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The article presents the author's comments on an article "Optimum Sample Size for a Problem in Choosing the Population With the Largest Mean," by statistician Paul N. Somerville, published in the June 1970 issue of "Journal of the American Statistical Association." In the article Somerville described a procedure for selecting the population with the largest mean from normal populations with unknown means and a common known variance. The author claims that his procedure gives a unique minimax solution and that the minimax is a reasonable solution to the problem. According to the author, Somerville has not made it clear that his procedure gives only the local minimax solution. This makes practical applications of his procedure severely limited for it is difficult to think of a situation in which an experimenter would like to determine a local minimax value.

In this paper an estimator of the finite population mean using auxiliary information in sample surveys has been proposed. The bias and mean squared error are obtained under large sample approximation. It has been shown that the proposed estimator performs better than some recently published estimators. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of estimating the population varianceS2yof the study variableyusing auxiliary information in sample surveys. We have suggested a class of estimators of the population varianceS2yof the study variableywhen the population varianceS2xof the auxiliary variablexis known. Asymptotic expressions of bias and mean squared error (MSE) of the proposed class of estimators have been obtained. Asymptotic optimum estimators in the proposed class of estimators have also been identified along with its MSE formula. A comparison has been provided. We have further provided the double sampling version of the proposed class of estimators. The properties of the double sampling version have been provided under large sample approximation. In addition, we support the present study with aid of a numerical illustration. [ABSTRACT FROM AUTHOR]

The mean past lifetime (MPL) function (also known as the expected inactivity time function) is of interest in many fields such as reliability theory and survival analysis, actuarial studies and forensic science. For estimation of the MPL function some procedures have been proposed in the literature. In this paper, we give a central limit theorem result for the estimator of MPL function based on a right-censored random sample from an unknown distribution. The limiting distribution is used to construct normal approximation-based confidence interval for MPL. Furthermore, we use the empirical likelihood ratio procedure to obtain confidence interval for the MPL function. These two intervals are compared with each other through simulation study in terms of coverage probability. Finally, a couple of numerical example illustrating the theory is also given. [ABSTRACT FROM AUTHOR]

In the wood industry, it is common practice to compare in terms of the ratio of the same-strength properties for lumber of two different dimensions, grades, or species. Because United States lumber standards are given in terms of population fifth percentile, and strength problems arise from the weaker fifth percentile rather than the stronger mean, so the ratio should be expressed in terms of the fifth percentiles rather than the means of two strength distributions. Percentiles are estimated by order statistics. This paper assumes small samples to derive new non parametric methods such as percentile sign test and percentile Wilcoxon signed rank test, construct confidence intervals with covergage rate 1 –αxfor single percentiles, and compute confidence regions for ratio of percentiles based on confidence intervals for single percentiles. Small 1 –αxis enough to obtain good coverage rates of confidence regions most of the time. [ABSTRACT FROM AUTHOR]

Lui [Five confidence intervals of the closed population size in the capturerecapture problem under inverse sampling with replacement. Biom J. 2004;46:474-480] considered five confidence intervals for the closed population size in a two-sample capture-recapture experiment under inverse sampling with replacement in the recapture phase. The results of his Monte Carlo study indicated that the exact confidence intervals and those based on X²-approximation perform very well. In this paper, we consider three other methods of interval estimation including the bootstrap, likelihood ratio and Jeffreys prior approaches. A Monte Carlo simulation is carried out to evaluate the performance of these intervals together with those based on existing methods in terms of the coverage probability, error rates and standardized average length. Our results show that confidence intervals based on Wald statistics, logarithmic transformation, and bootstrap methods are inappropriate, having coverage probabilities less than the desired nominal level. Also, the exact confidence intervals and those based on X²- approximation are not invariant with respect to the proportion of marked individuals in the capture phase, say p. When p is chosen to be small-tomoderate, the likelihood ratio method is preferred, since it gives confidence intervals with shorter length from among all methods that provide the coverage probability close to the desired nominal level. Overall, the Jeffreys method appears to be more robust than other competitors, providing intervals with nearest coverage probabilities to the desired nominal level and with balanced non-coverage rates. [ABSTRACT FROM AUTHOR]

Linearization methods are customarily adopted in sampling surveys to obtain approximated variance formulae for estimators of statistical functionals under the design-based approach. In the present paper, following the Deville [Variance estimation for complex statistics and estimators: linearization and residual techniques. Surv Methodol. 1999;25:193-203] approach stemming from the concept of design-based influence function, we provide a general result for linearizing a large family of population functionals which includes many of the inequality measures considered in social, economic and statistical studies, such as the Gini, Amato, Zenga, Atkinson and Generalized Entropy indices. The feasibility of our theoretical results is assessed by some simulation studies involving real and artificial data. [ABSTRACT FROM AUTHOR]

This paper examines the asymptotic and finite-sample properties of tests of equal forecast accuracy and encompassing applied to direct, multistep predictions from nested regression models. We first derive asymptotic distributions; these nonstandard distributions depend on the parameters of the data-generating process. We then use Monte Carlo simulations to examine finite-sample size and power. Our asymptotic approximation yields good size and power properties for some, but not all, of the tests; a bootstrap works reasonably well for all tests. The paper concludes with a reexamination of the predictive content of capacity utilization for inflation. [ABSTRACT FROM AUTHOR]

This paper proposed a modified ratio-cum-product estimator of finite population mean using information on coefficient of variation and coefficient of kurtosis of auxiliary variable in ranked set sampling. It has been shown that this method is highly beneficial to the estimation based on simple random sampling (SRS). The bias and mean squared error of the proposed estimators with large sample approximation are derived. Theoretically, it is shown that the suggested estimators are more efficient than the estimators in SRS. In addition, we support this theoretical result with the numerical illustration. [ABSTRACT FROM AUTHOR]

This paper suggested an alternative ratio-cum-product type class of estimators of population mean using exponentiation method in simple random sampling. Approximate bias and mean squared error formulae of the suggested class of estimators have been obtained up to the first order of approximation. Asymptotic optimum estimator in the suggested class of estimators has been obtained with its mean squared error formula. Regions of preferences have been obtained under which the suggested class of estimators has been better than the usual unbiased, ratio and product estimators and the estimators according to Singh and Agnihotri (2008). Some examples are cited with numerical study. [ABSTRACT FROM PUBLISHER]

The article discusses moments of the distribution of sample size, N in a sequential probability ratio test (SPRT). The present paper provides variance, the third and the fourth moments of N. The details are worked out in five common applications of the SPRIT. The relation of the variance of N to the truncation of a SPRT is discussed is also discussed in the paper. Scholar A. Wald indicated in passing how one can obtain the moments of N, but the only published literature where the author encountered a general expression for the variance of N. However, their expression is incorrect. Using scholar J. Wolfowitz's results, which they do, or differentiating Wald's, fundamental identity twice one gets provided. In many practical applications of the SPRT, μ and moments in an equation derived are differentiable functions of a real-valued parameter. The limiting expressions for the moments can then be determined by standard methods of mathematical analysis. However, for the third and fourth moments the actual technique may involve an excessive amount of arithmetic.

A generalized version of inverted exponential distribution (IED) is considered in this paper. This lifetime distribution is capable of modeling various shapes of failure rates, and hence various shapes of aging criteria. The model can be considered as another useful two-parameter generalization of the IED. Maximum likelihood and Bayes estimates for two parameters of the generalized inverted exponential distribution (GIED) are obtained on the basis of a progressively type-II censored sample. We also showed the existence, uniqueness and finiteness of the maximum likelihood estimates of the parameters of GIED based on progressively type-II censored data. Bayesian estimates are obtained using squared error loss function. These Bayesian estimates are evaluated by applying the Lindley's approximation method and via importance sampling technique. The importance sampling technique is used to compute the Bayes estimates and the associated credible intervals. We further consider the Bayes prediction problem based on the observed samples, and provide the appropriate predictive intervals. Monte Carlo simulations are performed to compare the performances of the proposed methods and a data set has been analyzed for illustrative purposes. [ABSTRACT FROM PUBLISHER]

This paper attempts to develop a repetitive group sampling (RGS) plan by variables inspection for controlling the process fraction defective or the number of nonconformities when the quality characteristic follows a normal distribution and has only the lower or upper specification limit. The proposed sampling plan is derived by the exact sampling distribution rather than the approximation approach. The plan parameters are solved by a nonlinear optimization model which minimizes the average sample number required for inspection and fulfills the classical two-point conditions on the operating characteristic (OC) curve. The efficiency of the proposed variables RGS is examined and also compared with the existing variables single sampling plan in terms of the sample size required for inspection. The results indicate that the proposed variables RGS plan could significantly reduce samples required for inspection compared to the traditional variables single sampling plan. [ABSTRACT FROM AUTHOR]

In this paper, a difference-in-regression estimator is proposed by using two auxiliary variables in simple random sampling. Variance of proposed estimator up to the first order of approximation is compared with other competing estimators. Additionally, by taking the known value of one of the population regression coefficients, another version of the proposed estimator is also obtained. The proposed estimator is found optimum in the class of estimators based on two auxiliary variables. A simulation study is carried out in support with theoretical results. If only the means of auxiliary variables are available, another estimator can be obtained for large trivariate normal population. [ABSTRACT FROM PUBLISHER]

In this paper, we consider the Bayesian inference of the unknown parameters of the randomly censored Weibull distribution. A joint conjugate prior on the model parameters does not exist; we assume that the parameters have independent gamma priors. Since closed-form expressions for the Bayes estimators cannot be obtained, we use Lindley's approximation, importance sampling and Gibbs sampling techniques to obtain the approximate Bayes estimates and the corresponding credible intervals. A simulation study is performed to observe the behaviour of the proposed estimators. A real data analysis is presented for illustrative purposes. [ABSTRACT FROM PUBLISHER]

This paper considers a varying-coefficient partially linear regression with spatial data. A global smoothing procedure is developed by using B-spline function approximations for estimating the unknown parameters and coefficient functions. Under mild regularity assumptions, the asymptotic distribution of the estimator of the unknown parameter vector is established. The global convergence rates of the B-spline estimators of the unknown coefficient functions are established. The asymptotic distributions of the B-spline estimators of the unknown coefficient functions are also derived. Finite sample properties of our procedures are studied through Monte Carlo simulations. A real data example about Boston housing data is used to illustrate our proposed methodology. [ABSTRACT FROM AUTHOR]

This paper suggests an efficient class of ratio and product estimators for estimating the population mean in stratified random sampling using auxiliary information. It is interesting to mention that, in addition to many, Koyuncu and Kadilar (2009), Kadilar and Cingi (2003, 2005), and Singh and Vishwakarma (2007) estimators are identified as members of the proposed class of estimators. The expressions of bias and mean square error (MSE) of the proposed estimators are derived under large sample approximation in general form. Asymptotically optimum estimator (AOE) in the class is identified alongwith its MSE formula. It has been shown that the proposed class of estimators is more efficient than combined regression estimator and Koyuncu and Kadilar (2009) estimator. Moreover, theoretical findings are supported through a numerical example. [ABSTRACT FROM PUBLISHER]

In stratified sampling, usually the cost function is taken as a linear function of sample sizes n h . In many practical situations, the linear cost function does not approximate the actual cost incurred adequately. For example, when the cost of travelling between the units selected in the sample within a stratum is significant, instead of a linear cost function, a cost function that is quadratic in √n h will be a more close approximation to the actual cost. In this paper, the problem is formulated as multi-objective nonlinear integer programming problem with quadratic cost under three different situations, i.e. complete, partial or null information about the population. A numerical example is also presented to illustrate the computational details. [ABSTRACT FROM AUTHOR]

This paper presents an asymptotic approximation for the marginal density of any parameter of interest of a joint posterior density in the case of independent parameters. The approximation is based on the signed-root-based importance sampling algorithm considered in Kharroubi and Sweeting [Posterior simulation via signed root log-likelihood ratios, Bayesian Anal. (2010), in press] and gives rise to the alternative simulation-consistent scheme to Markov chain Monte Carlo for marginal densities. The consideration is illustrated by a censored regression model. [ABSTRACT FROM PUBLISHER]

This article studies control-variate estimation where the control mean itself is estimated. Control-variate estimation in simulation experiments can significantly increase sampling efficiency and has traditionally been restricted to cases where the control has a known mean. In a previous paper the current authors generalized the idea of control variate estimation to the case where the control mean is only approximated. The result is a biased but possibly useful estimator. For that case, a mean square error optimal estimator was provided and its properties were discussed. This article generalizes classical control variate estimation to the case of Control Variates using Estimated Means (CVEMs). CVEMs replace the control mean with an estimated value for the control mean obtained from a prior simulation experiment. Although the resulting control-variate estimator is unbiased, it does introduce additional sampling error and so its properties are not the same as those of the standard control-variate estimator. A CVEM estimator is developed that minimizes the overall estimator variance. Both biased control variates and CVEMs can be used to improve the efficiency of stochastic simulation experiments. Their main appeal is that the restriction of having to know (deterministically) the exact value of the control mean is eliminated; thus, the space of possible controls is greatly increased. [ABSTRACT FROM PUBLISHER]

Recently, Sanjel and Balakrishnan [A Laguerre Polynomial Approximation for a goodness-of-fit test for exponential distribution based on progressively censored data, J. Stat. Comput. Simul. 78 (2008), pp. 503–513] proposed the use of Laguerre orthogonal polynomials for a goodness-of-fit test for the exponential distribution based on progressively censored data. In this paper, we use Jacobi and Laguerre orthogonal polynomials in order to obtain density approximants for some test statistics useful in testing for outliers in gamma and exponential samples. We first obtain the exact moments of the statistics and then the density approximants, based on these moments, are expressed in terms of Jacobi and Laguerre polynomials. A comparative study is carried out of the critical values obtained by using the proposed methods to the corresponding results given by Barnett and Lewis [Outliers in Statistical Data, 3rd ed., John Wiley & Sons, New York, 1993]. This reveals that the proposed techniques provide very accurate approximations to the distributions. Finally, we present some numerical examples to illustrate the proposed approximations. Monte Carlo simulations suggest that the proposed approximate densities are very accurate. [ABSTRACT FROM PUBLISHER]

In this article, the Bayes estimates of two-parameter gamma distribution are considered. It is well known that the Bayes estimators of the two-parameter gamma distribution do not have compact form. In this paper, it is assumed that the scale parameter has a gamma prior and the shape parameter has any log-concave prior, and they are independently distributed. Under the above priors, we use Gibbs sampling technique to generate samples from the posterior density function. Based on the generated samples, we can compute the Bayes estimates of the unknown parameters and can also construct HPD credible intervals. We also compute the approximate Bayes estimates using Lindley's approximation under the assumption of gamma priors of the shape parameter. Monte Carlo simulations are performed to compare the performances of the Bayes estimators with the classical estimators. One data analysis is performed for illustrative purposes. We further discuss the Bayesian prediction of future observation based on the observed sample and it is seen that the Gibbs sampling technique can be used quite effectively for estimating the posterior predictive density and also for constructing predictive intervals of the order statistics from the future sample. [ABSTRACT FROM AUTHOR]

In this paper, Anbar's (1983) approach for estimating a difference between two binomial proportions is discussed with respect to a hypothesis testing problem. Such an approach results in two possible testing strategies. While the results of the tests are expected to agree for a large sample size when two proportions are equal, the tests are shown to perform quite differently in terms of their probabilities of a Type I error for selected sample sizes. Moreover, the tests can lead to different conclusions, which is illustrated via a simple example; and the probability of such cases can be relatively large. In an attempt to improve the tests while preserving their relative simplicity feature, a modified test is proposed. The performance of this test and a conventional test based on normal approximation is assessed. It is shown that the modified Anbar's test better controls the probability of a Type I error for moderate sample sizes. [ABSTRACT FROM AUTHOR]

Manipulation planning is a complex task for robots with a manipulator arm that need to grasp objects in the environment, specifically under narrow spatial conditions restricting the workspace of the robot. A popular approach for generating motion plans is probabilistic roadmap planning. However, the sampling strategy of such planners is usually unguided, and hence may lead to motion plans that seem counterintuitive for a human observer. In this article we present an approach that generates heuristics for the probabilistic sampling strategy from spatial plans that abstract from concrete metric data. These spatial plans describe a free trajectory in the workspace of the robot on a purely qualitative level, i.e., by employing spatial relations from formalisms considered in the domain of Qualitative Spatial and Temporal Reasoning. We discuss how such formalisms and constraint-based reasoning methods can be applied to approximate geometrically feasible motions. The paper is completed by an evaluation of a hybrid planning system in different spatial settings showing that run-times are notably improved when an abstract plan is considered as a guidance heuristic. [ABSTRACT FROM AUTHOR]

One approach to monitoring autocorrelated data consists in applying a control chart to the residuals of a time series model estimated from process observations. Recent research shows that the impact of estimation error on the run length properties of the resulting charts is not negligible. In this paper a general strategy for implementing residual-based control schemes is investigated. The designing procedure uses the AR-sieve approximation assuming that the process allows an autoregressive representation of order infinity. The run length distribution is estimated using bootstrap resampling in order to account for uncertainty in the estimated parameters. Control limits that satisfy a given constraint on the false alarm rate are computed via stochastic approximation. The proposed procedure is investigated for three residual-based control charts: generalized likelihood ratio, cumulative sum and exponentially weighted moving average. Results show that the bootstrap approach safeguards against an undesirably high rate of false alarms. In addition, the out-of-control bootstrap chart sensitivity seems to be comparable to that of charts designed under the assumption that the estimated model is equal to the true generating process. [Supplementary materials are available for this article. Go to the publisher's online edition of IIE Transactions for the following free supplemental resource: Appendix] [ABSTRACT FROM AUTHOR]

In this paper, testing procedures based on double-sampling are proposed that yield gains in terms of power for the tests of General Linear Hypotheses. The distribution of a test statistic, involving both the measurements of the outcome on the smaller sample and of the covariates on the wider sample, is first derived. Then, approximations are provided in order to allow for a formal comparison between the powers of double-sampling and single-sampling strategies. Furthermore, it is shown how to allocate the measurements of the outcome and the covariates in order to maximize the power of the tests for a given experimental cost. [ABSTRACT FROM AUTHOR]

This paper provides closed form expressions for the sample size for two-level factorial experiments when the response is the number of defectives. The sample sizes are obtained by approximating the two-sided test for no effect through tests for the mean of a normal distribution, and borrowing the classical sample size solution for that problem. The proposals are appraised relative to the exact sample sizes computed numerically, without appealing to any approximation to the binomial distribution, and the use of the sample size tables provided is illustrated through an example. [ABSTRACT FROM AUTHOR]

In the growing literature of factor analysis, little is done to understand the finite sample properties of an approximate factor model solution. In empirical applications with relatively small samples, the asymptotic theory might be a poor approximation and the resulting distortions might affect the estimation (bias in the point estimate and the standard errors) and the statistical inference. The present paper uses the estimation method of Bai and Ng [Bai, J. and Ng, S., 2002, Determining the number of factors in approximate factor models. Econometrica , 70, 191–221.] and assesses the sampling behavior of the estimated common components, common factors and factor loadings. The study compares the empirical distributions to the asymptotic theory of Bai [Bai, J., 2003, Inference on factor models of large dimension. Econometrica , 71, 135–171.]. Simulation results suggest that the point estimates have a Gaussian distribution for panels with relatively small dimensions. However, these estimates have a significant finite sample bias and the dispersion of their sampling distribution is severely underestimated by the asymptotic theory. [ABSTRACT FROM AUTHOR]

In a graphical procedure for comparing k treatment means in a one-way ANOVA, one displays uncertainty intervals around the sample means and judges any pair to be significantly different if and only if their uncertainty intervals do not overlap. A graphical procedure is a Multiple Comparison Procedure (MCP) if and only if it controls the experimentwise error rate. In this paper we consider some new graphical MCP's for the unbalanced one-way ANOVA design. These procedures are based on different approximations to the Tukey-Kramer (TK) procedure (e.g., Kramer 1956). As such, they constitute alternatives to Gabriel (1978) (and its modification by Andrews, Snee, and Sarner 1980), which is based on approximating a less efficient MCP (the GT2 of Hochberg 1974). Two of the four procedures considered here are based on best and simple upper bounds to all the confidence-interval lengths of the TK method and hence must be conservative. The other two procedures are based on approximations (here too we have the best vs. the simple procedure), but simulations were used to find that their true experimentwise error rates are less than the nominal ones; that is, these procedures are still on the conservative side. The choice of a particular procedure will depend then on the relative importance of simplicity, efficiency, and the security of having a controlled experimentwise error rate. [ABSTRACT FROM AUTHOR]

Most of the literature on survey sampling deals with a single stratifying variable. In this paper an attempt is made to study the effect of using two stratifying variables. We present an approximation to the variance of the study variable under the assumption of a linear regression on the two stratifying variables. This approximation depends only on the number of strata, the simultaneous density of the stratifying variables, and the correlations between the study variable and each of the stratifying variables. The results indicate that in many practical situations the gain from using two stratifying variables over one is nontrivial. [ABSTRACT FROM AUTHOR]

This paper investigates the distribution-free outer confidence interval for the quantile interval introduced by Wilks. Besides exact expressions and a recurrence formula some bounds are derived for the probability of correct coverage of the quantile interval which improve bounds known up to now, and which are tested in several examples. Asymptotic approximations are discussed and applications of the developed methods to other statistics based on order statistics are indicated. [ABSTRACT FROM AUTHOR]

This paper proposes the use of approximate posterior distributions resulting from operational prior distributions chosen with regard to the realized likelihood function. L.J. Savage's "precise measurement" is generalized for approximation in terms of an arbitrary operational prior density, including mixed-type prior distributions with positive probabilities on singular subsets. A new approximation is also given relating such distributions to absolutely continuous distributions with high local concentrations of density, Mixed-type distributions constructed from the natural conjugate prior distributions are proposed and illustrated in the normal-sampling case for unified Bayesian inference in testing and estimation contexts. [ABSTRACT FROM AUTHOR]

Let X[sub 1], ... , X[sub m] and Y[sub 1], ... , Y[sub n] be independent random samples from populations having continuous d.f.'s psi((x-micro)/sigma) and psi((y-nu)/tau) respectively. The classical F-test of a hypothesis concerning angle = tau/sigma is known to be non-robust. This paper examines several robust alternative procedures and compares them on the basis of Pitman a.r.e and Monte Carlo studies of power functions. An approximate permutation test [13] and a "jackknife" procedure [9] are found to be most satisfactory; while a class of "rank-like" tests [10] are found to be "useful inefficient statistics" [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]

In this paper we examine how well the asymptotic null distribution of a two sample test due to Lehmann approximates the small sample distribution of the test, compare the validity of this Lehman test with the validity of the two sample t test under the null hypothesis of equal means, and compare the power of this Lehmannn test with the power of the t test. Our general conclusion is that experimenters will prefer to use the t test when the underlying distribution is the scale contaminated compound normal distribution and the sample sizes are less than thirty. [ABSTRACT FROM AUTHOR]

In this paper the first two moments of the ratio (treatment sum of squares)/(treatment sum of squares + error sum of squares)over all possible random assignment of treatments to the experimental plots, for a class of 2 associate PBIBD has been obtained. These two moments are compared with the corresponding moments of a continuous beta distribution to settle the question of approximating the randomization test by the usual F-test. It has been shown that a reasonable approximation to the randomization test based on the statistic F is equivalent to modifying the normal theory test by multiplying the numbers of d.f. of the F-distribution by a factor depending on the heterogeneity of the blocks. [ABSTRACT FROM AUTHOR]

The article presents author's comments on the paper entitled "Graphics for the Multivariate Two-Sample Problem." He suggested two variations that may be worth trying, each of which provides an alternative to statistician Jerome H. Friedman and Lawrence C. Rafsky's first sequencing method of obtaining a well-ordering of a multivariate data-set, using the MST. First, instead of using the MST, one could use a minimal solution to the Traveling Salesman or Hamiltonian Circuit problem. Unfortunately, in general these are hard to find, but fast algorithms are known that usually give good approximations. Second, using the MST, instead of traversing side subtrees, one could traverse each subbranch twice, once outwards and once inwards, giving fractional weight to each node at each visit.