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We suggest a new class of difference-type estimators under two-phase stratified sampling when using information from two auxiliary variables including their distribution functions. The bias and MSE...

Sousa et al. [Improved mean estimation of a sensitive variable using auxiliary information in stratified sampling. J Stat Manage Syst. 2014;17(5–6):503–518] presented a ratio estimator for mean est...

In this study, we discuss mean estimation of sensitive variables in the presence of measurement errors and non-response using Stratified Random Sampling, and present a comparison of the proposed es...

Poisson regression model is the most common method used to model count response in many studies. This paper proposes a new ratio-type estimators based on Poisson regression in simple random samplin...

Sousa et al. and Gupta et al. presented ratio and regression estimators of population mean of a sensitive variable using auxiliary information in simple random sampling without replacement. In this...

–Many well-known sufficient dimension reduction methods investigate the inverse conditional moments of the predictors given the response. The required linearity condition, the number and ar...

Recently, Irfan et al. developed ratio-type estimators for population mean estimation with simple random sampling (SRS) scheme, based on known median of a study variable and an auxiliary (supplemen...

This article studies interval estimation of the population mean in ranked set sampling. Eight types of confidence intervals are considered which are based on asymptotic theory, resampling methods, ...

In this paper, an efficient generalized estimation strategy has been proposed to present the problem of estimation of current population mean Y¯ of study variable y in two-occasion rotation samplin...

The problem of estimation of sensitive population mean has been investigated using the item sum technique (IST) with calibration estimators in two occasion successive sampling. Generic sampling des...

In case of sensitive research, estimation of mean is a major concern in survey studies and regression estimators utilizing traditional regression coefficient are the most favored choices for it. Re...

In this study we propose an improved mean estimator for a sensitive variable under simple random sampling using Optional RRT models when measurement errors are present. We discuss two scrambling op...

Motivated by some recent improvements for mean estimation in finite sampling theory, we propose, in a design-based approach, a new class of ratio-type estimators. The class is initially discussed o...

This paper analyzes the dynamics of pair comovements between different domestic European stock market returns (Spain, France, Germany, Switzerland and the United Kingdom) seeking to check whether there is a unique source of risk driving those dynamics. Once it is shown that the comovements are time-varying, the question is to find whether a global index such as the Euro Stoxx can be considered the main source of risk. To that end we estimate and test for time-varying global pair covariances and for time-varying remaining pair covariances once the effect of the Euro Stoxx is removed. The empirical results are obtained considering locally stationary variables, a family that includes variables with first and second time-varying moments. Under that framework time-varying means and covariances can be estimated using a spline-based procedure and Wald-type statistics can be computed to test for time-variations. A simulation study shows that the role of the mean estimation part is crucial to the good performance ...

In a missing-data setting, we want to estimate the mean of a scalar outcome, based on a sample in which an explanatory variable is observed for every subject while responses are missing by happenstance for some of them. We consider two kinds of estimates of the mean response when the explanatory variable is functional. One is based on the average of the predicted values and the second one is a functional adaptation of the Horvitz-Thompson estimator. We show that the infinite dimensionality of the problem does not affect the rates of convergence by stating that the estimates are root-n consistent, under missing at random (MAR) assumption. These asymptotic features are completed by simulated experiments illustrating the easiness of implementation and the good behaviour on finite sample sizes of the method. This is the first paper emphasizing that the insensitiveness of averaged estimates, well known in multivariate non-parametric statistics, remains true for an infinite-dimensional covariable. In this sense, this work opens the way for various other results of this kind in functional data analysis. Fil: Ferraty, Frédéric. Universite Paul Sabatier. Institut de Mathematiques de Toulouse; Francia Fil: Sued, Raquel Mariela. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina Fil: Vieu, Philippe. Universite Paul Sabatier. Institut de Mathematiques de Toulouse; Francia

We consider a fractional 3 m factorial design derived from a simple array (SA), which is a balanced array of full strength, where the non negligible factorial effects are the general mean and the linear and quadratic components of the main effect, and m ≥ 2. In this article, we give a necessary and sufficient condition for an SA to be a balanced fractional 3 m factorial design of resolution III. Such a design is characterized by the suffixes of indices of an SA.

For the distributions with decreasing density and decreasing failure rate, and decreasing density and decreasing failure rate on the average, the quantiles are less than the mean if their orders do not exceed fixed levels. We determine the sharp negative upper bounds on the differences of the small quantiles and means for the distributions from the respective families in terms of scale units generated by pth absolute central moments. We show that the bounds amount trivially to zero when p > 1, and are strictly negative for p = 1.

The goal of uniform mixture design is to scatter the design points in the experimental region uniformly. The commonly used criteria, such as mean square distance, are based on the Euclidean distance. Based on the Lee distance, a new criterion is proposed in this article. And an algorithm, called NTLBG, is also proposed to refine the randomly generated design for the experimental design with mixtures. Some examples show that the design generated by the NTLBG algorithm has a lower criteria value.

A multicriteria methodology for assessing the functional performance of urban Sewer Systems (SS) is presented. It passes through the quantification of the selected indicators and defined according ...

In this article, we give an alternative and much shorter proof for the invariance law of surrogate dimension reduction for measurement error regression that was established by Li and Yin (2007).

The issue of selecting suppliers or assessing the impact of process improvement has already been investigated based on several process capability indices. However, the statistical test for comparing the capability of two suppliers or processes based on the C pmk index has not been developed due to the complexity of the sampling distribution. In this article, we apply the concept of generalized pivotal quantities to derive the generalized confidence intervals (GCI) for the capability ratio and the capability difference between two given suppliers or processes. A simulation study is conducted to investigate the performance of the proposed methods and compare them with the coverage rates and the average width of confidence intervals. The numerical results indicate that the GCI method on the ratio is quite satisfactory for comparing the capability of two suppliers or processes since the attained coverage rates of the confidence interval are very close to the nominal confidence level.

In this article, we consider a repair-time limit replacement policy with estimation error. If a system fails, we estimate the repair time to recover the system failure. In reality, the estimation error occurs in the estimation of repair time. Considering the estimation error, we formulate the repair-time limit replacement policy and obtain analytically the long-run average profit rate and the total discounted profit. We obtain numerically the optimal repair-time limits to maximize the long-run average profit rate and the total discounted profit. Numerical examples are experimented to find trends of the optimal repair-time limit and the effect of model parameters on the optimal repair-time limit.

We consider testing hypotheses about a single Poisson mean. When prior information is not available, use of objective priors is of interest. We provide intrinsic priors based on the arithmetic intrinsic and fractional Bayes factors, and evaluate their characteristics.

The t-mean is a new characteristic of the central tendency of continuous distributions. In this article, we introduce a t-difference in the sample space, which is used for a construction of confidence intervals for the t-mean.

There have been many alternative strategies for implementing sampling survey on quantitative characteristic of sensitive issues by using randomized response (RR) technique. The efficiency of most of those strategies has been improved by choosing the suitable design parameters of model. However, the two different procedures with pre-assigned design parameter values cannot ensure that they possess the same protection degree to the respondents. Some earlier comparisons of those strategies are inadequate (as in Eichhorn and Hayre, 1983; Gupta et al., 2002). Some literature contains a more comprehensive comparison based on efficiency and protection degree to the respondents among the qualitative characteristic RR techniques (see Bhargava and Singh, 2002; Nayak, 1994; Zaizai and Zankan, 2004). As far as the comparisons are concerned that are based on efficiency and protection degree to the respondents among the quantitative characteristic RR techniques, very few related studies have been found so far. The purpo...

Conflicting decision signals resulting from Shewhart Mean and Variability Control Charts produce undesirable consequences. Therefore, we construct “six-sigma” control charts by alternative methods to avoid problems associated with Control Charts yielding different signals. By adjusting methods for control chart construction for dispersion charts, we produce new reference tables. The new tables provide consistent signals and appear similar and familiar to users of historical tables.

We consider a sequence of discrete time nearly critical branching processes with time-dependent immigration. Using a martingale approach, we prove that when the immigration mean tends to infinity depending on the time of immigration, the suitable normalized sequence can be approximated in Skorokhod metric by a deterministic process. Consequences related to the maxima and the total progeny of the process will be discussed.

To answer W. Edwards Deming's challenge to “make a new world,” statisticians in today's competitive environment must broaden their focus to include not only a comprehensive set of statistical tools but also an overarching framework in which those tools and other improvement methodologies are integrated, sequenced, and deployed for maximum effect. This article addresses how this can be done through a holistic approach to improvement designed to change the way an organization works and its people think. This holistic approach will mean that statisticians will have more impact on their organizations and more opportunities for leadership than ever before, but only if they see their activities in this larger context pioneered by Deming and extended by Six Sigma and other improvement methodologies.

In this study, we implement a random-effects model that estimates cubic spline-based time-dependent skill functions for 253 active PGA Tour golfers over the 1998–2001 period. Our model controls for the first-order autocorrelation of residual 18-hole scores and adjusts for round–course and player–course random effects. Using the model, we are able to estimate time-varying measures of skill and luck for each player in the sample. Estimates of spline-based player-specific skill functions provide strong evidence that the skill levels of PGA Tour players change through time. Using the model, we are able to rank golfers at the end of 2001 on the basis of their estimated mean skill levels and identify the players who experienced the most improvement and deterioration in their skill levels over the 1998–2001 period. We find that some luck is required to win PGA Tour events, even for the most highly skilled players. Player–course interactions contribute very little to variability in golfer performance, but the par...

Since the U.S. Environmental Protection Agency began widespread monitoring of PM2.5 (particulate matter

Dey and Suen (2002) obtained optimal fractional factorial plans for estimating mean, all main effects and specified two-factor interactions using finite projective geometry. In this article we obtain two new optimal fractional factorial plans for estimation of the mean, all main effects, specified two-factor interactions,… and specified (r − 1) factor interactions using PG(r − 1, m). We also provide tables of optimal fractional factorial plans.

It is well known that the Shewhart control chart is relatively insensitive to detect small process average shifts. In this article, we introduce and investigate the basic features of the modified r out of m control chart. The new control chart outperforms the Shewhart control chart for small to moderate process average shifts and the corresponding r out of m control chart which has been recently appeared in the literature.

We present sufficient conditions for log-concavity and log-convexity of the residual life and the inactivity time. We also make stochastic comparisons on the residual life and the inactivity time in terms of the failure rate order, the mean residual life order and the usual stochastic order. These results strengthen some conclusions in Li and Zuo [11] and Yue and Cao [19] .

The 2 × 2 crossover is commonly used to establish average bioequivalence of two treatments. In practice, the sample size for this design is often calculated under a supposition that the true average bioavailabilities of the two treatments are almost identical. However, the average bioequivalence analysis that is subsequently carried out does not reflect this prior belief and this leads to a loss in efficiency. We propose an alternate average bioequivalence analysis that avoids this inefficiency. The validity and substantial power advantages of our proposed method are illustrated by simulations, and two numerical examples with real data are provided.

The Anscombe dataset is popular for teaching the importance of graphics in data analysis. It consists of four datasets that have identical summary statistics (e.g., mean, standard deviation, and correlation) but dissimilar data graphics (scatterplots). In this article, we provide a general procedure to generate datasets with identical summary statistics but dissimilar graphics by using a genetic algorithm based approach.

This article develops constrained Bayes and empirical Bayes estimators under balanced loss functions. In the normal-normal example, estimators of the mean squared errors of the EB and constrained EB estimators are provided which are correct asymptotically up to O(m −1), m denoting the number of strata.

SAVE and PHD are effective methods in dimension reduction problems. Both methods are based on two assumptions: linearity condition and constant covariance condition. But in the situation where constant covariance condition fails, even if linearity condition holds, SAVE and PHD often pick the directions which are out side of the central subspace (CS) or central mean subspace (CMS). In this article, we generalize the SAVE and PHD under weaker conditions. This generalization make it possible to get the correct estimates of central subspace (CS) and central mean subspace (CMS).

In a market with a discontinuous filtration, whose price is influenced by a random factor, we study an optimization problem of an investor who is facing a sequence of losses driven by a Cox process. We give a form of variance-optimal martingale measure by changing the filtration. By using the solutions of the stochastic Riccati equation and another associated backward stochastic equation, we obtain a solution of the optimization problem of the investor.

This article studies the asymptotic confidence limits for the steady-state availability, failure frequency, and mean time to failure of a repairable K-out-of-(M + S) system with M operating devices, S spares, and an imperfect service station that may be interrupted by a breakdown when it is repairing for the failed devices.

The zero-truncated Poisson distribution (ZTPD) is a model that may be appropriate when observations commence only when at least one event occurs. Shanmugam (1985) introduced the intervened Poisson distribution (IPD) as a replacement for the ZTPD in situations when some intervention process may alter the mean of the rare event generating process under observation. Both of these zero-truncated distributions are underdispersed. In this paper, we discuss an intervened generalized Poisson distribution (IGPD) that extends the IPD, and that may be either underdispersed or overdispersed. Two numerical illustrations are included, one of which features a Bayesian analysis.

Let X 1, X 2,… be any sequence of [0,1]-valued random variables. A complete comparison is made between the expected maximum E(max j≤n Y j ) and the stop rule supremum sup t E Y t for two types of discounted sequences: (i) Y j = b j X j , where {b j } is a nonincreasing sequence of positive numbers with b 1 = 1; and (ii) Y j = B 1… B j−1 X j , where B 1, B 2,… are independent [0,1]-valued random variables that are independent of the X j , having a common mean β. For instance, it is shown that the set of points {(x, y): x = sup t E Y {(x, y): x=sup t E Y and y = E(max j≤n Y j ), for some sequence X 1,…,X n and Y j = b j X j }, is precisely the convex closure of the union of the sets {(b j x, b j y): (x, y) ∈ C j }, j = 1,…,n, where C j = {(x, y):0 ≤ x ≤ 1, x ≤ y ≤ x[1 + (j − 1)(1 − x 1/(j−1))]} is the prophet region for undiscounted random variables given by Hill and Kertz [8]. As a special case, it is shown that the maximum possible difference E(max j≤n β j−1 X j ) − sup t E(β t−1 X t ) is att...

In the design of CUSUM control charts, it is common to use charts, tables, or software to find an appropriate critical threshold (h). This article provides an approximate formula to calculate the threshold directly from prespecified values of the reference value (k) and the in-control average run length (ARL0). Formulas are also provided for choosing k and h from prespecified values of the in-control and out-of-control average run lengths.

Consider k(≥ 2) independent exponential populations Π1, Π2, …, Π k , having the common unknown location parameter μ ∈ (−∞, ∞) (also called the guarantee time) and unknown scale parameters σ1, σ2, …σ k , respectively (also called the remaining mean lifetimes after the completion of guarantee times), σ i > 0, i = 1, 2, …, k. Assume that the correct ordering between σ1, σ2, …, σ k is not known apriori and let σ[i], i = 1, 2, …, k, denote the ith smallest of σ j s, so that σ[1] ≤ σ[2] ··· ≤ σ[k]. Then Θ i = μ + σ i is the mean lifetime of Π i , i = 1, 2, …, k. Let Θ[1] ≤ Θ[2] ··· ≤ Θ[k] denote the ranked values of the Θ j s, so that Θ[i] = μ + σ[i], i = 1, 2, …, k, and let Π(i) denote the unknown population associated with the ith smallest mean lifetime Θ[i] = μ + σ[i], i = 1, 2, …, k. Based on independent random samples from the k populations, we propose a selection procedure for the goal of selecting the population having the longest mean lifetime Θ[k] (called the “best” population), under the su...

The majority of the artificial neural network (ANN) applications to water resources data involve the employment of the feed forward back propagation method (FFBP). In this study, an ANN algorithm, generalized regression neural network (GRNN), was employed in monthly mean flow forecasting. The performances of the GRNN and the FFBP methods were compared initially for forecasting of monthly mean river flows and training the neural networks using the observed data; then the forecasting study was carried out using the AR model-generated synthetic monthly mean flow series for training stage. The GRNN simulations did not face the frequently encountered local minima problem of the FFBP applications and did not generate forecasts that are physically implausible. It was seen that FFBP forecasting performance was sensitive to the randomly assigned initial weights. This problem, however, did not occur in the GRNN simulations. The GRNN approach does not require an iterative training procedure, unlike the FFBP method. ...

This article presents applicable bounds for distributions with monotone log-odds rate. The bounds are based on results obtained by Wang et al. (2003) and Zimmer et al. (1998). Due to the complexity of some of the equations, numerical analysis and computer algorithms were necessary to calculate some of the results of these bounds. Five different types of bounds are tabled in this research. Numerical examples of their application and comparisons to the results obtained by Barlow and Marshall (1965) of bounds on distributions with monotone hazard rate are also provided. The first type of tables is for lower bounds of increasing log-odds rate distributions with knowledge of two values of the reliability of the distribution. The second and third types of tables are for upper bounds under the same conditions. The fourth type of tables is for lower bounds of increasing log-odds rate distributions with knowledge of the mean and the median of the distribution. Finally, the fifth type of tables is for lowe...

The problem of identifying the minimum effective dose (MED) in a dose-response study is considered, where the MED is defined to be the lowest dose level with a mean response greater than that of the zero-dose control. This article adapts a step-down procedure with modified step contrasts to determine the MED. An approximation for obtaining the critical values and p-values of the proposed procedure is described. The proposed procedure is compared with some other contrasts procedures in a simulation study. It is pointed out that, when the true MED is the first dose level, in which no FWEs are involved, the proposed procedure has great power and is recommended for the use of identifying the MED.

Three methods of handling missing items in Quality of Life (QOL) studies are compared using data from a clinical trial. Complete case analysis can lead to a selection bias and a loss of precision if there is a low answer rate to one item. The two other methods, simple mean imputation and multiple imputation, lead to similar results. We conclude that when the scale has been carefully validated in the population of interest and includes only items with a high response rate (e.g., a mean response rate greater than 95% for the items of a given subscale), a simple imputation method can be used to handle incomplete observations.

We propose a new charting procedure, combining two or more Exponentially Weighted Moving Averages (EWMAs), which we call a Composite EWMA (CEWMA) Control Chart. In the case of two EWMAs, the CEWMA chart corresponds to the usual combined Shewhart-EWMA chart, although our plotting procedure remain, we feel, an improvement in application and interpretation. When three EWMAs are combined, the composite chart improves on the average run length performance of the combined Shewhart-EWMA chart. We also briefly discuss the combination of more than three EWMAs.

The scientific goal of a phase I oncology trial of a new chemotherapeutic agent is to find a dose with an acceptable level of toxicity. For ethical reasons, dose-finding is done adaptively, with doses chosen for successive cohorts of patients based on the data obtained from previous cohorts. Typically, patients are at risk for several qualitatively different toxicities, each occurring at several possible severity levels. In this article, we describe how we addressed the dose-finding problem in a phase I trial of gemcitabine for treatment of soft tissue sarcoma. The oncologists planning the trial wanted to account for differences in importance among the toxicities that they had identified. They also requested that the dose-finding method utilize the fact that a low-grade toxicity observed at a given dose, although not dose-limiting, provides a warning that a higher grade of that toxicity is likely to occur at a higher dose. Conventional phase I methods reduce each type of toxicity to an indicator of its oc...

In many experimental situations, the average treatment performance within its own group is used as a benchmark to be compared with each individual treatment. Multiple comparison procedures with the average (MCA) are thus proposed. A simulation comparison study of the traditional MCA, the single-stage MCA and the two-stage MCA for normal distribution under heteroscedasticity is investigated by the Monte-Carlo techniques in this paper. It was found that the two-stage MCA has shorter confidence length than the single-stage MCA for most cases and it is also more robust for non-normal distributions. Therefore, the two-stage MCA is recommended. But when the additional samples at the second stage could be costly, the data-analysis oriented single-stage MCA can be used. A biometrical example to illustrate the single-stage MCA and the two-stage MCA with equal confidence length is also given in this article.