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In the present paper we extend in two ways some results relating to the study of distributional aspects of effects of errors in inspection sampling: (1) Multistage sampling with k successive samples samples involving the possibili...
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In the present paper we extend in two ways some results relating to the study of distributional aspects of effects of errors in inspection sampling: (1) Multistage sampling with k successive samples samples involving the possibility of two types of errors in inspection (classifying a defective individual as non-defective, or a non-defective as defective); (2) Single-stage sampling considering several types of defects of which only one is tested on inspection. Both (1) and (2) lead to novel multivariate distributions. Their structural properties are analysed in some detail and some applications, in particular those in quality control are discussed.
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The admissible values of the coefficient in a bivariate Morgenstern distribution are found. For multivariate Morgenstern distributions necessary and sufficient conditions are given for its coefficients, and its conditional distrib...
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The admissible values of the coefficient in a bivariate Morgenstern distribution are found. For multivariate Morgenstern distributions necessary and sufficient conditions are given for its coefficients, and its conditional distributions are found and shown to belong to a family of distributions further extending the multivariate Morgenstern family. (Author)
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A new method is presented for flexible regression modeling of high dimensional data. The model takes the form of an expansion in product spline basis functions, where the number of basis functions as well as the parameters associa...
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A new method is presented for flexible regression modeling of high dimensional data. The model takes the form of an expansion in product spline basis functions, where the number of basis functions as well as the parameters associated with each one (product degree and knot locations) are automatically determined by the data. This procedure is motivated by the recursive partitioning approach to regression and shares its attractive properties. Unlike recursive partitioning, however this method produces continuous models with continuous derivatives. It has more power and flexibility to model relationships that are nearly additive or involve interactions in at most a few variables. In addition, the model can be represented in a form that separately identifies the additive contributions and those associated with the different multivariable interactions.
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The statistical techniques that can be used for extreme value analysis of multivariate data are outlined. All the techniques suggested are derived from multivariate statistical procedures, ranging from classic discriminant analysi...
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The statistical techniques that can be used for extreme value analysis of multivariate data are outlined. All the techniques suggested are derived from multivariate statistical procedures, ranging from classic discriminant analysis to modern cluster analysis algorithms. Also presented is an introduction to the Weibull or Fisher Type 3 Extreme Value distribution. This distribution is used in the study of reliability and in materials failure studies. The density and distribution functions are presented along with formulas for several estimable statistics. The Weibull distribution allows the option of including a third parameter, in addition to scale and shape parameters, which represents a threshold below which the probability of an effect or a measured response is zero. Simple parameter estimators are given, and it is noted that such estimators usually depend upon the logarithmic relationship between the Weibull and Extreme value distributions. The literature on parameter estimation is reviewed and papers are cited that propose unbiased and efficient estimators for parameter values, confidence intervals, and tolerance limits, and that can be used with censored samples. Finally, the use of life testing statistics for extreme value problems is discussed. (ERA citation 08:045307)
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This report covers the work done under the contract F49620-79-C-0161 during the period of June 1, 1979 - Dec. 14, 1981. All this work is reported in various papers and the abstracts of these papers are attached. The work in these ...
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This report covers the work done under the contract F49620-79-C-0161 during the period of June 1, 1979 - Dec. 14, 1981. All this work is reported in various papers and the abstracts of these papers are attached. The work in these papers is supported completely or partially by the above contract. (Author)
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摘要 :
This report covers the work done under the contract F49620-79-C-0161 during the period of June 1, 1979 - Dec. 14, 1981. All this work is reported in various papers and the abstracts of these papers are attached. The work in these ...
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This report covers the work done under the contract F49620-79-C-0161 during the period of June 1, 1979 - Dec. 14, 1981. All this work is reported in various papers and the abstracts of these papers are attached. The work in these papers is supported completely or partially by the above contract. (Author)
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By letting F(x) and G(y) be two probability functions and f(x) and g(y) the corresponding density functions, it has been shown that there are two-variate probability functions H(x,y) such that F(x) and G(y) are the marginal probab...
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By letting F(x) and G(y) be two probability functions and f(x) and g(y) the corresponding density functions, it has been shown that there are two-variate probability functions H(x,y) such that F(x) and G(y) are the marginal probabilities. A solution is obtained, and an analytical example is given. (ERA citation 09:030092)
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Multivariate calibration techniques have been used in a wide variety of spectroscopic situations. In many of these situations spectral variation can be partitioned into meaningful classes. For example, suppose that multiple spectr...
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Multivariate calibration techniques have been used in a wide variety of spectroscopic situations. In many of these situations spectral variation can be partitioned into meaningful classes. For example, suppose that multiple spectra are obtained from each of a number of different objects wherein the level of the analyte of interest varies within each object over time. In such situations the total spectral variation observed across all measurements has two distinct general sources of variation: intra-object and inter-object. One might want to develop a global multivariate calibration model that predicts the analyte of interest accurately both within and across objects, including new objects not involved in developing the calibration model. However, this goal might be hard to realize if the inter-object spectral variation is complex and difficult to model. If the intra-object spectral variation is consistent across objects, an effective alternative approach might be to develop a 'generic' intra-object model that can be adapted to each object separately. This paper contains recommendations for experimental protocols and data analysis in such situations. The approach is illustrated with an example involving the noninvasive measurement of glucose using near-infrared reflectance spectroscopy. Extensions to calibration maintenance and calibration transfer are discussed.
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A set of q responses, y = (y(sub 1), y(sub 2), ..., y(sub q))(sup T), is related to a set of p explanatory variables, x = (x(sub 1), x(sub 2), ..., x(sub p))(sup T), through the classical linear model, y(sup T) = a + x(sup T)B + e...
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A set of q responses, y = (y(sub 1), y(sub 2), ..., y(sub q))(sup T), is related to a set of p explanatory variables, x = (x(sub 1), x(sub 2), ..., x(sub p))(sup T), through the classical linear model, y(sup T) = a + x(sup T)B + e(sup T). The parameters, a and B, are estimated during calibration using a training set. The fitted calibration model that follows is then used repeatedly on a number of new observations where y is observed and x is to be inferred. This procedure is often referred to as prediction (or inverse prediction). The prediction procedure can be viewed as parameter estimation in errors-in-variables regression. By using the errors-in-variables connection and assuming normally distributed measurement errors, the maximum likelihood estimates of the new x's can be obtained either individually or jointly. The limiting (q (yields) (infinity)) normal distribution of the maximum likelihood estimates of the new x's, obtained jointly, can be used to construct approximate simultaneous confidence regions for the new x's. In situations where the new observations are numerous and well dispersed from the center of the training set, the uncertainty in a and B is substantial, and the specificity of the responses is poor, joint estimation can improve significantly on individual estimation, which is the traditional approach.
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摘要 :
A set of q responses, y = (y(sub 1), y(sub 2), ..., y(sub q))(sup T), is related to a set of p explanatory variables, x = (x(sub 1), x(sub 2), ..., x(sub p))(sup T), through the classical linear model, y(sup T) = a + x(sup T)B + e...
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A set of q responses, y = (y(sub 1), y(sub 2), ..., y(sub q))(sup T), is related to a set of p explanatory variables, x = (x(sub 1), x(sub 2), ..., x(sub p))(sup T), through the classical linear model, y(sup T) = a + x(sup T)B + e(sup T). The parameters, a and B, are estimated during calibration using a training set. The fitted calibration model that follows is then used repeatedly on a number of new observations where y is observed and x is to be inferred. This procedure is often referred to as prediction (or inverse prediction). The prediction procedure can be viewed as parameter estimation in errors-in-variables regression. By using the errors-in-variables connection and assuming normally distributed measurement errors, the maximum likelihood estimates of the new x's can be obtained either individually or jointly. The limiting (q (yields) (infinity)) normal distribution of the maximum likelihood estimates of the new x's, obtained jointly, can be used to construct approximate simultaneous confidence regions for the new x's. In situations where the new observations are numerous and well dispersed from the center of the training set, the uncertainty in a and B is substantial, and the specificity of the responses is poor, joint estimation can improve significantly on individual estimation, which is the traditional approach.
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