Showing papers on "Nonparametric statistics published in 1970"
Book•
01 Jan 1970
TL;DR: The introduction to Probability 2nd Edition Problem Solutions and Probability An Introduction With Statistical Applications, as well as an Introduction to Basic Statistics And Probability.
Abstract: (1966). Introductory Probability and Statistical Applications. Technometrics: Vol. 8, No. 4, pp. 720-722.
351 citations
Book•
01 Jun 1970
TL;DR: Handbook of probability and statistics with tables with tables as discussed by the authors, Handbook of Probability and Statistics with tables, مرکز فناوری اطلاعات و رسانی,
Abstract: Handbook of probability and statistics with tables , Handbook of probability and statistics with tables , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی
163 citations
159 citations
Book•
01 Jun 1970
TL;DR: This chapter discusses estimation in measurement and sampling models, and discusses the role of significance in estimation, which plays in the development of statistical models.
Abstract: Preface Part I. Probability: 1. Probability models 2. Sampling 3. Product models 4. Conditional probability 5. Random variables 6. Special distributions 7. Multivariate distributions Part II. Statistics. Introduction to Statistics: 8. Estimation 9. Estimation in measurement and sampling models 10. Optimum methods of estimation 11. Tests of significance 12. Tests for comparative experiments 13. Concept of power Tables Selected answers to problems Index Example index.
145 citations
122 citations
TL;DR: The nonparametric representation of the curve, which is widely used since it lends itself to realization by ordinary DDA technique, is shown to be fully competitive.
Abstract: The process of converting a mathematically defined curve into unit steps along a fixed axis in digital technique is known as interpolation. The representation of the curve may be parametric or nonparametric. The parametric representation is widely used since it lends itself to realization by ordinary DDA technique. However, the nonparametric representation is shown to be fully competitive. In many cases, e.g., circle generation, it seems to be advantageous because it eliminates the risk of curve degradation.
103 citations
TL;DR: In this paper, a nonparametric approach to the credit screening problem is presented, which does not assume multivariate normality nor apply any arbitrary scaling procedures to the qualitative variables.
Abstract: Most commonly used credit screening methods are based on Fisher's linear discriminant function for quantitative variates. The variables actually used in credit scoring are usually, however, qualitative occurring as high/low, or present/ absent. We present a nonparametric approach to the credit screening problem. In our method we do not assume multivariate normality nor do we apply any arbitrary scaling procedures to the qualitative variables. We classify an observation to that group with which it has most in common, this being done so as to minimize expected loss from misclassification. It is a variant of the “closest neighbor” rule. The misclassification probabilities of our screening rule are obtained by a jack-knife method. An empirical method for the selection of variates for screening is also given. The possibilities for adopting the method to an on-line computer system is discussed with an illustrative example.
89 citations
01 May 1970
TL;DR: In this article, the authors consider some of the simpler nonparametric detection schemes and compare their asymptotic relative efficiencies to those of detectors which are optimal in the Neyman-Pearson sense.
Abstract: This paper considers some of the simpler nonparametric detection schemes and compares their asymptotic relative efficiencies to those of detectors which are optimal in the Neyman-Pearson sense. In the one-input case, the nonparametric sign and Wilcoxon detectors are compared to the linear detector which is optimal for the detection of a dc signal of unknown amplitude in Gaussian noise. For two-input systems the nonparametric polarity coincidence correlator is compared to the system which is optimal for the detection of a common random Gaussian component in two-input Gaussian noises. The nonparametric detectors are shown to offer advantages in simplicity of implementation and in insensitivity to changes in input statistics while performing moderately well compared to the parametric detectors. More impressive results can be obtained with more complicated detectors utilizing nonlinear rank statistics.
85 citations
68 citations
TL;DR: In this article, the order statistics of independent random variables having the same negative binomial distribution are discussed and two limiting distributions are presented and moment approximations based on one of them are evaluated.
Abstract: SUMMARY The order statistics of independent random variables each having the same negative binomial distribution are discussed. Recurrence relations for probability generating functions and moments of the distributions of the order statistics are given. These have been used to provide tables of the expected values of the order statistics. Finally, two limiting distributions are presented and moment approximations based on one of them are evaluated.
TL;DR: The detection performance of some one-sample nonparametric rank tests for signals in Gaussian noise exhibiting a characteristic trend is presented in this paper for a finite number of observations and asymptotically.
Abstract: The detection performance of some one-sample nonparametric rank tests for signals in Gaussian noise exhibiting a characteristic trend is presented in this paper for a finite number of observations and asymptotically. The tests considered are the Kendall tau, the Spearman rho, and a version of the c_1 normal-scores test; both coherent and incoherent signal processing are considered. The asymptotic performance is determined through a simple extension of existing analytical results, whereas for a finite number of observations a direct Monte Carlo simulation is used. The latter requires a preliminary determination of false-alarm probability versus decision threshold. For the Spearman rho and the c_1 tests an importance-sampling technique is used in a Monte Carlo simulation to determine the required results. Finally an application of the Kendall tau test to conventional radar is considered, in which the characteristic trend due to the amplitude modulation of the received train of echoes by the scanning of the antenna is used for detecting the presence of a target.
TL;DR: In this article, an estimator of the scale parameter o which is asymptotically as efficient as the best estimator which can be constructed when the form of the density function is known to the statistician and all the observations are used is presented.
Abstract: The present paper is a continuation of the paper [1] of the same name. In [1] the authors showed how to construct (asymptotically) efficient estimators of scale and location parameters and of the two jointly, when the form of the density function is unknown to the statistician (i.e., in the non-parametric case). Their estimators are functions of the \"middle\" n(q-p) observations, where n is the total number of observations and 0 < p < q < 1. The estimators are efficient modulo this fact. Since p can be chosen close to zero and q close to 1, the demands of statistical applications would probably be better served by improving this estimator rather than by eliminating the restriction to the middle n(q-p) observations. However, for the purposes of statistical theory and the eventual development of a theory of nonparametric estimation, it seems of some interest to eliminate this \"waste\" of observations. In the present paper we construct an estimator of the scale parameter owhich is asymptotically as efficient as the best estimator which can be constructed when the form of the density function is known to the statistician and all the observations are used. (Actually, we estimate the ratio of two a's, because the assumptions we make are not sufficient to identify o-; see [1] and a remark in Section 15 below. If the parameter ois identified then the method given below gives an efficient estimator of it.) It will be readily seen that the same method is applicable to estimating a location parameter #, and p and ojointly. The parameter ~ was chosen because a choice had to be made (it is not necessary to do both) and because it is perhaps slightly the more difficult of the two 1. We believe that the method developed is of general interest and that it will be applicable in the development of a general theory of non-parametric estimation which has begun to emerge only recently. In the present paper we assume familiarity with [1], whose notation and definitions are assumed herewith. Other notation will be added in Section 10, where the assumptions are stated. The numbering of the sections follows that of [1 ] consecutively. The assumptions will be discussed in Section 15, where the relation of this paper to work by other authors will be discussed.
TL;DR: It is found that the effects of dependence on ARE with respect to a parametric test can be offset to some extent by appropriately grouping sample values, and either the form of the dependence must be known or some learning scheme must be applied.
Abstract: This paper investigates the effects of dependence on rank tests, in particular on a class of recently defined nonparametric tests called "mixed" statistical tests. It is shown that the mixed test statistic is asymptotically normal for Gaussian processes with mild regularity properties justifying the use of asymptotic relative efficiency (ARE) as a figure of merit. Results are presented in terms of variations on three well-known statistics--the one-sample Wilcoxon, the two-sample Mann-Whitney, and the Kendall \tau . It is found that the effects of dependence on ARE with respect to a parametric test can be offset to some extent by appropriately grouping sample values. If, however, a constant false-alarm rate is to be attained, either the form of the dependence must be known or some learning scheme must be applied.
TL;DR: In this paper, the omnibus hypothesis is used to test the null hypothesis of a randomized groups analysis of variance (ANOVA) or its nonparametric counterpart, the Kruskal-Wallis H test.
Abstract: VERY often a researcher employs a multiple group (G) design in which n observations are in each of k independent groups or samples. A randomized groups analysis of variance (ANOVA) or its nonparametric counterpart, the Kruskal-Wallis H test, is typically employed to test the null hypothesis: Gl = G2 = ... = Gk. Similarly, in the randomized blocks or matched groups design, ANOVA or the Friedman x2 test might be employed. In all four of these cases the alternative hypothesis is the omnibus: Gi 0:/= Gj for some i =A j. However, there are also specific alternatives which might be tested, for example, partially ordered hypotheses (Gi = G2 < ...
TL;DR: In this article, a method was considered for selecting mathematical models to fit frequency distributions of hydrologic data among ten commonly used methods of frequency analysis, including Gumbel, Lieblein, Chow, and the seven types of Gringorten.
Abstract: A method is considered for selecting mathematical models to fit frequency distributions of hydrologic data among ten commonly used methods of frequency analysis. The methods are those of Gumbel, Lieblein, Chow, and the seven types of Gringorten. The best fitting model is chosen on the basis of comparison for goodness of fit indicated by the coefficients of determination. Friedman's nonparametric statistical test was employed to detect significant differences between the models.
01 Jun 1970
TL;DR: The nonparametric density estimation technique is shown to produce acceptable results with real data and demonstrate a definite advantage over a parametric procedure when multimodal data is involved.
Abstract: : The report investigates two approaches to pattern recognition which utilize information about pattern organization. First, a nonparametric method is developed for estimating the probability density functions associated with the pattern classes. The dispersion of the patterns in the feature space is used in attempting to optimize the estimate. The second approach involves the structural relationships of pattern components, an approach called 'linguistic' because it employs the concepts and methods of formal linguistics. The nonparametric density estimation technique is shown to produce acceptable results with real data and demonstrate a definite advantage over a parametric procedure when multimodal data is involved. Two alternative techniques are investigated for analyzing linguistic descriptions of patterns. Stochastic automata are considered as recognizers of stochastic pattern languages. The other technique is a stochastic generalization of the recently proposed programmed grammar which is developed as a grammar for pattern description. (Author)
TL;DR: In this article, a rank table technique is given in which temporal data from a number of stations is ranked time-wise, and rank sums for each time obtained by summing ranks over the total numbers of stations.
Abstract: Principal components or empirical orthogonal functions are virtually the sole statistical tool used to date for investigations of space-time variability of meteorological elements. Maximum statistical efficiency and possible physical interpretation of empirical orthogonal functions derives from the assumptions of stationarity and homoscedasticity of the scalar variables in space and time. In this study, a rank table technique is given in which temporal data from a number of stations is ranked time-wise, and rank sums for each time obtained by summing ranks over the total number of stations. The technique offers some advantages for investigations of joint space-time variability. First, it is nonparametric; second, analysis of variance schemes are simplified; and third, a test of homoscedasticity can easily be performed. Networks of streamflow and precipitation data over the conterminous 48 States are used to illustrate the use of the technique. As a result, streamflow and precipitation data are sh...
TL;DR: A new general approach to the formulation of a non-parametric detector using dependent samples is introduced and applied to a space-diversity system employing dc signaling and demonstrates an improvement in transmission efficiency.
Abstract: A new general approach to the formulation of a non-parametric detector using dependent samples is introduced and applied to a space-diversity system employing dc signaling. A comparison based on a form of asymptotic relative efficiency is made between the new detector and a Mann-Whitney detector. Under certain conditions the new procedure demonstrates an improvement in transmission efficiency.
TL;DR: In this paper, the authors consider three nonparametric tests which may be used to provide a one-sided test for detecting a difference in location of two populations, where the criterion for termination may be a preselected period of time from the start of the experiment or the occurrence of a given order statistic in one of the samples.
Abstract: SUMMARY This paper deals with some properties of three nonparametric tests which can be used for detecting a difference in location of two populations wlhen samples are censored on the occurrence of a given order statistic. The null distributions of the test statistics are presented together with some tables of critical values. Exact expressions are obtained for the powers of the tests under exponential and rectangular alternatives. Finally, the expected durations of the tests are compared. A number of tests which permit early termination of an experiment have been proposed for detecting a difference in the location of two populations. These tests have important applications in life-testing situations where testing time may be costly. The criterion for termination may be a preselected period of time from the start of the experiment or the occurrence of a given order statistic in one of the samples or the two samples combined. In this paper we consider three nonparametric tests which may be used to provide a one-sided test for difference in location of two populations. The common feature of the tests is that the experiment is terminated on or before the occurrence of a preselected order statistic in one of the samples. We first consider the distributions of the test statistics under the null hypothesis that the two samples have been drawn randomly from populations with identical cumulative distribution functions. Some tables of critical values are presented. Expressions are given for the test powers under the alternative of a translation in an exponential distribution and for changes in the location and scale parameters of a rectangular distribution. Finally some results are given for the expected durations of the tests.
TL;DR: In this article, some optimum nonparametric tests and estimates for contrasts of interactions in two-factor models with replications are proposed and discussed, and confidence intervals based on the above procedures are investigated.
Abstract: Some optimum nonparametric tests and estimates for contrasts of interactions in two-factor models with replications are proposed and discussed. These procedures are based on nonparametric estimates of the type considered by Hodges and Lehmann [4]. Unbiasedness and joint asymptotic normality of the estimates are proved and the asymptotic efficiencies relative to the least squares procedure is found. It is shown that, in the special cases of Wilcoxon and normal scores, these methods are more robust than least squares against changes in the underlying distribution. Also, confidence intervals based on the above procedures are investigated (c.f. [12]). An example is given to explain the computations.
Dissertation•
01 Jan 1970
TL;DR: In this paper, a class of nonparametric procedures for estimating and testing the various main effects and interactions are considered, based on a simple alignment process and involve the use of some well known rank statistics.
Abstract: For experiments involvingm factors (A
1,…,A
m), each at 2 levels (1, 2), and replicated inn(≧2) blocks, a class of nonparametric procedures for estimating and testing the various main effects and interactions are considered. The procedures are based on a simple alignment process and involve the use of some well known rank statistics. Their performance characteristics are compared with those of the standard (normal-theory) parametric procedures. Extensions to confounded or partially confounded designs are also considered.
TL;DR: In this article, the Pitman A.R.E.s of the three nonparametric tests of David and Fix for the two-sample bivariate location problem are given.
Abstract: Some large-sample properties of the three nonparametric tests of David and Fix for the two-sample bivariate location problem are given. In particular the Pitman A.R.E.s of the tests against some ‘normal-theory’ competitors are shown to be satisfactory in most cases for a number of ‘near-normal’ bivariate distributions. Their performances in some mixtures of bivariate normal distributions prove to be particularly convincing. A useful relationship between the three test statistics is indicated.