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Various methods based on Student t variates have been suggested and used for obtaining simultaneous confidence intervals for several means, or for several contrasts among means. Determination of an overall confidence level for such intervals involves evaluating the probability mass of a multivariate t distribution over a hypercube centered at the origin, with sides paralleling the coordinate planes, or obtaining bounds for this probability mass. Since such distributions involve many nuisance parameters, an impossible number of tables would be necessary in order to make exact confidence intervals. In the virtual absence of tables, approximations and bounds become important. In this paper, an attempt has been made to investigate the adequacy of certain suggested approximations [2], [5], [8] by computing the exact distributions for some particular cases. These exact distributions have been compared with approximations. This paper is concerned with two-sided confidence intervals, rather than one-sided intervals. [ABSTRACT FROM AUTHOR]

This paper presents the results of a Monte Carlo study of the accuracy of an approximation to the power of the chi-square goodness of fit test with small but equal expected frequencies. Various combinations of sample size, number of groups, and alpha level are considered, and in most instances the actual power of the test is estimated to be less than the nominal power. The degree of accuracy appears to be more related to the size of the sample than to the size of the expected frequencies. The following rule of thumb is offered for obtaining crude estimates of the actual power from the nominal power for sample sizes from 10 to 50: The actual power of the test equals about eight-tenths of the nominal power. [ABSTRACT FROM AUTHOR]

The decision-theoretic approach to point estimation involves the choice of an estimate to minimize the expected loss associated with the estimate. The purpose of this paper is to indicate the influence of risk aversion on point estimates for classes of payoff functions including the piecewise linear and quadratic payoff functions. Increased risk aversion results in a point estimate closer to zero for a quadratic pay. off function and a lower estimate with a piecewise linear payoff function, for example. [ABSTRACT FROM AUTHOR]

This paper develops a theoretical framework for the unrelated question randomized response technique suggested by Walt R. Simmons. The statistical efficiency of this technique is compared with the Warner technique under situations of both truthful and untruthful responses. Methods of allocating the total sample to each of two subsamples required by the unrelated question approach are developed. Recommendations are made concerning choices of values for those parameters which can be assigned at the discretion of the investigator. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to make the reader aware of the applicability and advantage of a particular mathematical model. The application is typified by an example and the advantage is via confidence intervals; that is, shorter confidence intervals are possible using the model than if one ignores it, providing the applicability is valid. It is also shown that an improved estimate can be obtained through use of the model. Let f(y|mu, sigma) be a normal density with mean mu and variance sigma[sup 2] and let g(mu|lambda, beta) be a normal density with mean lambda and variance beta[sup 2]. A sequence y[sub 1], y[sub 2],..., y[sub n+1] of independent observations from the mixture off and g can be considered as follows: An unobservable mu [sub i] is first drawn from g(mu|lambda, beta) and then y[sub i] which can be observed is drawn from f(y|mu[sub i], sigma). Confidence intervals on mu[sub n+1] are obtained which are based on the observations y[sub 1],..., y[sub n+1] and which are shorter than the standard interval based on y[sub n+1] only for any n. Shorter intervals are obtained for two cases: (i) lambda unknown, sigma, beta known; (ii) only sigma/beta = c known. [ABSTRACT FROM AUTHOR]

In a linear regression model, when errors are autocorrelated, several asymptotically efficient estimators of parameters have been suggested in the literature. In this paper we study their small sample efficiency using Monte Carlo methods. While none of these estimators turns out to be distinctly superior to the others over the entire range of parameters, there is a definite gain in efficiency to be had from using some two-stage procedure in the presence of moderate high levels of serial correlation in the residuals and very little loss from using such methods when the true rho is small. Where computational costs are a consideration a mixed strategy of switching to a second stage only if the estimated rho is higher than some critical value is suggested and is shown to perform quite well over the whole parameter range. [ABSTRACT FROM AUTHOR]

An algorithm for the determination of the economic design of X-charts based on Duncan's model is described in this paper. This algorithm consists of solving an implicit equation in design variables n (sample size) and k (control limit factor) and an explicit equation for h (sampling interval). The use of this algorithm not only yields the exact optimum but also provides valuable information so that the sensitivity of the optimum loss-cost (L*) can be evaluated. Loss-cost contours are used to discuss the nature of the loss-cost surface and the effect of the design variables. The effect of two parameters, the delay factor (e), and the average time for an assignable cause to occur (1/lambda), on the optimum design is evaluated. Numerical examples are used for illustrations. [ABSTRACT FROM AUTHOR]

In this paper the problem of choosing among point estimators on the basis of their small sample properties is discussed from the sampling point of view. The indeterminacy of most Monte Carlo studies is analysed and resolved within the framework of statistical decision theory. A first order autoregressive model is worked through in detail both for its own sake and to illustrate how a complete Monte Carlo study might be done. [ABSTRACT FROM AUTHOR]

The multivariate acceptance sampling problem is discussed and a solution for a particular sub-class of the general problem developed. This is where the related quality variables have a multivariate normal distribution with known covariance matrix, and where the specification region may be set in the form of a general ellipsoid. Single sampling acceptance procedures by variables for fraction defective are developed. Methods are given for determining the sample size n and acceptance number c so as to achieve desired operating characteristics. [ABSTRACT FROM AUTHOR]

When data are transformed to satisfy a spherical normal linear model, the mean θ of a variate in the original scale is a function of the mean μ and variance σ² of a normal variate. We consider several approximate confidence interval methods for θ, including a new method based on exact confidence intervals for linear functions of μ and σ² Monte Carlo estimates of coverage probabilities demonstrate the suitability of the new method for applications involving a wide range of data transformations, parameter values and sample sizes. [ABSTRACT FROM AUTHOR]