ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488751

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

The amount of statistics, numerical analysis, mathematics and computer programming involved in the design of experiments for estimating parameters in non-linear models is such that most potential users are discouraged from considering nonlinear design techniques, and since too few statisticians are available to assist in and direct such work, an easy-to-use flexible computer program for experimental design has been developed. To use this program, it is only necessary to provide a routine to compute the model, since the program obtains the various terms needed to accumulate the design determinant by numerical differentiation. Using given values for the variances of the quantities actually measured, the program computes the effective variance of each experiment, and then makes use of this knowledge in determining the optimal design. The program can of course be used in a sequential mode, with small groups of experiments being designed, performed and analysed in turn. The change in the total number of experiments required caused by measuring additional responses, or by measuring more precisely those responses already recorded, is also discussed.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488752

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

For them-way contingency table, we consider models that describe the possible multiplicative interactions among themvariables of the table, and we show how to select models that fit the data in the table, using methods that are, in part, somewhat analogous to the usual stepwise procedures in regression analysis. (Themvariables here are dichotomous or, more generally, polytomous variables.) These methods can be applied to build models for any of the following situations: (a) themvariables are response variables and the mutual relationships among the variables are of interest; (b) one of the variables is a response variable and the otherm– 1 variables are factors that may affect the response; (c)m′ of the variables are response variables (1 < m′ <m) and the otherm-m′variables are factors that may affect them′ variables and the mutual relationships among them′ variables. For illustrative purposes, we analyze a 4-way table (actually, a 3 × 23table), considering both linear and quadratic interaction effects.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488753

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

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.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488754

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

Two procedures for treatment of outliers are considered for samples of normally distributed observations with known variance. The first procedure is a sequential adaptation of the usual maximum residual test for one outlier. If the maximum residual exceeds a predetermined constant, the largest observation is declared an outlier. In this event the test is repeated using the remaining observations. In the second procedure the two largest observations are declared outliers if the sum of the two largest residuals exceeds a predetermined constant. The performance of the two procedures is investigated for samples which contain two observations of mean higher than the common mean of the other observations. For the sequential procedure samples containing one high and one low outlier are also considered.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488755

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

The performances of three procedures for treatment of outliers in normal samples are evaluated. The first procedure is the sequential application of the usual maximum residual test. The largest observation is declared an outlier if the largest studentized residual exceeds a predetermined value. If one outlier is detected, the test is repeated on t.he remaining observations, the process continuing until no further outliers are detected. In the second procedure the two largest observations are declared outliers if the sum of the two largest studentized residuals exceeds a predetermined value. In the third procedure the two largest observations are considered outliers if the ratio of the corrected sum of squares omitting these values to the total corrected sum of squaresis less than a critical ratio. The performances of these procedures are evaluated for samples in which two of the observations have means different from the common mean of the remainder of the sample.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488756

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

The performance of three rules for dealing with outliers in small samples of size n from the normal distributionN(μ, σ2) is investigated when the primary objective of sampling is to obtain an accurate estimate of σ2. It is assumed that at most one observation in the sample may be biased, arising from eitherN(μ + aσ, σ2) orN(μ, (1 +b) σ2). Performance of each rule is measured in terms of “Protection”, the fractional decrease in MSE obtained by using the rule when a biased observation actually is present in the sample. Numerical results have been obtained forn5 ≤ 11 when μ is known andn= 3 when μ is unknown.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488757

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488758

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

The Student's test ofH0: μ = μ0againstH1: μ ≠ μ0of the location parameter μ of the normal, logistic and Cauchy distributions when the scale parameter σ is unknown based on a few selected sample percentiles is considered. Tables facilitating the computation of the testing statistic are provided and the effects of the biases of the linear estimates involved on the test are investigated.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488759

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

Some age replacement policies are investigated for the case in which the cost of keeping an individual unit operating in a system increases with the age of the unit. The optimum age replacement policy is the one which minimizes the average expected cost per unit time over an infinite time span. The case in which the life distribution of the units is exponential is investigated in detail, with numerical examples included.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488760

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor