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Showing papers on "Parametric statistics published in 1980"


Journal ArticleDOI
TL;DR: The Lagrange multiplier (LM) statistic as mentioned in this paper is based on the maximum likelihood ratio (LR) procedure and is used to test the effect on the first order conditions for a maximum of the likelihood of imposing the hypothesis.
Abstract: Many econometric models are susceptible to analysis only by asymptotic techniques and there are three principles, based on asymptotic theory, for the construction of tests of parametric hypotheses. These are: (i) the Wald (W) test which relies on the asymptotic normality of parameter estimators, (ii) the maximum likelihood ratio (LR) procedure and (iii) the Lagrange multiplier (LM) method which tests the effect on the first order conditions for a maximum of the likelihood of imposing the hypothesis. In the econometric literature, most attention seems to have been centred on the first two principles. Familiar " t-tests " usually rely on the W principle for their validity while there have been a number of papers advocating and illustrating the use of the LR procedure. However, all three are equivalent in well-behaved problems in the sense that they give statistics with the same asymptotic distribution when the null hypothesis is true and have the same asymptotic power characteristics. Choice of any one principle must therefore be made by reference to other criteria such as small sample properties or computational convenience. In many situations the W test is attractive for this latter reason because it is constructed from the unrestricted estimates of the parameters and their estimated covariance matrix. The LM test is based on estimation with the hypothesis imposed as parametric restrictions so it seems reasonable that a choice between W or LM be based on the relative ease of estimation under the null and alternative hypotheses. Whenever it is easier to estimate the restricted model, the LM test will generally be more useful. It then provides applied researchers with a simple technique for assessing the adequacy of their particular specification. This paper has two aims. The first is to exposit the various forms of the LM statistic and to collect together some of the relevant research reported in the mathematical statistics literature. The second is to illustrate the construction of LM tests by considering a number of particular econometric specifications as examples. It will be found that in many instances the LM statistic can be computed by a regression using the residuals of the fitted model which, because of its simplicity, is itself estimated by OLS. The paper contains five sections. In Section 2, the LM statistic is outlined and some alternative versions of it are discussed. Section 3 gives the derivation of the statistic for

5,826 citations


Journal ArticleDOI
TL;DR: Two algorithms for parametric piecewise polynomial evaluation and generation are described and are shown to generalize to new algorithms for obtaining curve and surface intersections and for the computer display of parametric curves and surfaces.
Abstract: Two algorithms for parametric piecewise polynomial evaluation and generation are described. The mathematical development of these algorithms is shown to generalize to new algorithms for obtaining curve and surface intersections and for the computer display of parametric curves and surfaces.

538 citations


Journal ArticleDOI
TL;DR: In this article, a method for calibrating photodetectors based on some characteristics of the statistics of the field of spontaneous parametric light scattering is described, and a phenomenological theory of parametric scattering is used to demonstrate that photons are only emitted in pairs.
Abstract: A description is given of a method for calibrating photodetectors based on some characteristics of the statistics of the field of spontaneous parametric light scattering. A phenomenological theory of parametric scattering is used to demonstrate that photons are only emitted in pairs. It is shown that, in principle, a priori information on the two-photon character and directionality of parametrically scattered light can be used for absolute calibration of photodetectors operated both in the analog linear regime and in the discrete photoelectron pulse counting regime.

218 citations


Journal ArticleDOI
TL;DR: An algorithm that generates an MRF on a finite toroidal square lattice from an independent identically distributed (i.i.d.) array of random variables and a given set of independent real-valued statistical parameters is presented.

209 citations


Journal ArticleDOI
TL;DR: It is established that in the worst case, the computational effort required for solving a parametric linear program is not bounded above by a polynomial in the size of the problem.
Abstract: We establish that in the worst case, the computational effort required for solving a parametric linear program is not bounded above by a polynomial in the size of the problem.

146 citations


Journal ArticleDOI
TL;DR: In this paper, a finite-difference procedure was used to predict the flow distribution in parallel and reverse flow manifold systems by a one-dimensional elliptic formulation, where an iterative numerical scheme solved the differential equations for momentum in the longitudinal direction and continuity.

86 citations


Journal ArticleDOI
TL;DR: Procedures for the cases of two independent samples and two matched samples of response curves are proposed, each curve is approximated by an orthogonal polynomial.

71 citations


Journal ArticleDOI
TL;DR: In this paper, a review of statistical strategies for the analysis of data from split-plot experiments and repeated measurements experiments is presented. And a selected bibliography of references for these and related methods is given.
Abstract: A common feature of many statistical investigations is the collection of data from groups of experimental units each of which is observed under two or more conditions. Such studies are generally called either split-plot experiments or repeated measurements experiments. This paper is concerned with reviewing general statistical strategies for the analysis of data from these types of research designs. For this purpose, primary attention is directed at two basic dimensions. One of these is the nature of the randomization processes for the data as obtained among and within the experimental units. The other is the level of the measurement scale as either nominal, ordinal, or interval. This framework is then used as the basis of discussion of alternative statistical methods such as repeated measurements analysis of variance, multivariate analysis of variance, and their non-parametric rank and categorical data counterparts in both a general sense and for some specific classes of examples. Finally, a selected bibliography of references for these and related methods is given.

64 citations


Journal ArticleDOI
TL;DR: Monte Carlo results presented here further confirm the relatively good performance of non-parametric Bayes theorem type algorithms compared to parametric (linear and quadratic) algorithms and point out certain procedures which should be used in the selection of the density estimation windows for non- Parametric algorithms to improve their performance.

55 citations


Journal ArticleDOI
TL;DR: In this article, a computational scheme for determining global geometric properties of solid object models is presented, which operates directly on the boundary representation of the model and is tested on a number of models produced by an experimental modelling system.
Abstract: A computational scheme for determining global geometric properties of solid object models is presented. The method operates directly on the boundary representation of the model. The scheme is tested on a number of models produced by an experimental modelling system. Primitive objects combined for the tests are all represented in terms of parametric bicubic patches.

54 citations


Book ChapterDOI
01 Jan 1980
TL;DR: A survey of the literature on statistical theory with stochastic expansions can be found in this paper, where the authors explain the possibility of developing a general statistical theory based on asymptotic methods.
Abstract: Publisher Summary This chapter explains the possibility of developing a general statistical theory based on asymptotic methods It presents a survey of the literature on this subject The chapter presents estimators and tests based on statistics with stochastic expansions The emphasis on such procedures is justified by the fact that that this class contains procedures having certain optimum properties of order o(n-1/2) in a wider class Where nonasymptotic theory is applicable, it can at best be used to improve given estimators or to establish their optimality There are no fixed sample size properties recommending the maximum likelihood estimator It may even be inadmissible under neg-unimodal (bowl-shaped) loss functions The unsatisfactory state of nonasymptotic theory is not the fault of those working in this area If there is not enough structure in the assumptions, no structure can appear in the results

Journal ArticleDOI
TL;DR: The techniques of chance constrained programming are applied to solve the resulting stochastic optimization problem and the optimum results obtained from the probabilistic formulation are compared with those given by the deterministic formulation.

Journal ArticleDOI
TL;DR: In this article, the theory of parametric upconversion is extended to describe the mixing of two focused optical beams with unequal confocal parameters, and the effects of phase matching, walk-off, and diffraction are examined.
Abstract: In the present paper, the theory of parametric upconversion is extended to describe the mixing of two focused optical beams with unequal confocal parameters. The results obtained apply particularly well to the case where focusing of one input beam is limited to physical constraints, e.g., damage. The effects of phase matching, walk-off, and diffraction are examined.

Journal ArticleDOI
TL;DR: The theory of general chi-square statistics for testing fit to parametric families of distributions is extended to samples censored at sample quantiles by employing sample percentiles as cell boundaries as mentioned in this paper.
Abstract: The theory of general chi-square statistics for testing fit to parametric families of distributions is extended to samples censored at sample quantiles. Data-dependent cells with sample quantiles as cell boundaries are employed. Asymptotic distribution theory is given for statistics in which unknown parameters are estimated by estimators asymptotically equivalent to inear combinations of functions of order statistics. Emphasis is placed on obtaining statistics having a chi-square limiting null distribution. Examples of such statistics for testing the fit of Type II censored samples to the negative exponential, normal, two-parameter uniform and two-parameter Weibull families are given. 1. Introduction. Censored data occur frequently in engineering (life testing and reliability) and medical studies. Since inference procedures for such data commonly make distributional assumptions, a considerable body of recent literature concerns tests of fit for censored samples. When data are censored at fixed points (Type I censoring), chi-square tests of fit apply, since the censored observations fall in one or more fixed cells. In this paper we extend the applicability of chi-square tests to data censored on one or both sides at sample percentiles (Type II censoring) by employing sample percentiles as cell boundaries. Type II censored data arise in engineering settings. Medical data typically display more complex random censoring, as when studies of survival after treatment encounter dropouts and deaths from other causes. Such general random censoring is not considered here. Moore and Spruill (1975), hereafter referred to as MS, provide a general large sample theory for chi-square statistics using data-dependent cells, general estimators of unknown parameters, and quadratic forms in the standardized cell frequencies other than the Pearson sum of squares. We here extend that development to the case of Type II censoring. Though the results are parallel, the proofs are quite different due to the dependence of the observations in the present case. Our goal, achieved in Section 4, is to provide tests of fit to common parametric families of distributions having chi-square limiting null distributions. Such tests require only standard tables, and in many cases the test statistic itself can be computed by hand.

Journal ArticleDOI
TL;DR: In this article, a parametric-deterministic urban rainfall runoff model is described, which uses a parameterized soil-moisture-accounting procedure to determine antecedent moisture conditions and the Philip equation to compute infiltration.
Abstract: A parametric-deterministic urban rainfall-runoff model is described. The model uses a parametric soil-moisture-accounting procedure to determine antecedent-moisture conditions and the Philip equation to compute infiltration. Kinematic-wave theory is used for deterministic routing of flows over contributing areas and through a branched system of pipes or natural channels or both, to the watershed outlet. An option is included in the model to calibrate the soil moisture and infiltration parameters using a modified-Rosenbrock optimization technique. The model is conceptually simple, but a set of model segments can be arranged easily into a network that will represent many complex drainage basins.

Journal ArticleDOI
TL;DR: In this article, a survey of approaches to solving inverse problems for lossless layered systems can be found in two different ways, by nonparametric or parametric models, and the authors focus their attention on inverse and estimation procedures for parametric model.
Abstract: In this paper, we survey approaches to solving inverse problems for lossless layered systems Such systems can be modeled in two different ways, by nonparametric or parametric models We review both models, but concentrate our attention on inverse and estimation procedures for parametric models Algebraic inverse procedures are described for determining the reflection coefficient parameters when measurements are noise free An extension of these procedures to the case of noisy data is also discussed; but, resulting reflection coefficient values are suboptimal Finally, we describe two procedures for estimating reflection coefficients from noisy data One of these, which is very promising, is a maximum-likelihood procedure, which is not only able to provide estimates of reflection coefficients, but is also able to provide estimates of another set of parameters, layer travel times These maximum-likelihood estimates are optimal

Journal ArticleDOI
TL;DR: In this article, a parametric study of 5fN and 5n7s configurations by application of both Slater-Condon theory and the generalized least-squares method to the whole sequence of actinides has led to the simultaneous interpretation of 72 levels in first spectra (5fN7s2) and of 112 levels in second spectra.
Abstract: The parametric studies of 5fN and 5fN7s configurations by application of both Slater-Condon theory and the generalized least-squares method to the whole sequence of actinides has led to the simultaneous interpretation of 72 levels in first spectra (5fN7s2) and of 112 levels in second spectra (5fN7s). The determination of the N-dependence of various electrostatic parameters of the 5fN core improves the reliability for prediction of missing configurations. Revised interpretations and new energy levels are reported in a number of spectra.

Journal ArticleDOI
TL;DR: Theorems concerning weak convergence of non-Markovian processes to diffusions, together with an averaging and a stability method, are applied to two (learning or adaptive) processes of current interest: an automata model for route selection in telephone traffic routing, and an adaptive quantizer for use in the transmission of random signals in communication theory.
Abstract: Recently proven theorems concerning weak convergence of nonMarkovian processes to diffusions, together with an averaging and a stability method, are applied to two (learning or adaptive) processes of current interest: (1) an automata model for route selection in telephone traffic routing; (2) an adaptive quantizer for use in the transmission of random signals in communication theory The models are chosen because they are prototypes of a large class to which the methods can be applied The technique of application of the basic theorems to such processes is developed Suitably interpolated and normalized “learning or adaptive” processes converge weakly to a diffusion, as the “learning or adaptation” rate goes to zero For small learning rates, the qualitative properties (eg, asymptotic (large-time) variances and parametric dependence) of the processes can be determined from the properties of the limit

Journal ArticleDOI
TL;DR: In this paper, distribution-free extensions of the indicator tests, based on the placements of the sequentially obtained observations among the previously collected fixed size sample, are considered, and properties of these sequential placements procedures are obtained.
Abstract: The concept of a partially sequential hypothesis test was introduced by Wolfe (1977a), an{associated procedures were developed for both parametric and nonparametric assumptions In this paper we consider distribution-free extensions of those indicator tests, based on the placements of the sequentially obtained observations among the previously collected fixed size sample Exact and asymptotic, as the fixed sample size in¬creases to infinity, properties of these sequential placements procedures are obtained, including statements about the power and expected number of sequentially obtained observations The results of a Monte Carlo study are used to differentiate be¬tween various placement scoring schemes

Journal ArticleDOI
TL;DR: In this article, the authors proposed a new approach for making inferences from accelerated life tests based on prior information which is generally available to the engineer by adopting a Bayesian point of view.
Abstract: In a recent paper, the authors have proposed a new approach for making inferences from accelerated life tests. Their approach is appreciably different from those that have been considered in the past, and is motivated by what is actually done in practice. Prior information which is generally available to the engineer is incorporated by adopting a Bayesian point of view. The usual assumptions about the failure distributions and the acceleration functions, which are appealing from a statistical point of view, have been sacrificed to achieve greater reality. We apply this new approach to some real life data arising from an accelerated life test. In the process, we explain our new approach in a manner which makes it easy to understand and apply by the reliability practitioner. Because of the nonparametric nature of the approach, the statistical precision of the results is less than that which can be achieved by making parametric assumptions. On the other hand, the chance of selecting an incorrect model is diminished.

Journal ArticleDOI
TL;DR: In this article, the authors derived the asymptotic distribution of the one period ahead prediction of a model with autocorrelated errors for the model with exogenous variables, whose disturbances obey either autoregressive or moveing average processes.
Abstract: Estimation of parametric multiple time series models has been a major topic in recent work in statistics and econometrics (e.g., Hannan [1970], Wilson [1973], Dhrymes and Erlat [1974], and Hatanaka [1976]). However, relatively little has been reported on their prediction property, particularly when the model involves autocorrelated errors. For the model with uncorrelated errors, Goldberger, Nagar and Odeh [1962] and Dhrymes [1973] have obtained the asymptotic distribution of the reduced form coefficient estimates derived from the structural form estimates. It obviously serves as the asymptotic distribution of the one period ahead prediction of the model. Schmidt [1974] recently derived the asymptotic distribution of multiperiod ahead predictions for such a model, i.e., simultaneous equation autoregressive model (or alternatively called "dynamic model" in econometrics) with exogenous variables (ARX) (see also Brissimis and Gill [1978]). When the disturbances of the models are autocorrelated, it is known that the derivation of the simplified prediction scheme, not to mention its asymptotic distribution, becomes complicated even for the single equation model. Bloomfield [1972] and Yamamoto [1978] derived the asymptotic mean square error of one period and multiperiod predictions for the single equation autoregressive moving average (ARMA) models, respectively. In this paper, first we derive the optimal prediction scheme for multiperiod prediction of a simultaneous equation autoregressive model with exogenous variables, whose disturbances obey either autoregressive or moveing average process. The complication due to the error autocorrelation is handled by the introduction of the backward representation of the model, and the optimal predictor is given by a relatively simple formula with matrix notations. Secondly, for the unknown parameter case, we derive the asymptotic distribution of the optimal prediction scheme with the consistent estimates of the parameters. Our results are quite general, and we show, with a few examples, that they are easily modified to various single and simultaneous equation models of simpler specifications. The scope of this paper is as follows. Section 2 presents two types of model representation. The first is the state variable representation suggested by


Journal ArticleDOI
TL;DR: A representation for parametric cubic curves and surfaces is presented which incorporates the polygonal approach popularized by the Bezier and B-spline schemes, and a discussion of the relationship between continuity and redundant data storage is included.
Abstract: A representation for parametric cubic curves and surfaces is presented which incorporates the polygonal approach popularized by the Bezier and B-spline schemes. Since the curves more closely mimic the polygon than their counterparts employing the Bezier or B-spline schemes, the method is potentially useful for creating and manipulating geometric models. In connection with the logical extension of the approach from curves to surfaces, a discussion of the relationship between continuity and redundant data storage is included.

Journal ArticleDOI
TL;DR: This paper proposes a parametric approach for the solution of the fractional program via its equivalent linear complementarity formulation and outlines how the method can take advantage of the special structure arising from the model.
Abstract: The general single-period optimal portfolio selection problem with a risk-free asset can be solved by a two-stage approach. In the first stage, one solves a certain fractional program, and in the second, a simple stochastic program with one single variable. This paper proposes a parametric approach for the solution of the fractional program via its equivalent linear complementarity formulation. In the latter part of the paper, we specialize the proposed method to a specific model of the portfolio problem with upper bounds and outline how the method can take advantage of the special structure arising from the model. Finally, we report some computational results and a brief comparison between our method and Lemke's algorithm.

Journal ArticleDOI
TL;DR: The optimal design and performance analysis of nonuniform quantizers are considered in the context of data quantization in detection systems for stochastic signals, and the performance of the optimal quantizer-detector generally exhibits considerable performance improvement over the suboptimal schemes.
Abstract: The optimal design and performance analysis of nonuniform quantizers are considered in the context of data quantization in detection systems for stochastic signals. The case of detection with small signal-to-noise ratio is treated using two different statistical models for the presence of the signal in this situation. A general data-quantized detection system is proposed, and analytical expressions are presented for the asymptotic performance comparison of such systems within each of the two signal models. A design procedure for the optimal choice of quantizer parameters as also discussed, and optimal parameter values are presented for the particular case of four-level quantization for a class of noise propability densities exhibiting generalized exponential decay. Two suboptimal quantizer-detectors are also proposed, one based on minimum-distortion quantization and the other based on an approximation to the quadratic detector, and the performance of the optimal quantization scheme relative to these is analyzed with the result that the optimal quantizer-detector generally exhibits considerable performance improvement over the suboptimal schemes.

Journal ArticleDOI
TL;DR: In this article, the authors proposed to use the extreme points on the 95% joint confidence ellipsoid to estimate the uncertainty of a parameter in linear and nonlinear multiple regression.

Patent
29 Dec 1980
TL;DR: In this paper, a surface-acoustic-wave parametric device characterized in that a width of a parametric interaction region in a direction perpendicular to the propagation direction of surface acoustic wave is varied so as to correspond to a desired frequency characteristic.
Abstract: A surface-acoustic-wave parametric device characterized in that a width of a parametric interaction region in a direction perpendicular to the propagation direction of surface acoustic wave is varied so as to correspond to a desired frequency characteristic.


Journal ArticleDOI
TL;DR: In this paper, a method of construction of asymptotically minimal tolerance sets based on uniformly consistent density estimates is developed and application of the method in both parametric and nonparametric situations based on parameter estimates and window estimates of the density is considered.
Abstract: Multivariate β-content tolerance sets with asymptotic confidence level γ(0<γ⩽1) are defined and the requirement of asymptotic minimality for such sets is formulated. A method of construction of asymptotically minimal tolerance sets baFed on uniformly consistent density estimates ia developed. Application of the method in certain parametric situations based on parameter estimates and certain nonparametric situations based on window estimates of the density is considered.

Journal ArticleDOI
TL;DR: A simple, easy to construct, system which exhibits parametric instability is presented in this article, where the two lowest-order resonances are described and analyzed in detail, and the analysis stresses the physical and intuitive aspects of the problem.
Abstract: A simple, easy to construct, system which exhibits parametric instability is presented. The two lowest‐order resonances are described and analyzed in detail. The analysis stresses the physical and intuitive aspects of the problem. The purpose of the paper is to give the reader some familiarity with parametric oscillators and parametric instability.