摘要:

AbstractThis paper gives a general formula for the first two moments of the non‐circular product moment statistic, which is used as a test for the statistical independence of the interarrival times of certain time series data, e.g., neuronal spike discharges. For the special cases of rank and exponential score product moment statistics, the mean and variance are formulate

ISSN:0319-5724    

DOI:10.2307/3315095

出版商:Wiley‐Blackwell    

年代:1975

数据来源: WILEY

摘要:

AbstractBounds are obtained for the product moments of an arbitrary finite number of ordered random variables. These bounds are obtained with the help of a representation of an arbitrary function in terms of a complete orthonormal system in a pre‐Hilbert space of square integrable functions defined in a k‐dimensional unit c

ISSN:0319-5724    

DOI:10.2307/3315096

出版商:Wiley‐Blackwell    

年代:1975

数据来源: WILEY

摘要:

AbstractFor the generalized MANOVA model of Potthoff and Roy [7], Gleser and Olkin [3]give a likelihood ratio test criterion for testing double linear parametric functions of the regression parameters. Their theory is extended in this paper to the testing of double linear parametric functions with double linear restrictions on the parameters. The theory is presented in terms of the original variates unlike Gleser and Olkin [3] who resort to canonical transformations of the original variates.

ISSN:0319-5724    

DOI:10.2307/3315097

出版商:Wiley‐Blackwell    

年代:1975

数据来源: WILEY

摘要:

AbstractIn this paper correlation has been introduced between two successive transitions in the model investigated by Moyal and Heathcote (1959). The transition rate has been taken to be constant and for simplicity of mathematical expressions the time scale has been so chosen that this rate is unity. For the unrestricted walk we find that the mean position of the particle at time t is that position for which the probability of the particle arriving at some earlier instant from the left is 1/2. With both the barriers either absorbing or reflecting, we have obtained the Laplace Transform of the distributions, but because of the complicated nature of the mathematical expressions involved we are able to find only the asymptotic distributions. For the reflecting barrier case, we find that the process tends to a stationary distribution and that the expected position is eventually the middle point between the barriers.

ISSN:0319-5724    

DOI:10.2307/3315098

出版商:Wiley‐Blackwell    

年代:1975

数据来源: WILEY

摘要:

AbstractA nonparametric method is developed to estimate the minimum dosage level required to induce a given response rate in an experiment. The only assumption used about the response rate is that it is a nondecreasing function with respect to the dosage level. Let nisubjects be independently tested at dosage level xix1x2xk. This paper presents methodology for the estimation of the smallest i such that the response probability at xiis no less than a required level p. A comparison with well‐known nonparametric methods shows that this method is better in some cases. A design of minimum required sample size for a given accuracy is also develope

ISSN:0319-5724    

DOI:10.2307/3315099

出版商:Wiley‐Blackwell    

年代:1975

数据来源: WILEY

摘要:

AbstractThe objective of this study is to evaluate the performance of Winsorized t which was proposed to be used as one alternative to the student's t statistic when the parent population is non‐normal. The criterion we use is the power of the test. Comparative performance of the Winsorized t, trimmed t, and Studen$tCs t for normal populations and for Studen$tCs t distribution with 8, 4, and 2 degrees of freedom was investigate

ISSN:0319-5724    

DOI:10.2307/3315100

出版商:Wiley‐Blackwell    

年代:1975

数据来源: WILEY

摘要:

AbstractThis paper deals with the aggregation problem of autoregressive functions. The macrocoefficients of the simplified specification are separated into three components, namely, a true value, an aggregation bias, and an implicit sampling error. Relative importance of these components is studied by using empirical data on a sample of 40 Canadian firms. The notion of aggregation gain of Grunfeld and Griliches is also examined.

ISSN:0319-5724    

DOI:10.2307/3315101

出版商:Wiley‐Blackwell    

年代:1975

数据来源: WILEY

摘要:

AbstractFor the general linear model Y = X$sZ + e in which e has a singular dispersion matrix $sG2A, $sG>0, where A is n x n and singular, Mitra [2] considers the problem of testing F$sZ, where F is a known q x q matrix and claims that the sum of squares (SS) due to hypothesis is not distributed (as a x2variate with degrees of freedom (d. f.) equal to the rank of F) independent of the SS due to error, when a generalized inverse of A is chosen as (A + X'X)–. This claim does not hold if a pseudo‐inverse of A is taken to be (A + X'X)+where A+denotes the unique Moore‐Penrose inverse (MPI)

ISSN:0319-5724    

DOI:10.2307/3315102

出版商:Wiley‐Blackwell    

年代:1975

数据来源: WILEY

摘要:

AbstractLet X1X2… XNbe independent normal p‐vectors with common mean vector $$ = ($$) and common nonsingular covariance matrix $$ = Diag ($sGi) [(1–p) I + pE] Diag ($sGi), $sGi>0, i = 1… p, 1>p>=1/p–1. Write rij= sample correlation between the i th and the j th variable i j = 1,… p. It has been proved that for testing the hypothesis H0: p = 0 against the alternative H1: p>0 where $$ and $sG1,…, $sGpare unknown, the test which rejects H0for large value of $$ rijis locally best invariant for every $aL: 0>$aL>1 and locally minimax as p $$ 0 in the sense of Giri and Kiefer, 1964, for every $aL: 0>$aL $$ $aL0>1 wher

ISSN:0319-5724    

DOI:10.2307/3315103

出版商:Wiley‐Blackwell    

年代:1975

数据来源: WILEY

摘要:

AbstractBradley (1958) proposed a very simple procedure for constructing latin square designs to counterbalance the immediate sequential effect for an even number of treatments. When the number of treatments is odd, balance in a single latin square is not possible. In the present note we have developed an analogous method for the construction of such designs which may be used for an even or odd number of treatments. A proof has also been offered to assure the general validity of the procedure.

ISSN:0319-5724    

DOI:10.2307/3315104

出版商:Wiley‐Blackwell    

年代:1975

数据来源: WILEY