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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...

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...

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...

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.

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...

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.

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).

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.

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 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.

Some moment inequalities are well known in the literature to be valid for several continuous ageing families. In this article, we establish moment inequalities for D-ILR [D-DLR], DS-IFR, DS-DMRL [DS-IMRL], DW-NBU [DS-NWU], DW-NBUE [DS-NBUE] and DW-HNBUE [DS-HNWUE] families of discrete non-negative integer-valued random variables, and also give some minor results about moment inequalities of random variables that are ordered in the mean residual life order.

The mixture of Type I and Type I1 censoring schemes, called the hybrid censoring, is quite important in life–testing experiments. Epstein(1954, 1960) introduced this testing scheme and proposed a two–sided confidence interval to estimate the mean lifetime, θ, when the underlying lifetime distribution is assumed to be exponential. There are some two–sided confidence intervals and credible intervals proposed by Fairbanks et al. (1982) and Draper and Guttman (1987) respectively. In this paper we obtain the exact two–sided confidence interval of θ following the approach of Chen and Bhattacharya (1988). We also obtain the asymptotic confidence intervals in the Hybrid censoring case. It is important to observe that the results for Type I and Type II censoring schemes can be obtained as particular cases of the Hybrid censoring scheme. We analyze one data set and compare different methods by Monte Carlo simulations.

Let X be a p 0-normal random vector with unknown μ and known variance-covariance matrix Σ and let X be partitioned as X = (X′(1),X′(2))′ where X (j) is a subvector of X with dimension p j such that . Some optimum properties of the maximum likelihood estimator (m.l.e.) of μ, the mean vector, are given. This estimator is computed on the basis of a sample drawn from the whole vector X of dimension p 0 and two additional samples drawn from X (1) X (2) respectively. All three samples are assumed to be independent. This estimator is also compared with the usual estimator X which is based solely on the sample from the entire vector X and hence ignores the extra information provided by the other two samples.

Jennlson and Turnbull (1984,1989) proposed procedures for repeated confidence intervals for parameters of interest In a clinical trial monitored with group sequential methods. These methods are extended for use with stochastic curtailment procedures for two samples in the estimation of differences of means, differences of proportions, odds ratios, and hazard ratios. Methods are described for constructing 1) confidence intervals for these estimates at repeated times In the course of a trial, and 2) prediction intervals for predicted estimates at the end of a trial. Specific examples from several clinical trials are presented.

For the multivariate normal mean (vector) estimation problem, some characterizations of the Pitman closest property of a general class of shrinkage (or Stein-rule) estimators (including the so called positive-rule versions) are studied. Further, for the same model when the parameter is restricted to a positively homogeneous cone, Pitman closeness of restricted shrinkage maximum likelihood estimators is established.

A new class of estimators is introduced for the problem of estimating the mean of the selected population. These estimators are found by subtracting from the largest sample mean an estimator of its bias. The new estimators are compared with those introduced by Cohen and Sackrowitz (1982) and in terms of frequentist risk they are found to perform quite similarly.

The uniformly minimum variance unbiased estimator and the maximum likelihood estimator of μ for the inverse Gaussian distribution I(μc,μ ) with known c are constructed, and they are shown to be asymptoti- cally equivalent.

In this article Pathak's (1964) results on estimation of mean and variance for k-equal subsamples and Rao's (1975) result on the expectation of the reciprocal of the number of distinct units obtained from two unequal subsamples , for interpenetrating subsampling scheme, have been extended to the case of k-unequal subsamples.

Suppose , where Yidenotes the value of a characteristic of interest associated with the unit i(i=1,..., N). Ghosh and Meeden (1986) considered an empirical Bayes approach to the estimation of the finite population mean , under squared error loss and the model i=∊+∊i(i=1,…N), where θ, ∊1,…,∊n are independently distributed with and . In this paper we extend their results to the case where ∊i's are independent with , and , where 0 < c ≤ 1.

Let π1 πk be k independent exponential populations with means θ1 θkrespectively. Let Y1, ,Yk denote the sample means based on n independent observations from each population. For selecting a nonempty subset containing the best population (the one associated with the largest θi ) we consider the rule of Gupta which selects πi. if and only if where 0 < c < 1 is determined such that the probability of including the best population in the selected subset is at least P*, a pre-designed level. We consider the problem of estimating M, the mean of all θi 's in the selected subset, for k = 2. It is shown that the ‘natural’ estimator T is positively biased. An adjustment for bias of T is considered so that this adjusted estimator Tλ1 is unbiased when θ1 = θ2 The performances of T and Tλ1 are compared in terms of bias and mean square error for selected values of P*, n, and ρ - θ1./(θ1+θ2.

Our main purpose is to give a method of constructing prediction intervals for the mean of us future observations in the random intercept linear model, A method is also indicated for constructing exact confidence intervals on the expected value of a future observation.

Richmond (1982) uses a linear programming approach to the construction of simultaneous confidence intervals for a set of linear estimable parametric functions of the normal mean vector. We present a quadratic programming approach which constructs narrower confidence intervals than the linear programming approach given by Richmond (1982).