Sequential Fixed Width Confidence Intervals for the Offset Between Two Network Clocks

Abstract

Estimation of the offset between two network clocks has received a lot of attention in the literature, with the motivating force being data networking applications that require synchronous communication protocols. Statistical modeling techniques have been used to develop improved estimation algorithms, with a recent development being the construction of a confidence interval based on a fixed sample size. Lacking in the fixed sample size confidence interval procedures is a useable relationship between sample size and the width of the resulting confidence interval. Were that available, an optimum sample size could be determined to achieve a specified level of precision in the estimator and thereby improve the efficiency of the estimation procedure by reducing unnecessary overhead in the network that is associated with collecting the data used by the estimation schemes. A fixed sample size confidence interval that has a prescribed width is not available for this problem. However, in this paper we develop and compare alternative sequential intervals with fixed width and demonstrate that an effective solution is available.     

CONFIDENCE INTERVALS FOR ROBUST ESTIMATES OF THE FIRST ORDER AUTOREGRESSIVE PARAMETER

Abstract. The confidence interval properties of several estimators of the transition parameter, φ, in the first order autoregressive model are examined by a Monte Carlo study. The least squares confidence interval estimator, as well as two forms of a proposed robust confidence interval based on a generalized M-estimator, are examined under two model alternatives to the classical time series approach: the innovations model (the time series is observed 'perfectly') and the additive effects model (the time series is observed plus an added 'effect'). Samples were generated from a number of symmetric distributions, including the Gaussian and a variety of contaminated distributions with mild to heavy contamination. Over a range of outlier models, values of φ (.25 to.9), and sample sizes (20 to 100), it was found that the GM-estimators possess desirable confidence interval robustness properties in terms of validity and efficiency. In general, the least squares confidence interval is not robust against symmetric heavy-tailed contamination in the innovations model or against the additive effects model.     

Estimating a minimum set of physically based dynamic parameters to enhance statistical inference in block-oriented modeling

In process identification (i.e., dynamic model development) information on the precision and reliability of a parameter estimate is conveyed by a confidence interval. The best confidence interval is the one with the shortest width for a given level of confidence. Confidence intervals widen as the standard error increases or as the number of estimated parameters increases. When the value of a parameter is needed for physical understanding of process characteristics, its precision and reliability, i.e., certainty, is crucial. Parameter certainty increases as the number of estimated parameters decreases because this causes confidence intervals to shorten and confidence levels to increase. Hence, this article focuses on maximizing parameter certainty of physically interpretable dynamic parameters under block-oriented modeling by obtaining accurate values for all the dynamic parameters from a minimum set of estimated parameters. This objective is accomplished by the development of a procedure that identifies equivalent sets of parameters and estimates one parameter for each set. For a seven (7) input, five (5) output, simulated CSTR, its 84 physically based dynamic parameters were accurately determined from 23 estimated parameters that resulted in an increase in confidence level from 50% to 99.9% for a fixed interval width.     

Profit optimization for chemical process plant based on a probabilistic approach by incorporating material flow uncertainties

This paper reports how the economic performance of a chemical process plant is affected by material flow uncertainties from the plant inlet and outlet. Two chance-constrained optimization models were proposed. The models were tested using case studies of an existing gas processing plant. Profit optimization for the case studies was made with respect to the reliability of holding the process constraints at a certain confidence level [0.5, 1]. The optimal profit change for uncertainty from the plant inlet within the confidence interval [0.96, 1] was 86%. On the other hand, the optimal profit change for uncertainty from the plant outlet was only 2% for the same confidence level interval considered. This suggests that the uncertainty from the plant inlet has a major impact on the overall economic performance of the plant. Sensitivity analysis showed how uncertain parameters from both plant sides can affect the overall profit significantly.     

An asymptotically optimal fixed-width confidence interval for the difference of two normal means

We consider the problem of providing a fixed width confidence interval for the difference of two normal means when the variances are unknown and unequal. We propose a two-stage procedure that differs from those of Chapman (1950) and Ghosll (1975). The procedure provides the desired confidence, subject to the restriction on the width, for certain values of the design parameter h. Values of h are given by the Monte Carlo rnethod for various combinations of first stage sample size and confidence level. Finally, it is shown that the procedure is asymptotically more efficient than those of Chapmail and Ghosh with respect to total sample size, as the width of the interval approaches zero.     

Empirical likelihood confidence intervals for the mean of a long‐range dependent process

Abstract. This paper considers blockwise empirical likelihood for real‐valued linear time processes which may exhibit either short‐ or long‐range dependence. Empirical likelihood approaches intended for weakly dependent time series can fail in the presence of strong dependence. However, a modified blockwise method is proposed for confidence interval estimation of the process mean, which is valid for various dependence structures including long‐range dependence. The finite‐sample performance of the method is evaluated through a simulation study and compared with other confidence interval procedures involving subsampling or normal approximations.     

基于岭估计的化工过程测量置信水平研究(英文)

Ordinary least squares （OLS） algorithm is widely applied in process measurement, because the sensor model used to estimate unknown parameters can be approximated through multivariate linear model. However, with few or noisy data or multi-collinearity, unbiased OLS leads to large variance. Biased estimators, especially ridge es-timator, have been introduced to improve OLS by trading bias for variance. Ridge estimator is feasible as an esti-mator with smaller variance. At the same confidence level, with additive noise as the normal random variable, the less variance one estimator has, the shorter the two-sided symmetric confidence interval is. However, this finding is limited to the unbiased estimator and few studies analyze and compare the confidence levels between ridge estima-tor and OLS. This paper derives the matrix of ridge parameters under necessary and sufficient conditions based on which ridge estimator is superior to OLS in terms of mean squares error matrix, rather than mean squares error. Then the confidence levels between ridge estimator and OLS are compared under the condition of OLS fixed sym-metric confidence interval, rather than the criteria for evaluating the validity of different unbiased estimators. We conclude that the confidence level of ridge estimator can not be directly compared with that of OLS based on the criteria available for unbiased estimators, which is verified by a simulation and a laboratory scale experiment on a single parameter measurement.     

A Confidence Interval That Is Consistent and More Informative Than a Sequential Equivalence Test for a Normal Mean

Abstract

This note shows how to construct a 1 ? β level symmetric confidence interval for a normal mean θ that is consistent with and more informative than a size β sequential equivalence test of H ₀ :|θ| > δ against the alternative H_a :|θ | ≤ δ, where δ>0 is a prespecified limit of equivalence. If the null hypothesis H ₀ is rejected and so equivalence can be declared by the test, then the confidence interval is contained in the interval [? δ, δ]. If the null hypothesis H₀ is not rejected and so equivalence cannot be declared by the test, then the confidence interval contains the interval [? δ, δ]. Therefore the test and the confidence interval are consistent in rejection or non-rejection of H ₀. But the confidence interval provides extra information on the magnitude of θ, and is therefore more informative than the test.     

Efficient interval estimation for age-adjusted cancer rates

The age-adjusted cancer rates are defined as the weighted average of the age-specific cancer rates, where the weights are positive, known, and normalized so that their sum is 1. Fay and Feuer developed a confidence interval for a single age-adjusted rate based on the gamma approximation. Fay used the gamma approximations to construct an F interval for the ratio of two age-adjusted rates. Modifications of the gamma and F intervals are proposed and a simulation study is carried out to show that these modified gamma and modified F intervals are more efficient than the gamma and F intervals, respectively, in the sense that the proposed intervals have empirical coverage probabilities less than or equal to their counterparts, and that they also retain the nominal level. The normal and beta confidence intervals for a single age-adjusted rate are also provided, but they are shown to be slightly liberal. Finally, for comparing two correlated age-adjusted rates, the confidence intervals for the difference and for the ratio of the two age-adjusted rates are derived incorporating the correlation between the two rates. The proposed gamma and F intervals and the normal intervals for the correlated age-adjusted rates are recommended to be implemented in the Surveillance, Epidemiology and End Results Program of the National Cancer Institute.     

On stopping times for fixed-width confidence regions

Analogous to the usual stopping time for fixed-width confidence interval estimation of a real-valued parameter θ(F), a stopping time for fixed-width confidence band estimation of, a statistical functional process R^F is considered. Techniques for showing that the resulting sequential confidence region has the correct asymptotic coverage probability are illustrated in several examples. Sufficient conditions for asymptotic efficiency and normality of the stopping time are given. Some implications of using the stopping time in conjunction with a bootstrap confidence band procedure are investigated in the context of estimating a dstribution function.     

Gas emission source term estimation with 1-step nonlinear partial swarm optimization-Tikhonov regularization hybrid method

Source term identification is very important for the contaminant gas emission event.Thus,it is necessary to study the source parameter estimation method with high computation efficiency,high estimation accuracy and reasonable confidence interval.Tikhonov regularization method is a potential good tool to identify the source parameters.However,it is invalid for nonlinear inverse problem like gas emission process.2-step nonlinear and linear PSO (partial swarm optimization)-Tikhonov regularization method proposed previously have estimated the emission source parameters successfully.But there are still some problems in computation efficiency and confidence interval.Hence,a new 1-step nonlinear method combined Tikhonov regularization and PSO algorithm with nonlinear forward dispersion model was proposed.First,the method was tested with simulation and experiment cases.The test results showed that 1-step nonlinear hybrid method is able to estimate multiple source parameters with reasonable confidence interval.Then,the estimation performances of different methods were compared with different cases.The estimation values with 1-step nonlinear method were close to that with 2-step nonlinear and linear PSO-Tikhonov regularization method.1-step nonlinear method even performs better than other two methods in some cases,especially for source strength and downwind distance estimation.Compared with 2-step nonlinear method,1-step method has higher computation efficiency.On the other hand,the confidence intervals with the method proposed in this paper seem more reasonable than that with other two methods.Finally,single PSO algorithm was compared with 1-step nonlinear PSO-Tikhonov hybrid regularization method.The results showed that the skill scores of 1-step nonlinear hybrid method to estimate source parameters were close to that of single PSO method and even better in some cases.One more important property of 1-step nonlinear PSO-Tikhonov regularization method is its reasonable confidence interval,which is not obtained by single PSO algorithm.Therefore,1-step nonlinear hybrid regularization method proposed in this paper is a potential good method to estimate contaminant gas emission source term.     

Adaptive sequential confidence intervals for A location Parameter

Let θ + X₁, θ + X₂... be a random sample and X_i's have a common distribution function F, where F has an absolutely continuous density f that is symmetric about origin. For a given confidence coefficient, a fully sequential procedure is proposed for constructing a fixed-width confidence interval for the location parameter θ. The result is based on Stone's (1975) adaptive maximum likelihood estimator. under mild conditions the procedure is shown to be asymptotically consistent and fully efficient.     

Prediction of observer variation in estimating colorimetric values

This article describes a method for computing easily the contribution of observer variation to colorimetric values. Stiles's 20 observers are used for representing color-normal observers. Deviation functions are derived by applying singular-decomposition analysis to their 20 color-matching functions. It is shown that variances and covariances of the 20 color-matching functions are estimated correctly by using the four deviation functions with high contribution factors. By using these deviation functions, a method is developed to derive the confidence ellipsoid of tristimulus values, the confidence ellipse of chromaticity coordinates, and the confidence interval of tristimulus value Y, in the colorimetric computations of a reflecting sample and an illuminant. With a slight modification, the method also can be used to predict the degree of mismatch found by color-normal observers for pairs of reflecting samples that are a metameric match with respect to the average observer and a standard illuminant.     

Comparison of non-parametric confidence intervals for the area under the ROC curve of a continuous-scale diagnostic test

The accuracy of a diagnostic test with continuous-scale results is of high importance in clinical medicine. It is often summarised by the area under the ROC curve (AUC). In this article, we discuss and compare nine non-parametric confidence intervals of the AUC for a continuous-scale diagnostic test. Simulation studies are conducted to evaluate the relative performance of the confidence intervals for the AUC in terms of coverage probability and average interval length. A real example is used to illustrate the application of the recommended methods.     

Dealing with discreteness: making 'exact' confidence intervals for proportions,differences of proportions,and odds ratios more exact

'Exact' methods for categorical data are exact in terms of using probability distributions that do not depend on unknown parameters. However, they are conservative inferentially. The actual error probabilities for tests and confidence intervals are bounded above by the nominal level. This article examines the conservatism for interval estimation and describes ways of reducing it. We illustrate for confidence intervals for several basic parameters, including the binomial parameter, the difference between two binomial parameters for independent samples, and the odds ratio and relative risk. Less conservative behavior results from devices such as (1) inverting tests using statistics that are 'less discrete', (2) inverting a single two-sided test rather than two separate one-sided tests each having size at least half the nominal level, (3) using unconditional rather than conditional methods (where appropriate) and (4) inverting tests using alternative p-values. The article concludes with recommendations for selecting an interval in three situations-when one needs to guarantee a lower bound on a coverage probability, when it is sufficient to have actual coverage probability near the nominal level, and when teaching in a classroom or consulting environment.     

Circulating miR-208b and miR-34a Are Associated with Left Ventricular Remodeling after Acute Myocardial Infarction

Left ventricular remodeling after acute myocardial infarction (AMI) is associated with adverse prognosis. It is becoming increasingly clear that circulating miRNAs could be promising biomarkers for various pathological processes in the heart, including myocardial infarction, myocardial remodeling and progression to heart failure. In the present study, a total of 359 consecutive patients were recruited. Plasma samples were collected on admission. Echocardiographic studies were performed during the admission and at six months follow-up after AMI. Remodeling was defined as an at least 10% increase from baseline in the left ventricular end-diastolic volume. Plasma miRNA levels were assessed for association with six months mortality or development of heart failure. Results showed that levels of plasma miR-208b and miR-34a were significantly higher in patients with remodeling than those without. Increased miRNA levels were strongly associated with increased risk of mortality or heart failure within six months for miR-208b (OR 17.91, 95% confidence interval = 2.07–98.81, p = 0.003), miR-34a (OR 4.18, 95% confidence interval = 1.36–12.83, p = 0.012) and combination of the two miRNAs (OR 18.73, 95% confidence interval = 1.96–101.23, p = 0.000). The two miRNA panels reclassified a significant proportion of patients with a net reclassification improvement of 11.7% (p = 0.025) and an integrated discrimination improvement of 7.7% (p = 0.002). These results demonstrated that circulating miR-208b and miR-34a could be useful biomarkers for predicting left ventricular remodeling after AMI, and the miRNA levels are associated with increased risk of mortality or heart failure.     

Effects of experimental design on calibration curve precision in routine analysis

A computational program which compares the effciencies of different experimental designs with those of maximum precision (D-optimized designs) is described. The program produces confidence interval plots for a calibration curve and provides information about the number of standard solutions, concentration levels and suitable concentration ranges to achieve an optimum calibration. Some examples of the application of this novel computational program are given, using both simulated and real data.     

杀菌剂氟吗啉和多菌灵对蚯蚓的急性毒性

采用自然土和OECD标准人工土研究了氟吗啉和多菌灵对蚯蚓的急性毒性，并对试验过程中蚯蚓的中毒症状和形态、行为变化进行了观察。结果表明，氟吗啉在自然土壤中对蚯蚓的LC50为592．73mg／kg，95％置信区间为562．41～623．80mg／kg；氟吗啉在人工土壤中对蚯蚓的LC50为318．79mg／kg，95％置信区间为181．63-543．79mg／kg。多菌灵在自然土壤中对蚯蚓的LC50为26．53mg／kg，95％置信区间为15．98-42．93mg／kg；多菌灵在人工土壤中对蚯蚓的LC50为5．57mg／kg，95％置信区间为2．48～11．83mg／kg。依据农药对蚯蚓的毒性等级划分标准，氟吗啉在自然土壤和人工土壤中对蚯蚓的毒性均为低毒级；多菌灵在自然土壤中对蚯蚓的毒性为低毒级，而在人工土壤中对蚯蚓的毒性为中毒级。     

氯胺磷对松褐天牛幼虫的室内毒力测定

采用室内药液点滴法,测定了氯胺磷对钻蛀马尾松枝干的松褐天牛3龄幼虫的致死中量(LD50)、90%致死量(LD90)和致死中量的95%置信区间,为进一步研究林间最佳的应用施药量,达到高效、经济和安全的防治目标提供依据。结果表明,氯胺磷的LD50及95%置信区间、LD90分别为0.0007(0.0002～0.0011)、0.0712μg/头,乙酰甲胺磷的LD50及95%置信区间、LD90分别为0.001 2(0.000 5～0.001 8)、0.114 7μg/头,在室内毒力方面,氯胺磷优于乙酰甲胺磷。     

Inference for Autocorrelations in the Possible Presence of a Unit Root

Abstract.  We consider the problem of making inference for the autocorrelations of a time series in the possible presence of a unit root. Even when the underlying series is assumed to be strictly stationary, the robustness against a unit root is a desirable property to ensure good finite-sample coverage in case the series has a near unit root. In addition to discussing a confidence interval for the autocorrelation at a given lag, we also consider a simultaneous confidence band for the first k autocorrelations. We suggest the use of the subsampling method applied to properly studentized statistics, which results in confidence intervals and bands with asymptotically correct coverage probability. An application to practical model selection is given, while a simulation study examines finite-sample performance.