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## Publications

Publications (83)

Ranked set sampling (RSS) is a data collection technique that combines measurement with judgment ranking for statistical inference. This paper lays out a formal and natural Bayesian framework for RSS that is analogous to its frequentist justification, and that does not require the assumption of perfect ranking or use of any imperfect ranking models...

Ranked set sampling is an alternative to simple random sampling that has been receiving considerable attention in the statistics literature. Researchers have shown that ranked set sampling outperforms simple random sampling in many situations by reducing the variance of a parameter estimator, thereby providing the same accuracy with a smaller sampl...

Ranked set sampling is an alternative to simple random sampling that has been shown to outperform simple random sampling in many situations by reducing the variance of an estimator, thereby providing the same accuracy with a smaller sample size than is needed in simple random sampling. Ranked set sampling involves preliminary ranking of potential s...

This study compares the statistical precision of simple random sampling with balanced ranked set sampling in an inventory valuation scenario. Computer simulation is used to calculate standard errors for the ranked set sampling mean, and those standard errors are then compared to the corresponding standard error achieved under simple random sampling...

The most common sampling approach for collecting data from a population with the goal of making inferences about unknown features of the population is a simple random sample (SRS). There is a probabilistic guarantee that each measured observation in an SRS can be considered representative of the population. Despite this assurance, there remains a d...

Ranked set sampling (RSS) is a sample selection technique that makes use of expert knowledge to rank sample units before measuring them. Even though rankings are not always perfect, RSS is useful in situations where obtaining measurements is costly, difficult, or destructive. Research in this area has tended to focus on the case where all set sizes...

One of the major goals of statistics is to use data collected from a population to make inferences (hypothesis tests, confidence regions, and point estimators) about unknown attributes of the population. When there are good reasons to believe that the basic features of a population can be well approximated by a standard probability distribution, su...

The application of unbalanced ranked set sampling (RSS) to estimation of a population proportion has been studied for the perfect ranking situation. When the rankings are not perfect, the probabilities of success ranks for the judgment order statistics incorporate information on ranking errors as well as ranks. The objective of this article is to i...

In this paper we consider generalizations of the distribution-free one-way ANOVA test procedures studied by Puri (1965), such generalizations allowing for possibly different scoring functions for different pairs of samples. The asymptotic distributions of the test statistics are derived and formulas for the asymptotic relative efficiencies of these...

The motivation behind distribution-free hypothesis tests and confidence intervals based on signs and ranks is discussed and standard text references are provided. Distribution-free test and confidence interval procedures for the one-sample, two-sample, one-way analysis of variance, two-way analysis of variance, and independence settings are present...

The authors show how ranked set sampling, both balanced and unbalanced, can be extended to ordered categorical variables with the goal of estimating the probabilities of all categories. They use ordinal logistic regression to aid in the ranking of the ordinal variable of interest. They also propose an optimal allocation scheme and methods for imple...

Abstract In this paper we propose distribution-free treatments versus control tests for the one- and two-way classifications. The null distribution properties are shown to be equivalent to those of well-known statistics for which critical values have been extensively tabled. Asymptotic relative efficiencies with respect to corresponding normal the...

Abstract In this paper we consider a class of distribution-free two-stage two-sample median tests. These procedures are based on a fixed size sample from one population, while the observations from the second population are collected in a truncated sequential fashion. Necessary tables are provided enabling us to select a particular member from the...

A sufficient condition for the induced exchangeability or partial exchangeability of linear functions of exchangeable random variables is presented. The use of this result is illustrated through the establishment of conditional exchangeability for two sets of dependent random variables that are important in constructing conditionally distribution–f...

Balanced ranked-set sampling (RSS) offers improved statistical inference in situations where the units to be sampled can be ranked relative to each other prior to formal measurement. Recent work has shown that provided the ranking process is perfect, unbalanced RSS can do even better. In this article, we examine the performance of one unbalanced RS...

A statistical model was developed to rationalize the effect of grain structure on the localized corrosion kinetics in 7xxx alu-minum alloys. The model utilized a two-dimensional brick-wall description of the grain structure. Differences in localized cor-rosion kinetics in different orientations were attributed to dif-ferences in path lengths calcul...

Ranked set sampling (RSS) is a sampling procedure that can be considerably more efficient than simple random sampling (SRS). When the variable of interest is binary, ranking of the sample observations can be implemented using the estimated probabilities of success obtained from a logistic regression model developed for the binary variable. The main...

A generalized brick wall model is developed to describe intergranular corrosion in Equi-axed AA7178-T6 and Wingskin AA7178-T6 aluminum alloys. The intergranular corrosion rate is highly related to grain size and shape. High strength aluminum alloys are often elongated and anisotropic, with the fastest nominal IGC growth rate in the longitudinal dir...

The application of ranked set sampling (RSS) techniques to data from a dichotomous population is currently an active research topic, and it has been shown that balanced RSS leads to improvement in precision over simple random sampling (SRS) for estimation of a population proportion. Balanced RSS, however, is not in general optimal in terms of varia...

Ranked set sampling (RSS) involves ranking of potential sampling units on the variable of interest using judgment or an auxiliary variable to aid in sample selection. Its effectiveness depends on the success in this ranking. We provide an empirical assessment of RSS ranking accuracy in estimation of a population proportion.

Ranked set sampling (RSS) is a sampling procedure that can be considerably more efficient than simple random sampling (SRS). It involves preliminary ranking of the variable of interest to aid in sample selection. Although ranking processes for continuous variables that are implemented through either subjective judgement or via the use of a concomit...

Ranked set sampling is a sampling technique that provides substantial cost efficiency in experiments where a quick, inexpensive ranking procedure is available to rank the units prior to formal, expensive and precise measurements. Although the theoretical properties and relative efficiencies of this approach with respect to simple random sampling ha...

Ranked set sampling (RSS) is a sampling approach that leads to improved statistical inference in situations where the units
to be sampled can be ranked (either through some subjective judgment or via the use of an auxiliary variable) relative to
each other prior to formal measurement. It has the most promise for leading to improved methodology in s...

An extension of a brick wall model developed in a previous paper (Technometrics, to appear) was used to describe intergranular corrosion in AA2024-T3 aluminum alloys. The extended model simulates the behavior of corrosion paths at intersections of grain boundaries within the metal sample. Situations considered include the cases where a corrosion pa...

This paper develops a non-parametric multi-sample inference for simple-tree alternatives for ranked-set samples. The multi-sample inference provides simultaneous one-sample sign confidence intervals for the population medians. The decision rule compares these intervals to achieve the desired type I error. For the specified upper bounds on the exper...

Ranked set sampling where sampling is based on visual judgment of the differences between the sizes of pairs of units or on a concomitant variable is reviewed. An alternative model for judgment ranking based on ratios of sizes of pairs of units is presented. Computation of the variance of a visual ranked set sampling estimator of the mean of a dist...

Judgement post-stratification, which is based on ideas similar to those in ranked set sampling, relies on the ability of a ranker to forecast the ranks of potential observations on a set of units. In practice, the authors sometimes find it difficult to assign these ranks. This note shows how one can borrow techniques from the literature on finite p...

In this article a brick wall model is developed to describe the relationship between the minimum intergranular corrosion path length and the aspect ratio of grains of high-strength wrought aluminum alloy AA2024-T3. We study the distribution of the horizontal distance that a corrosion path will travel in the metal and fit the model to an actual corr...

One of the major problems for which satisfactory small-sample rank-based test procedures are only recently being developed is that of evaluating the possible presence of interaction in the standard two-way layout. This is especially true when there is only one observation on each treatment-block combination. In this paper we take a goodness-of-fit...

In this paper we assign subsets of the permutations of the integers 1 through n into classes with similar structure. This structure is an extension of the decomposability classes first defined by L. Comtet [C. R. Acad. Sci., Paris, Sér. A 275, 569-572 (1972; Zbl 0246.05003)]. Comtet divided the n! permutations into n classes according to the number...

A statistical model has been developed to predict the anisotropy of intergranular corrosion (IGC) kinetics and effect of microstructure on IGC kinetics in high strength AA2024-T3 alloys. The methodology is to estimate the statistical distribution of minimum IGC path length that will be found through the thickness of a given thickness ST sample usin...

McIntyre (1952, Australian Journal of Agricultural Research 3, 385-390) introduced ranked set sampling (RSS) as a method for improving estimation of a population mean in settings where sampling and ranking of units from the population are inexpensive when compared with actual measurement of the units. Two of the major factors in the usefulness of R...

We develop an unbiased estimator of the variance of a population based on a ranked set sample. We show that this new estimator is better than estimating the variance based on a simple random sample and more efficient than the estimator based on a ranked set sample proposed by Stokes. Also, a test to determine the effectiveness of the judgment order...

We consider the setting where a group of n judges are to rank independently a series of k objects. When all judges rank all treatments, this coincides with the no-interaction two-way lay-out setting with one observation per cell. However, many times the intended complete rankings are not realized and we are faced with analysing randomly incomplete...

In this paper, we construct a new ranked set sampling protocol that maximizes the Pitman asymptotic efficiency of the signed rank test. The new sampling design is a function of the set size and independent order statistics. If the set size is odd and the underlying distribution is symmetric and unimodal, then the new sampling protocol quantifies on...

In this paper we consider the setting where a group of n judges are to independently rank a series of k objects, but the intended complete rankings are not realized and we are faced with analyzing randomly incomplete ranking vectors. In this paper we propose a new testing procedure for dealing with such data realizations. We concentrate on the prob...

This paper considers the problem of testing for umbrella alternatives in the one-way layout when survival data are subject to random right censorship. Testing procedures based on two-sample weighted logrank statistics are suggested for both cases when the peak of the umbrella is known or unknown. The Pitman efficacy of the peak-known umbrella test...

The authors present an improved ranked set two-sample Mann-Whitney-Wilcoxon test for a location shift between samples from two distributions F and G. They define a function that measures the amount of information provided by each observation from the two samples, given the actual joint ranking of all the units in a set. This information function is...

In this paper we investigate the effects of different ranked set sampling protocols on the sign test statistic. Sampling protocols considered include sequential, mid-range and fixed sampling designs. We show that in all of these sampling protocols the introduction of any correlation structure on the quantified observations leads to a reduction in t...

This paper presents a ranked set sample allocation procedure that is optimal for a number of nonparametric test procedures. We define a function that measures the amount of information provided by each observation given the actual joint ranking of all the units in a set. The optimal ranked set sample allocates order statistics by maximizing this in...

We consider the problem of estimating the derivatives of a regression func-tion by the corresponding derivatives of regression splines. Unlike kernel smoothers, these spline derivative estimators do not have boundary problems. In addition, they have simple expressions and are easy to compute. In this paper, we study the local asymptotic properties...

This paper presents an optimal ranked set sample allocation scheme for a two-sample ranked set sample median test for a location shift between X- and Y-sample distributions F and G. It is shown that the optimal design based on maximizing the asymptotic Pitman efficiency quantifies only the middle observation(s) in a set of X- and Y-samples uniforml...

New aligned-rank test procedures for the composite null hypothesis of no interaction effects (without placing restrictions on the two main e#ects) against appropriate composite general alternatives are developed for the standard two-way layout with a single observation per cell. Relative power performances of the two new aligned-rank procedures and...

The authors present an improved ranked set two-sample Mann-Whitney-Wilcoxon test for a location shift between samples from two distributions F and G. They define a function that measures the amount of information provided by each observation from the two samples, given the actual joint ranking of all the units in a set. This information function is...

In settings where measurements are costly and/or difficult to obtain but ranking of the potential sample data is relatively easy and reliable, the use of statistical methods based on a ranked-set sampling approach can lead to substantial improvement over analogous methods associated with simple random samples. Previous nonparametric work in this ar...

Appropriate rank procedures are not presently available for the problem of testing for equality of treatment-effect patterns in several two-way layouts. In this paper, we consider a rank-based contingency table approach to address this problem. We propose an asymptotically distribution-free test procedure that is based on position vectors, using th...

In this paper, we propose a new nonparametric estimator called the local piecewise linear regression estimator. The proposed estimator has the advantages of the regression spline and the local linear regression estimator but overcomes the drawbacks of both. Here we study the asymptotic behavior of the proposed estimator. Under suitable conditions,...

We generalize the problem of detecting qualitative interaction between treatments and subsets in a two treatment clinical trial to the more practical problem of detecting a qualitative interaction greater than a non-negative value d, corresponding to the minimal treatment difference of clinical significance. We develop a test based on simultaneous...

In comparing several regression lines with a control, we propose a rank test of whether there is at least one line with slope that is greater than that of the control. An example is given and the results of a Monte Carlo power study are discussed.

One commonly observed response pattern in a one-factor design with ordered treatment levels is the umbrella or unimodal ordering, in which the response variable increases with an increase in the treatment level up to a point, then decreases with further increase in the treatment level. The turning point is called the peak of an umbrella ordering. I...

One of the commonly observed one-factor response patterns in practice is the umbrella ordering in which the response variable increases with an increase in the treatment level up to a point, then decreases with further increase in the treatmentlevel. Among two populations with umbrella orderings, for example, male and female populations, it is ofte...

In this paper we propose a class of distribution-free tests for the treatments versus control setting using the partially sequential sampling technique. Expressions for the asymptotic distributions and power for the tests are provided and criteria for adapting a particular test to have asymptotic power restrictions against alternatives of interest...

In this article we address the issue of imperfect judgment rankings in ranked-set sampling and, in particular, their effect on the properties of test procedures based on the ranked-set samples analog of the Mann-Whitney-Wilcoxon statistic, Urss. We consider the impact of these imperfect rankings on the null distribution of the statistic and the res...

Two different two-sample tests for dispersion differences based on placement statistics are proposed. The means and variances of the test statistics are derived, and asymptotic normality is established for both. Variants of the proposed tests based on reversing the X and Y labels in the test statistic calculations are shown to have different small-...

We investigate some small sample and asymptotic properties for a class of distribution-free two-sample procedures based on placements. We also discuss Hodges-Lehmann type location estimators associated with such linear placement statistics.

Ranked-set samples have been shown to lead to improved methods of estimation in parametric settings under specific distributional forms when actual measurement of the sample observations is difficult but ranking them is relatively easy. The earliest work with ranked-set data concentrated on estimating a population mean or variance. More recently, a...

In spite of an extensive literature dealing with rank approaches to testing for main effects when an additive model is assumed, virtually no consideration has been given to developing nonparametric main effects test procedures that adjust for the possible presence of interaction in a non-additive model. This problem has been briefly discussed in Im...

Let (Xi1,…,Xin), i = 1,…, m, be m mutually independent, identically distributed, continuous n-dimensional random vectors. The setting where (Xi1,…,Xir) is an exchangeable vector and (Xi,r+1,…,Xin) is an exchangeable vector but the complete vector (Xi1,…,Xin) is not exchangeable for i = 1, 2,…, m, and some unknown integer r, l < r < n - l, is referr...

One of the major unresolved problems in the area of nonparametric statistics is the need for satisfactory rank-based test procedures for non-additive models in the two-way layout, especially when there is only one observation on each combination of the levels of the experimental factors. In this paper we consider an arbitrary non-additive model for...

In this paper we present the required exact null distribution of a rank statistic used in making treatments versus control multiple comparisons in one- way layout designs. If we let Xi1, i=1,...,n1, denote the ith observation in a random sample from a control population and Xij, i=1,...,nj and j=2,...,k, denote the ith observation from the jth trea...

Let X 1 ,X 2 ,···,X r ,X r+1 ,···,X n be independent, continuous random variables such that X i , i=1,···,r, has an unknown distribution function F(x), and X j , j=r+1,···,n, has distribution function F(x-θ), with θ unknown (-∞<θ<∞). The integer r, which is called the changepoint, is also taken to be unknown. The hypothesis to be tested is H 0 :θ=0...

David (1963) and Davidson & Farquhar(1976) contain extensive bibliographies of proposed approaches to problems involving paired comparisons. However, each of the discussed methods that is based on a hypothesis test, relies heavily on the assumption that all paired comparisons are made independently. In this paper we eliminate this assumption and de...

In this paper we present the exact null distribution of a rank statistic used in making all treatments multiple comparisons in one-way layout designs. If we let denote the ith observation from the jth population, then we are dealing with independent random samples of sizes from populations respectively. Letting is the combined samples rank of xij a...

The problem of agreement between two or more groups of judges has received considerable attention during the past decade, beginning with the papers by Schucany & Frawley(1973) and Hollander & Sethuraman(1978). Two very different definitions of agreement have emerged in the literature. The first states that two groups of judges agree if they use the...

In this paper we consider several procedures for estimating the sites of multiple changepoints in the distribution of a sequence of independent, continuous observations. Each of these estimation schemes is based on the statistic proposed by Schechtman (1982) for testing hypotheses about a single change-point, in conjunction with a variety of techni...

Let X1,…,Xr−1,Xr,Xr+1,…,Xn be independent, continuous random variables such that Xi, i = 1,…,r, has distribution function F(x), and Xi, i = r+1,…,n, has distribution function F(x−Δ), with -∞ <Δ< ∞. When the integer r is unknown, this is refered to as a change point problem with at most one change. The unknown parameter Δ represents the magnitude of...

We consider a class of two-sample distribution-free tests that are appropriate for situations where one of the sample sizes is large relative to the other. These procedures are based on the placements of the observations in the smaller sample among the ordered observations in the larger sample, and this class of tests generalizes the Mann-Whitney (...

Distribution-free test procedures are proposed for the k-sample problem, where the alternatives of interest are of the form F1(x) ≥ ··· ≥ Fℓ(x) ≤ ··· ≤ Fk (x) for all x, with at least one strict inequality. These are referred to as umbrella alternatives, and both the ℓ (point of umbrella) known and ℓ unknown settings are considered. Small sample nu...

An asymptotically distribution-free procedure is proposed for testing whether a univariate population is symmetric about some unknown value versus a broad class of asymmetric distribution alternatives. The consistency class of the test is discussed and two competing tests are described, one based on the sample skewness, and the other on Gupta's non...

The concept of a partially sequential hypothesis test was introduced by Wolfe (1977a), an{associated procedures were developed for both parametric and nonparametric assumptions. In this paper we consider distribution-free extensions of those indicator tests, based on the placements of the sequentially obtained observations among the previously coll...

In this paper some quality control applications of distribution-free prediction intervals for the median of a future sample are described. Methods for obtaining such intervals are presented, and their use is illustrated by examples. Tables are provided for calculating such prediction intervals for small samples; approximations are provided for samp...

In this article distribution-free prediction intervals for a future sample median are discussed. Large-sample normal approximations to the coverage probabilities are presented. Asymptotic relative efficiency comparisons are made between the distribution-free procedures and analogous parametric prediction intervals, the resulting values demonstratin...

Wolfe (1977a) introduced the concept of a partially sequential two-sample hypothesis test and studied some of the properties
for a general class of such procedures. In this paper we deal with criteria for selecting an indicator set for use in a partially
sequential test. In particular, we show how the Neyman-Pearson lemma can be used to generate an...

In this article we consider a class of test statistics that are useful for testing against ordered alternatives in balanced or unbalanced block designs. The approach consists of forming a statistic on each block and then combining the block statistics as a weighted sum to obtain one overall test statistic. Large-sample properties such as asymptotic...

In this paper we consider a class of distribution-free two-stage two-sample median tests for location differences. Exact null distribution tables are provided and a negative binomial approximation is presented for obtaining approximate α level cutoff points. The test procedures have the capability of obtaining asymptotic power restrictions against...

Let (X1, X2, Xs) be a continuous, trivariate random vector for which it is of interest to compare the correlation between X1 and X2 with that between X3 and X1. This problem is important, for example when both X2 and X3 are potential linear predictors for X1 or, more generally, whenever the variable (X1. X2, X3) represents a triplet of measurements...

A class of distribution-free tests for ordered alternatives in a block design is presented. On each block a distribution-free statistic is selected, and a weighted sum of these statistics is then formed. A procedure for selecting the weighting constants which maximize the asymptotic relative efficiency is presented. The improvement in the efficienc...

Ranked set sampling (RSS) is a sampling method whereby auxiliary infor- mation is used to rank the units in the population. A unit is included in the sample based on its rank amongst the other units. The method was first pro- posed over fifty years ago as a way to increase the precision of estimates of pasture yields without increasing the sample s...

Ranked set sampling (RSS) is a method of data collection that makes use of the sampler's judgment of relative sizes of potential sample units. In a simple form of RSS, the observations quantified by the researcher generally will be more representative of the range of values in the population than those obtained from a simple random sampling (SRS)....

Applications of nonparametric test procedures involving censored data often rely on asymptotic approximations. The unconditional and conditional censored Wilcoxon rank sum null distributions, described briefly here and in more detail elsewhere [1, 2], provide small sample critical values for Type I censored data. This paper focuses on presenting su...