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81.
82.
ROBERT L. PAIGE A. ALEXANDRE TRINDADE P. HARSHINI FERNANDO 《Scandinavian Journal of Statistics》2009,36(1):98-111
Abstract. We propose an easy to implement method for making small sample parametric inference about the root of an estimating equation expressible as a quadratic form in normal random variables. It is based on saddlepoint approximations to the distribution of the estimating equation whose unique root is a parameter's maximum likelihood estimator (MLE), while substituting conditional MLEs for the remaining (nuisance) parameters. Monotoncity of the estimating equation in its parameter argument enables us to relate these approximations to those for the estimator of interest. The proposed method is equivalent to a parametric bootstrap percentile approach where Monte Carlo simulation is replaced by saddlepoint approximation. It finds applications in many areas of statistics including, nonlinear regression, time series analysis, inference on ratios of regression parameters in linear models and calibration. We demonstrate the method in the context of some classical examples from nonlinear regression models and ratios of regression parameter problems. Simulation results for these show that the proposed method, apart from being generally easier to implement, yields confidence intervals with lengths and coverage probabilities that compare favourably with those obtained from several competing methods proposed in the literature over the past half-century. 相似文献
83.
《Journal of Statistical Computation and Simulation》2012,82(1-3):87-113
An important problem in process adjustment using feedback is how often to sample the process and when and by how much to apply an adjustment. Minimum cost feedback schemes based on simple, but practically interesting, models for disturbances and dynamics have been discussed in several particular cases. The more general situation in which there may be measurement and adjustment errors, deterministic process drift, and costs of taking an observation, of making an adjustment, and of being off target, is considered in this article. Assuming all these costs to be known, a numerical method to minimize the overall expected cost is presented. This numerical method provides the optimal sampling interval, action limits, and amount of adjustment; and the resulting average adjustment interval, mean squared deviation from target, and minimum overall expected cost. When the costs of taking an observation, of making an adjustment, and of being off target are not known, the method can be used to choose a particular scheme by judging the advantages and disadvantages of alternative options considering the mean squared deviation they produce, the frequency with which they require observations to be made, and the resulting overall length of time between adjustments. Computer codes that perform the required computations are provided in the appendices and applied to find optimal adjustment schemes in three real examples of application. 相似文献
84.
Kallappa M. Koti 《统计学通讯:理论与方法》2013,42(10):3671-3676
Some inequalities are established in P1(r, s) and P1(r+1, s), where P1(r, s) is the confidence coefficient of Wilks’ (1962) outer confidence interval (X(r) X(s)) for the quantile interval (ξp1, ξp2). An inequality concerning incomplete beta functions is also presented and it is shown to be an improved version of one of Koti's (1989) inequalities. 相似文献
85.
Thomas A. Louis 《The American statistician》2013,67(3)
The easily computed, one-sided confidence interval for the binomial parameter provides the basis for an interesting classroom example of scientific thinking and its relationship to confidence intervals. The upper limit can be represented as the sample proportion from a number of “successes” in a future experiment of the same sample size. The upper limit reported by most people corresponds closely to that producing a 95 percent classical confidence interval and has a Bayesian interpretation. 相似文献
86.
This article studies the hypothesis testing and interval estimation for the among-group variance component in unbalanced heteroscedastic one-fold nested design. Based on the concepts of generalized p-value and generalized confidence interval, tests and confidence intervals for the among-group variance component are developed. Furthermore, some simulation results are presented to compare the performance of the proposed approach with those of existing approaches. It is found that the proposed approach and one of the existing approaches can maintain the nominal confidence level across a wide array of scenarios, and therefore are recommended to use in practical problems. Finally, a real example is illustrated. 相似文献
87.
《统计学通讯:理论与方法》2013,42(5):935-954
Abstract Asymptotic confidence intervals are given for two functions of multinomial outcome probabilities: Gini's diversity measure and Shannon's entropy. “Adjusted” proportions are used in all asymptotic mean and variance formulas, along with a possible logarithmic transformation. Exact confidence coefficients are computed in some cases. Monte Carlo simulation is used in other cases to compare actual coverages to nominal ones. Some recommendations are made. 相似文献
88.
Vasileios Alevizakos 《统计学通讯:理论与方法》2013,42(20):5138-5144
AbstractThe use of indices as an estimation tool of process capability is long-established among the statistical quality professionals. Numerous capability indices have been proposed in last few years. Cpm constitutes one of the most widely used capability indices and its estimation has attracted much interest. In this paper, we propose a new method for constructing an approximate confidence interval for the index Cpm. The proposed method is based on the asymptotic distribution of the index Cpm obtained by the Delta Method. Under some regularity conditions, the distribution of an estimator of the process capability index Cpm is asymptotically normal. 相似文献
89.
《Australian & New Zealand Journal of Statistics》1999,41(4):493-501
Book Reviews
Chris Wild & George Seber, Chance Encounters: a First Course in Data Analysis and Inference
A. J. Underwood, Experiments in Ecology
Lawrence L. Lapin, Modern Engineering Statistics
M. E. Thompson, Theory of Sample Surveys
Fima C. Klebaner, Introduction to Stochastic Calculus with Applications
Frank Lad, Operational Subjective Statistical Methods: a Mathematical, Philosophical, and Historical Introduction 相似文献
Chris Wild & George Seber, Chance Encounters: a First Course in Data Analysis and Inference
A. J. Underwood, Experiments in Ecology
Lawrence L. Lapin, Modern Engineering Statistics
M. E. Thompson, Theory of Sample Surveys
Fima C. Klebaner, Introduction to Stochastic Calculus with Applications
Frank Lad, Operational Subjective Statistical Methods: a Mathematical, Philosophical, and Historical Introduction 相似文献
90.
This paper generalizes the tolerance interval approach for assessing agreement between two methods of continuous measurement for repeated measurement data—a common scenario in applications. The repeated measurements may be longitudinal or they may be replicates of the same underlying measurement. Our approach is to first model the data using a mixed model and then construct a relevant asymptotic tolerance interval (or band) for the distribution of appropriately defined differences. We present the methodology in the general context of a mixed model that can incorporate covariates, heteroscedasticity and serial correlation in the errors. Simulation for the no-covariate case shows good small-sample performance of the proposed methodology. For the longitudinal data, we also describe an extension for the case when the observed time profiles are modelled nonparametrically through penalized splines. Two real data applications are presented. 相似文献