Showing papers on "Parametric statistics published in 1971"
TL;DR: In this paper, two very closely related definitions of robustness of a sequence of estimators are given which take into account the types of deviations from parametric models that occur in practice.
Abstract: Two very closely related definitions of robustness of a sequence of estimators are given which take into account the types of deviations from parametric models that occur in practice. These definitions utilize the properties of the Prokhorov distance between probability distributions. It is proved that weak $^\ast$-continuous functionals on the space of probability distributions define robust sequences of estimators (in either sense). The concept of the "breakdown point" of a sequence of estimators is defined, and some examples are given.
949 citations
TL;DR: In this article, the observation of x-ray parametric conversion was reported, and the appropriate nonlinear mechanisms were described in terms of classical free electrons, which were then used to calculate the susceptibility of free electrons to x-rays.
Abstract: The observation of x-ray parametric conversion is reported. Results are in accord with the calculated nonlinear x-ray susceptibility. The appropriate nonlinear mechanisms are described in terms of classical free electrons.
82 citations
TL;DR: In this paper, it is shown that distribution-free estimators may be poor and that their distribution, even in large samples, depends on knowledge of G for small x that may be unobtainable.
Abstract: SUMMARY Data consisting of the intersections of a planar or linear probe with a field of spheres, with a diameter distribution G(x), is often used to estimate linear functionals or their ratios. It is shown that distribution-free estimators may be poor and that their distribution, even in large samples, depends on knowledge of G for small x that may be unobtainable. The parametric approach is arduous and not robust against errors in the lower tail. It seems that this experimental method should be avoided when there is a practicable alternative. Suppose that a population of particles, geometrically similar with a size distribution function G(x) are randomly dispersed through space. Roughly, their centres will be placed by a Poisson process. The space may be probed in some way; we will consider only planar and linear probes. In the former the data are the intersections of the particles and some area of the probing plane. In the latter the data are a set of chords on some interval of the probing line. From such data, the object is to estimate functionals of the form
71 citations
TL;DR: Methods of estimating the probability of error for the Bayes' classifier which must be designed and tested with a finite number of classified samples are discussed and the expected difference between estimates is discussed.
Abstract: This paper discusses methods of estimating the probability of error for the Bayes' classifier which must be designed and tested with a finite number of classified samples. The expected difference between estimates is discussed. A simplifled algorithm to compute the leaving-one-out method is proposed for multivariate normal distributions wtih unequal co-variance matrices. The discussion is extended to nonparametric classifiers by using the Parzen approximation for the density functions. Experimental results are shown for both parametric and nonparametric cases.
69 citations
IBM1
TL;DR: In this paper, a probabilistic model of failure due to competing causes of failure operating on a unit during its lifetime is discussed, which is referred to as the Multi-Risk Model.
Abstract: In this paper we discuss a probabilistic model of failure due to competing causes of failure operating on a unit during its lifetime. Following Cox we term this the Multi-Risk Model. We impose some well-known parametric forms on the underlying distributions of the model and obtain maximum likelihood estimates for the parameters of the distributions. The asymptotic variance-covariance matrix of the estimates is derived. We give examples using the exponential and Weibull distributions. The theory is applied to data published by Mendenhall and Hader, who studied a Single-Risk Model.
44 citations
TL;DR: In this paper, the authors examined and developed new techniques for analyzing life test data and obtained estimates for the life distribution in the use environment on based data from both the use and the accelerated environments.
Abstract: This study examines and develops new techniques for analyzing life test data. It obtains estimates for the life distribution in the use environment on based data from both the use and the accelerated environments. The techniques require only physically plausible assumptions, not the usual ones involving specification of a family of parametric probability distributions. Procedures are given for testing those assumptions that are made.
29 citations
01 Mar 1971
TL;DR: The bounds, applicable to general non-gaussian densities and especially mixture densities encountered in adaptive pattern recognition, are simple to calculate and hence valuable for on-line performance evaluation of pattern recognition system.
Abstract: : Simplified upper and lower bounds to the probability of error for general M-ary hypotheses pattern recognition are obtained. The bounds, applicable to general non-gaussian densities and especially mixture densities encountered in adaptive pattern recognition, are simple to calculate and hence valuable for on-line performance evaluation of pattern recognition system. Computer evaluation of the bounds, established their tight nature and computational simplicity. Based on the bounds, feature extraction criteria are derived for supervised as well as parametric adaptive pattern recognition. (Author)
28 citations
TL;DR: In this paper, a parametric action of a periodic vertical support motion on the lateral oscillation of a simple shear-type building is examined theoretically, and the experimental demonstration of the various instability regions for simple two-and five-degree-of-freedom structures of this type is described and the results of analytical and computational procedures for the estimation of the regions are given.
27 citations
TL;DR: In this paper, the threshold power required for excitation of the parametric instability was found to be in reasonably good agreement with the theory for inhomogeneous plasmas, and exceeds the threshold for a uniform plasma by an order of magnitude.
Abstract: Experimental observation of the threshold power required for excitation of the parametric instability is found to be in reasonably good agreement with the theory for inhomogeneous plasmas, and exceeds the threshold for a uniform plasma by an order of magnitude.
22 citations
TL;DR: In this paper, it is shown that the rotating diffuser is effectively a parametric modulator which introduces new frequencies in the room and the remarkable performance of rotating diffusers is described in terms of their improvement in the statistical accuracy of the measured mean.
22 citations
TL;DR: In this article, an analytic search technique using two classic search procedures in parametric combination is described, which enables one at each iteration to concentrate attention on minimizing sumof-squares deviation with respect to the single combination parameter using projected gradients.
Abstract: A procedure for solving nonlinear estimation problems, designed with the special case of fitting nonlinear regression relationships in mind, will be described It is an analytic search technique using two classic search procedures in parametric combination This enables one at each iteration to concentrate attention on minimizing sumof-squares deviation with respect to the single combination parameter Using projected gradients, the procedure may also be applied to linearly constrained problems
TL;DR: In this paper, maximum likelihood estimates of the probability of the eventual extinction of a possibly age-dependent branching process are given for both the parametric and nonparametric cases, and their asymptotic properties derived.
Abstract: SUMMARY Maximum likelihood estimates of the probability of the eventual extinction of a possibly age-dependent branching process are given for both the parametric and nonparametric cases, and their asymptotic properties derived. It is found that the nonparametric estimate performs very well relative to the parametric estimate in a large variety of situations, and therefore would often be preferable to the parametric estimate in view of the latter's lack of
TL;DR: In this article, the authors used breakthrough curves and batch parapump runs to determine the lumped-parameter mass transfer coefficient λ and its dependence on velocity and temperature, and computer simulation of additional batch runs verified both the model and the STOP-GO algorithm used to solve it.
Abstract: Direct thermal parametric pumping separations of a NaCl-H2O-ion retardation resin system have been investigated. Experimental breakthrough curves and batch parapump runs were used to determine the lumped-parameter mass transfer coefficient λ and its dependence on velocity and temperature. Computer simulation of additional batch runs verified both the model and the STOP-GO algorithm used to solve it. Computer estimates of open-system behavior are presented.
TL;DR: In this paper, the problem of selecting the t best of k populations is considered; the common number of observations from each population is determined so that the probability of a correct selection is not less than a specified quantity whenever the parameters lie in a pre-assigned parametric sub-space.
Abstract: Consider k independent normal populations with unknown means and a common unit variance and let a better population be defined to be one with a larger absolute value of the mean. The problem of selecting the t best of k populations is considered; the common number of observations from each population is determined so that the probability of a correct selection is not less than a specified quantity whenever the parameters lie in a pre-assigned parametric sub-space. A procedure for this problem is proposed and tables and bounds for probability of a correct selection are provided; some properties of the proposed procedure are also discussed. The problem of selecting a small non-empty subset containing the best population is also considered; a procedure is proposed and the constant involved in the procedure is determined so that the probability of a correct selection is not less than a specified quantity. The expected size of the selected subset is derived and its supremum obtained. Two secondary problems for...
TL;DR: In this paper, a general geometric optics theory of visible or near-visible image formation in parametric upconversion is described, and a formula is derived that relates the location of the image to the locations of the object and the pump.
Abstract: This paper describes a general geometric optics theory of visible or near‐visible image formation in parametric upconversion. A formula is derived that relates the location of the image to the locations of the object and the pump. Aberrations are caused by the finite thickness of the nonlinear material; these aberrations vanish when both the pump waves and the object waves are parallel plane waves. The primary factor that limits the field of view of parametric image upconversion is the phase‐match condition.
TL;DR: In this paper, a brief history of parametric phenomena is given from Faraday and Lord Rayleigh through modern day physics, and the general characteristics of "parametric generators" are viewed through a specific example from acoustics, which is treated in detail.
Abstract: Parametric excitation of a resonant system is a self-excitation caused by a periodic variation of some parameter of the system. A brief history of parametric phenomena is given from Faraday and Lord Rayleigh through modern day physics. The general characteristics of “parametric generators” are viewed through a specific example from acoustics, which is treated in detail.
Patent•
18 Oct 1971TL;DR: In this article, a parametric surface acoustic wave apparatus including means for establishing two acoustic surface waves in a piezoelectric medium in a fashion to establish the conditions for parametric interaction so that various functions of signal processing can be carried out including, for example, signal convolution and correlation, time delay and time inversion, amplification, and oscillation.
Abstract: Parametric surface acoustic wave apparatus including means for establishing two acoustic surface waves in a piezoelectric medium in a fashion to establish the conditions for parametric interaction so that various functions of signal processing can be carried out including, for example, signal convolution and correlation, time delay and time inversion, amplification, and oscillation.
TL;DR: In this article, the first spatial and temporal modes of cantilevered columns having longitudinal inertia and end mass have been determined experimentally and analytically in the parametric space.
TL;DR: This note describes a parametric solution for the class of bicriterion mathematical programs identified by Geoffrion based on a "parametric resource" optimization as opposed to the “parametric price” optimization suggested by GeoffRion.
Abstract: This note describes a parametric solution for the class of bicriterion mathematical programs identified by Geoffrion [Opns. Res. 15, 39–54 (1967)]. The algorithm described is based on a “parametric resource” optimization as opposed to the “parametric price” optimization suggested by Geoffrion. The relative merits of the two approaches are indicated.
TL;DR: In this article, the results of an experimental investigation of a parametric end-fire array which is produced by the non-linear interaction of two coincident acoustic waves underwater are reported, and low-intensity measurements of far-field difference-frequency pressures and beamwidths for different interacting wave geometries are recorded.
TL;DR: In this article, the authors investigate the operating characteristics of an estimation procedure which utilizes simple linear combinations of one or two values in the order statistic generated by an observation vector, and show that such estimates appear to be remarkably efficient compared to the estimates generated by simple parametric procedures.
Abstract: When losses are piecewise linear, optimal decision-making hinges on estimating a specified fractile of a probability distribution. In this article we investigate, through examples, the operating characteristics of an estimation procedure which utilizes simple linear combinations of one or two values in the order statistic generated by an observation vector. Such estimates appear to be remarkably efficient compared to the estimates generated by simple parametric procedures; moreover, this efficiency does not appear to be damaged excessively by the presence of moderate amounts of autocorrelation in the sample values. It also appears to be possible to exploit informal knowledge about the shape of the distribution to improve the efficiency of this procedure.
TL;DR: In this article, it was shown that the optimal solution to the generalized linear fixed-charge problem is an extreme point of the polyhedral set defined by the constraints, and that the optimum of the generalized fractional fixed charge problem is also a vertex of this set.
Abstract: Fractional fixed-charge problems arise in numerous applications, where the measure of economic performance is the time rate of earnings or profit (equivalent to an interest rate on capital investment). This paper treats the fractional objective function, after suitable transformation, as a linear parametric fixed-charge problem. It is proved, with wider generality than in the case of Hirsch and Dantzig, that some optimal solution to the generalized linear fixed-charge problem is an extreme point of the polyhedral set defined by the constraints. Furthermore, it is shown that the optimum of the generalized fractional fixed-charge problem is also a vertex of this set. The proof utilizes a suitable penalty function yielding an upper bound on the optimal value of the objective function; this is particularly useful when considering combinations of independent transportation-type networks. Finally, it is shown that the solution of a fractional fixed-charge problem is obtainable through that of a certain linear fixed-charge one.
TL;DR: In this article, the effects of these parameters and of the material properties of the case-bonded grain were investigated, and parametric curves showing the variation of the maximum stress with those parameters were presented.
Abstract: Problems involving three-dimensional bodies which possess axial symmetry reduce to two-dimensional analytical problems. If a wedge-shaped portion of an axisymmetric body is tested subjected to the proper boundary condition, then a pseudo two-dimensional photoelastic method of testing may be used. This results in tremendous simplification in testing procedures, particularly when slight changes in model geometry are to be made during the course of testing. This method has been applied to axisymmetric solidpropellant rocket grains to conduct a parametric study of various conicyl geometries. Both pressure and thermal loads were considered for a case-bonded grain. Six parameters were required to define the geometry. The effects of these parameters and of the material properties of the grain were investigated, and parametric curves showing the variation of the maximum stress with those parameters are presented. The experimental results are compared with results obtained from a finite-element computer solution. Good agreement is obtained.
01 Aug 1971
TL;DR: In this article, the authors make use of the theory of two-dimensional moment invariants for planar geometric figures developed by Ming-kue Hu to identify objects and determine their orientation and position in space.
Abstract: : The approach presented here makes use of the theory of two- dimensional moment invariants for planar geometric figures developed by Ming-kue Hu. Complete systems of moment invariants under translation, similitude and orthogonal transformations are derived. By carefully utilizing these properties, a sample set is constructed in which each sample is represented by a vector which characterizes the image for a certain orientation of some object from the given group. A pattern recognition technique is then described in which a parametric representation of the input signal is employed. The decision process using typical samples partitions the space into regions that envelop the chosen samples of a class. A simulation program based on the above outline is successfully developed which not only identifies objects, but also determines their orientation and position in space.
TL;DR: The parametric approach to watershed modeling as mentioned in this paper attempts to find functional relationships between numerically defined hydrologic and physical characteristics of a drainage area, which is similar to our approach.
Abstract: The parametric approach to watershed modeling is shown to lie between the stochastic and deterministic approaches. Essentially, the parametric approach attempts to find functional relationships between numerically defined hydrologic and physical characteristics of a drainage area. Successful parametric modeling requires progression through sequential stages of data processing, model formulation, optimization of parameters, examination of results, association of characteristics, and conversion to prediction procedures. Selected examples of the various stages are discussed.
TL;DR: Detailed discussions concerning missing data, statistical tests, random number generation, and interpretation of results are presented along with a review of the generation schemes that have been used in the stochastic generation of hydrologic data.
Abstract: The stochastic approach to watershed modeling refers to the techniques used to generate synthetic hydrologic data. These data may be used either for input to a parametric watershed model or to provide directly an estimate of the output of a hydrologic process. In both cases the basic techniques of the generation processes are the same. The type of process depends primarily on the purpose for which the data are being generated and on the quality and quantity of sample data. Techniques are presented which can be used to generate data for one or any number of variates. The data generated can be normal, skewed, or log normal, and include serial correlation. If two or more variates are involved, cross correlation may also be considered. Brief discussions concerning missing data, statistical tests, random number generation, and interpretation of results are presented along with a review of the generation schemes that have been used in the stochastic generation of hydrologic data.