebyshev polynomials of the second kind readily evaluated by an electronic computer.
TL;DR: In this article, ten variants of the procedure are defined for giving interval estimates for coefficient alpha, and the empirical results indicate that out of the ten variants, defined by five transformations and two methods of data subdivision, only two are justifiable competitors to Feldt's approach.
Abstract: Following a general introduction to Tukey's Jackknife technique and the construction of approximate confidence intervals, ten variants of the procedure are defined for giving interval estimates for coefficient alpha. A data base of known population characteristics was generated and used to compare the robustness of the ten Jackknife alternatives with Feldt's well-known sampling theory based upon the assumptions of normality. The empirical results indicate that out of the ten variants, defined by five transformations and two methods of data subdivision, only two are justifiable competitors to Feldt's approach.
TL;DR: In this paper, the confidence limits of correlation between marker horizons where correlation is uncertain are derived and the confidence curves are used as general tools in correlation in the East Midlands Coalfield.
Abstract: Correlation in coalfields depends on the recognition of suitable reference points in the succession. In the East Midlands coal seams and marker horizons provide the most dependable reference points recognizable in borehole records. Distinctive marker horizons provide especially useful reference points as they may be considered to mark points of absolute time equivalence, but their use is limited owing to their irregular distribution. A graphic technique is used to formulate ‘confidence limits of correlation’ between marker horizons where correlation is uncertain. Functions are derived which describe the confidence limits. Coal-seam correlation data from a set of boreholes are used to derive confidence curves in a number of cases. It is concluded that one set of curves may be used for all the Middle Coal Measures of the East Midlands Coalfield. Use of these curves as general tools in correlation is demonstrated.
TL;DR: In this article, the authors treat some of the special and unfamiliar problems encountered in presenting in a courtroom setting the result of a sample survey which leads to reporting an estimate, and develop that the minor problem of non-response in surveys is very much aggravated in legal evidentiary evaluation, leading to the necessity of exercising much more stringent follow-up procedures.
Abstract: This paper treats some of the special and unfamiliar problems encountered in presenting in a courtroom setting the result of a sample survey which leads to reporting an estimate. It develops that the minor problem of non-response in surveys is very much aggravated in legal evidentiary evaluation, leading to the necessity of exercising much more stringent follow-up procedures. It is claimed that the interval estimate form is almost ideally suited to presentation before a judge, jury, and legal counsel.
TL;DR: In this article, an outline of the general problems related to the operation of an analytical system with a detection function based on a two-step model is given, and an experimental example illustrates the calculation of both the detection limit and its confidence interval.
Abstract: An outline is given of the general problems related to the operation of an analytical system with a detection function based on a two-step model. Account is taken of both the false-detection probabilityP
10 to which corresponds the detection levelyk, and the true-detection probabilityP
11. For the frequentometric estimation of the detection limit one uses the detection characteristic of an analytical system, which has two variants. In the first variant the discrimination of the analytical signal is made relative to the background signaly0, whereas in the second variant, the discrimination is made relative to the detection levelyk. An experimental example illustrates the calculation of both the detection limit and its confidence interval.
15 Dec 1975
TL;DR: In this article, the authors deal with the problem of estimating the reliability function of integrated systems by point and confidence interval Bayes estimators, compared to the classical minimum variance and unbiased estimators in terms of their mean-squared errors at different combinations of the parameters.
Abstract: : The present paper deals with some problems of estimating the reliability function of integrated systems, by point and confidence interval Bayes estimators. The Bayes point estimators are compared to the classical minimum variance and unbiased estimators in terms of their mean-squared-errors at different combinations of the parameters. The deviation of the exact Bayes confidence limits is discussed. Since it is difficult to determine the exact confidence limits, conservative small sample approximations and the most sufficient large sample normal approximations are derived. The coverage probabilities of the corresponding Bayes confidence intervals and the expected values of these Bayes lower confidence are estimated by simulation experiments. (Author)
TL;DR: In this article, the authors show the potential benefits for managerial accounting in constructing confidence limits for the mean, the standard deviation, and the coefficient of variation, which is a measure similar to risk measures discussed in the finance literature.
Abstract: Previous work on probabilistic profit budgets has dealt with the construction of probability intervals for the items in the planning and control statements (e.g., direct costs, marginal contributions, profits, etc.). This paper expands that work by demonstrating the potential benefits for managerial accounting in constructing confidence limits for the mean, the standard deviation, and the coefficient of variation. The adequacy of the confidence interval for any account balance depends on the credibility of the sample standard deviation, s, as an estimate of the population standard deviation, σ. The confidence interval of the standard deviation assesses, in a sense, the precision of the point estimate, s. Furthermore, it takes on a meaning similar to risk measures discussed in the finance literature. Given confidence intervals for the mean and standard deviation, one can construct corresponding bands for the coefficient of variation. These bands give insight into the goodness of the accounting system and the stability of the budgetary model.
TL;DR: In this article, lower confidence limits for the impact probability within a circle of fixed radius in the bivariate normal case with zero mean vector were derived for independent coordinates and known ratio of variances.
Abstract: : Lower confidence limits are derived for the impact probability within a circle of fixed radius in the bivariate normal case with zero mean vector. For independent coordinates and known ratio of variances, the lower confidence limit is a strongly consistent estimator of the impact probability and is uniformly most accurate (UMA). When the ratio of the variances is also unknown, the lower confidence limit is a strongly consistent estimator of the impact probability. Some discussion is provided when the correlation between the coordinates is unknown. A Table of the impact probability function is provided which can be employed for both point estimation and for obtaining lower confidence limits and the use of the table is demonstrated. A FORTRAN program for the computation of the impact probability is included. (Author)
TL;DR: In this article, the most accurate unbiased confidence interval of level 1 − α for σ 1 2/σ2 2 is given for tests of level α of hypotheses specifying the value of σ1 2 /σ 2 2 2.
Abstract: Tables for constructing the uniformly most accurate unbiased confidence interval of level 1 − α for σ1 2/σ2 2, where σ1 2 and σ2 2 are the variances of two normal distributions, and for tests of level α of hypotheses specifying the value of σ1 2/σ2 2 are given for α = .1, .05, .01, .001, n 1,n 2 = 1(1)20(2)30, 36, 45, 60, 90, 180, ∞, where ni is the degree of freedom of the estimate of σi 2. The present tables, more accurate than previous ones, may also be applied to make similar inferences about the ratio of the means of two gamma distributions. Illustrations include applications in archaeology and telephony.
01 Jan 1975
TL;DR: In this paper, the problem of determining confidence intervals of preassigned length and confidence coefficient for the mean of a normal population with unknown variance is solved by the same procedure, and the stopping rules employed in sequential testing might not be meaningful in sequential estimation.
Abstract: Publisher Summary
In some problems, hypothesis-testing seems to be somewhat artificial. In fixed-sample size situation, there is a close connection between acceptance regions and confidence regions, whereas, such an analogy does not hold in the sequential situation—therefore, the need for a theory of sequential estimation. The stopping rules employed in sequential testing might not be meaningful in sequential estimation. The problem of determining confidence intervals of preassigned length and confidence coefficient for the mean of a normal population with unknown variance is solved by the same procedure. To make either the power of the test or the length of the confidence interval free of the variance, it seems necessary to waste a small portion of the information contained in the sample.
TL;DR: In response to an inquiry by Dr W. Mapleson regarding the solubility of halothane in dog blood (sec article in this issue), the following additional statistical information was obtained.
Abstract: Sir,—In response to an inquiry by Dr W. W. Mapleson regarding the solubility of halothane in dog blood (sec article in this issue), I would like to make note of the following additional statistical information which we obtained (Cowles, Borgstedt and Gillies, 1971). The relation between haemoglobin and solubility showed a mean solubility at 37.5°C of 3.11 at a haemoglobin concentration of 15.0 g/100 ml and 95% confidence Limits for the true mean of 2.94 to 3.27 (±0.17). The regression line had a slope of —0.003 with 95% confidence limits of —0.097 to +0.090. The relation between haematocrit and solubility gave the following: mean solubility at a haematocrit of 45% : 3.10, 95% confidence Limits for the true mean: 2.92 to 3.29 (±0.18), slope: —0.002, and 95% confidence limits: —0.033 to +0.029. The standard errors given in our publication were for a single observation of solubility.