摘要:

AbstractIn the paper [11], the authors have shown that the familiar centralF‐distribution can be considered as an asymptotically approximate distribution, in a heuristic sense, of the null distribution of theF‐statistic for testing a partial null hypothesis in a randomized PBIB design withmassociate classes under the Neyman model. This result is the most general among those given in previous related papers [6, 7, 8, 9, 11]. The term “asymptotically approximate distribution” has been used, however, in a rather heuristic and unsophisticated way and the rigorous formulation of the notion of asymptotically approximate distribution has not yet been attempted. The purposes of the present article are to give a satisfactory formulation of the asymptotically approximate distribution based on Ikeda's theory of the asymptotic equivalence of probability distributions [2, 5]and to show that the familiar centralsF‐distribution is “an asymptotically approximate distribution”, in the sense just defined, of theF‐statistic for testing a partial null hypothesis in the analysis of a PBIB design withmassociate classes, even under the Neyman model when it is randomized. The tedious calculations of the previous paper [11] are eliminated and the rather rigid uniformity conditions are weakened in the present article. The present work throws some light on the asymptotic nature of the power function of theF‐statistic under consideration; this will be presented in a forthcoming p

ISSN:0319-5724    

DOI:10.2307/3314644

出版商:Wiley‐Blackwell    

年代:1973

数据来源: WILEY

摘要:

AbstractThe h‐statistic h (Dwyer [1]) is extended to the generalized h‐statistic hP1…Pssuch that E(hP1…Ps) with properties similar to polykays. In order to obtain their sampling moments, formulas expressing their products as linear combinations of the same are required. The paper presents a combinatorial method to achieve this. Certain rules are developed and applied to obtain products through w

ISSN:0319-5724    

DOI:10.2307/3314645

出版商:Wiley‐Blackwell    

年代:1973

数据来源: WILEY

摘要:

AbstractIn this paper the problem of classifying an individual into one of two multivariate normal populations with common covariance matrix is considered. An attempt is made to provide some idea about the errors of misclassification for the Welch‐Anderson statistic. It is shown that in most cases the usual asymptotic expression (the one when all the parameters are known) is an underestimate of the actual error committed. In Part II, an alternative classification procedure, known as a step‐down procedure, is proposed. In this the errors of misclassification are easily computa

ISSN:0319-5724    

DOI:10.2307/3314646

出版商:Wiley‐Blackwell    

年代:1973

数据来源: WILEY

摘要:

AbstractThis paper is concerned with some computational aspects of Fisher's simultaneous‐equation estimator in its modified version [15] and with the alternative of using this computational scheme as the first stage of the two‐stage instrumental variables (2 SIV) estimator [1, p. 11]. The main disadvantage of the above estimation process arises out of the repeated investigation of a given set of instruments to determine how significantly some of their combinations contribute to R̄2. A short‐cut procedure that eliminates this computational inconvenience is suggested in this paper. The new method treats the problem within the framework of operations research, i.e., by isolating the optimum combination through the shortest way possible. The resulting step‐wise algorithm leads to the optimum combination of the given instrumental variables in, at most, n steps, where n is the number of instruments. The results of the application of this procedure to the estimation of the Ontario Econometric Model [9] are discussed, tested and compared with other methods of es

ISSN:0319-5724    

DOI:10.2307/3314647

出版商:Wiley‐Blackwell    

年代:1973

数据来源: WILEY

摘要:

AbstractThis is part one of a study of the demand for energy in Canada in the industrial, residential and residential‐commercial markets. The study focuses on the four major sources of energy: gas, oil, coal and electricity. The contents of this paper are as follows:1. The economic background. The main ideas; a diagrammatic derivation of the free and captive demand; the model.2. Estimation.The interdependence of demand and price: Natural gas, oil, electricity and coal; the price variables that enter the relationships; data and operational definitions of the variables.3. Estimation and simulation results for the industrial demand for natural gas. The price‐additive model, the problem of multicollinearity, the alternat

ISSN:0319-5724    

DOI:10.2307/3314648

出版商:Wiley‐Blackwell    

年代:1973

数据来源: WILEY

摘要:

AbstractSuppose that in a random sample of size n from a population with probability density function f(x), the order statistics are X(1)

ISSN:0319-5724    

DOI:10.2307/3314649

出版商:Wiley‐Blackwell    

年代:1973

数据来源: WILEY

摘要:

AbstractLet x1, x2,…, xrrepresent the first r failures among n items being life tested. It is of interest to estimate the future failure times and thereby acquire an overall idea of the total test time. Prediction of xs(s>r) was studied by Lawless [4], An improved procedure is developed here based on a different statistic. Special cases of s = r + l and s = n are treated. Illustrative examples are given. A comparison in savings is made with the above metho

ISSN:0319-5724    

DOI:10.2307/3314650.o

出版商:Wiley‐Blackwell    

年代:1973

数据来源: WILEY

摘要:

AbstractConsider a random sample (X1, X2,…, Xn) where one observation (or out‐lier) is determined by the density f(x, θ/α), θ>0, 00. The statistic Tmn= 1/m+1 [Σmi=1x(i)+(n‐m)x(m)], 0

ISSN:0319-5724    

DOI:10.2307/3314651

出版商:Wiley‐Blackwell    

年代:1973

数据来源: WILEY

摘要:

AbstractIt is known [Z] that if X is any positive random variable, thenE(Xn)>[E(X)]nfor any integer n, provided the expectations exist. A matrix generalization of this result for n = ‐1 was given in [1]. We will show that a simple exercise in matrix analysis yields the matrix generalization for any integer n, positive or negativ

ISSN:0319-5724    

DOI:10.2307/3314652

出版商:Wiley‐Blackwell    

年代:1973

数据来源: WILEY

摘要:

AbstractIn this paper we propose classification rules with respect to the mean, variance, and the coefficient of variation forc(≥2)univariate normal populations. Two different approaches to the problem have been studied (a) where the probability of correct classification is at least a pre‐assigned numberp*(l/c ≤ p*<1), and(b)where the probability of correct classification has to be evaluated. For the two approaches(a)and(b), classification rules with respect to the mean have been studied when thecpopulations have(i)common known variance,(ii)common unknown variance. The classification rules of approach(b)in the case of common known or unknown variance is also valid when the variances are not all equal and are known or unknown. Classification rules with respect to the coefficient of variation are also given for the two approaches when the population parameters are unknown. Classification rules with respect to the variance for the two approaches are explored when the means are unknown. In each case of approach(b), the classification rule has been shown to possess a certain optimum pro

ISSN:0319-5724    

DOI:10.2307/3314996

出版商:Wiley‐Blackwell    

年代:1973

数据来源: WILEY