Estimating the variances of ratio estimates in complex sample surveys with two primary sampling units per stratum—a comparison of balanced replication and jackknife techniques

The balanced half-sample and jackknife variance estimation techniques are used to estimate the variance of the combined ratio estimate. An empirical sampling study is conducted using computer-generated populations to investigate the variance, bias and mean square error of these variance estimators and results are compared to theoretical results derived elsewhere for the linear case. Results indicate that either the balanced half-sample or jackknife method may be used effectively for estimating the variance of the combined ratio estimate.     

A Monte Carlo comparison of some variance estimators of the Horvitz–Thompson estimator

At the design and estimation stage of a survey, large survey organization often uses auxiliary information. This article discusses various procedures for improving variance estimation of the Horvitz–Thompson estimator of a finite population total with the aid of auxiliary information. To study the design-based properties of the proposed variance estimators relative to the standard one, a small scale Monte Carlo study is performed.     

The robustness of the two—sample t—test over the Pearson system

The present paper has as its objective an accurate quantification of the robustness of the two–sample t-test over an extensive practical range of distributions. The method is that of a major Monte Carlo study over the Pearson system of distributions and the details indicate that the results are quite accurate. The study was conducted over the range β ₁ =0.0(0.4)2.0 (negative and positive skewness) and β ₂ =1.4 (0.4)7.8 with equal sample sizes and for both the one-and two-tail t-tests. The significance level and power levels (for nominal values of 0.05, 0.50, and 0.95, respectively) were evaluated for each underlying distribution and for each sample size, with each probability evaluated from 100,000 generated values of the test-statistic. The results precisely quantify the degree of robustness inherent in the two-sample t-test and indicate to a user the degree of confidence one can have in this procedure over various regions of the Pearson system. The results indicate that the equal-sample size two-sample t-test is quite robust with respect to departures from normality, perhaps even more so than most people realize.     

Stein's two sample test of a general linear hypothesis and a noncentral f–type distribution

Stein's two–sample procedure for a general linear model is studied and derived in terms of matrices in which the error tems are distributed as multivatriate student t–error terms. Tests and confidence regions are constructed in a similar way to classical linear models which involves percentage points of student t and F distributions. The advantages of taking two samples are: the variance of the error terms is known, and the power of tests are size of confidence regions are controllable. A new distribution called noncentral F–type distribution different from the nencentral F is found when considerinf the power of the test of general linear hypothesis.     

Estimation and comparison of the stress-strength models with more than two states under Weibull distribution and type II censoring scheme

This paper presents the extension of the inferences on the stress-strength reliability in more than two states to the system depending on the ratio of the strength and stress values when the stress and strength follow independent exponential distributions. The main objective of present paper is to consider different method of estimation, under Type II censoring, for the stress-strength models and to compare them, in more than two states, to the system depending on the ratio of the strength and stress values, when the stress and strength follow independent Weibull distributions, sharing the common shape parameter α.     

A new method for the estimation of variance matrix with prescribed zeros in nonlinear mixed effects models

We propose a new method for the Maximum Likelihood Estimator (MLE) of nonlinear mixed effects models when the variance matrix of Gaussian random effects has a prescribed pattern of zeros (PPZ). The method consists of coupling the recently developed Iterative Conditional Fitting (ICF) algorithm with the Expectation Maximization (EM) algorithm. It provides positive definite estimates for any sample size, and does not rely on any structural assumption concerning the PPZ. It can be easily adapted to many versions of EM.     

Goodness—of—fit for the two—parameter weibull distribution with estimated parameters

Goodness—of—fit statistics based on the empirical distribution function (EDF) are not distribution—free when parameters for the hypothesized distribution are estimated. Tables are percentile values of several EDF statistics are available for the two—parameter Weibull distribution when parameters are estimated by maximum likelihood. To determine how these tabled values change when simpler estimators are employed, percentile scores for EDF goodness—of—fit tests were obtained by Monte—Carlo simulation for maximum likelihood estimators (MLEs), good linear unbiased estimators (GLUEs), and modified Cramer—von Mises, Anderson—Darling, and Watson statistics are presented for GLUEs for both complete and censored samples. Critical values for Kolmogorov—Smirnov statistics were less affected by the method of estimation than were closer for MLEs and MGLUEs than for MGLUEs and GLUEs. On the other hand, MGLUE and GLUE results were much more similar to each other than to the MLE results when censoring was light and sample sizes were large.     

How precise is the finite sample approximation of the asymptotic distribution of realised variation measures in the presence of jumps?

This paper studies the impact of jumps on volatility estimation and inference based on various realised variation measures such as realised variance, realised multipower variation and truncated realised multipower variation. We review the asymptotic theory of those realised variation measures and present a new estimator for the asymptotic ‘variance’ of the centered realised variance in the presence of jumps. Next, we compare the finite sample performance of the various estimators by means of detailed Monte Carlo studies. Here we study the impact of the jump activity, of the jump size of the jumps in the price and of the presence of additional independent or dependent jumps in the volatility. We find that the finite sample performance of realised variance and, in particular, of log-transformed realised variance is generally good, whereas the jump-robust statistics tend to struggle in the presence of a highly active jump process.     

A class of one sample tests based on the Mann–Whitney–Wilcoxon functional

The main idea behind the proposed class of tests is rooted on an extension of the technique used in the derivation of the Mann–Whitney–Wilcoxon test. Just like the case of two-sample rank-based tests, the new class consists of tests defined through score functions. When properly selected, these score functions lead to consistent and often more powerful tests compared with classical goodness-of-fit tests. Theoretical results are supported by an extensive simulation study.     

A simple method for estimating parameters of the location–scale distribution family

The purpose of this paper is to estimate the parameters of the location–scale distribution family. As a special case, the method is used for estimating the parameters of the normal distribution and Cauchy distribution. For the Cauchy distribution, neither the moment estimation method nor the maximum likelihood estimation method works properly for estimating the parameters. The quantiles for obtaining confidence intervals and point estimates for the parameters of the two-parameter Cauchy distribution are given in the paper. It is shown that the estimators obtained in this paper are unbiased with respect to the median and possess some optimal properties.     

On the small sample estimation of the log odds ratio in 2×2 contingency tables with one set of fixed margins

For the analysis of 2 × 2 contingency tables with one set of fixed margins, a number of authors (e.g. Wolf, 1955; Cox, 1970) have proposed the use of various modified estimators based upon the empirical logistic transform. In this paper the moments of such estimators are considered and their small sample properties are investigated numerically.     

A comparison of confidence intervals generated by the scheffé and bonferroni methods

Simultaneous confidence intervals for the p means of a multivariate normal random variable with known variances may be generated by the projection method of Scheffé and by the use of Bonferroni's inequality. It has been conjectured that the Bonferroni intervals are shorter than the Scheffé intervals, at least for the usual confidence levels. This conjecture is proved for all p≥2 and all confidence levels above 50%. It is shown, incidentally, that for all p≥2 Scheffé's intervals are shorter for sufficiently small confidence levels. The results are also applicable to the Bonferroni and Scheffé intervals generated for multinomial proportions.     

Covariance and variance evaluations of two estimators for drug–placebo difference in a trial with sequential parallel design

Chen et al. [Contemp. Clin. Trials, 32: 592–604 (2011)] heuristically proved that the covariance of two estimators is zero assuming equal correlation coefficients. In this article, the above covariance is analytically and rigorously re-derived without any strong assumption in equality between two correlation coefficients. Under rigorous analytic derivations plus assuming number of subjects continuing into Period 2 is a random variable, covariance is reconfirmed to be zero for both normal and binomial data.     

Ties in one block comparison experiments: a generalization of the Mallows–Bradley–Terry ranking model

This study is concerned with the extension of the Mallows–Bradley–Terry ranking model for one block comparison consisting of all the items of interest to situations which allow an expression of no preference. We consider a modification of the Mallows–Bradley–Terry ranking model by introducing an additional parameter, called an index of discrimination, in the model. This permits ties in the model. The maximum likelihood estimates of the parameters are found using a Maximization–Minimization algorithm: the evaluation of the mathematical expectations involved in the log-likelihood equation is obtained by generating samples of Monte Carlo Markov chain from the stationary distribution. In addition, a simulation study for asymptotic properties assessment has been made. The proposed method is applied to analyze data election.     

A new extension of the Fréchet distribution: Properties and its characterization

A new lifetime model, which extends the Fréchet distribution called the generalized transmuted Fréchet distribution is proposed and studied. Various of its structural properties including ordinary and incomplete moments, generating function, residual and reversed residual lifes, order statistics and probability weighted moments are derived. Two characterization theorems are presented. The maximum likelihood method is used to estimate the model parameters. The flexibility of the new distribution is illustrated using a real data set. It can serve as an alternative model to other lifetime models available in the literature for modeling positive real data in many areas.     

Ranking and estimation of related means in two—way models—a Bayesian approach

A hierarchical Bayesian approach to ranking and selection as well as estimation of related means in two—way models is considered. Using the method of Monte Carlo simulation with importance sampling, we are able to carry out efficiently the three or four dimensional integrations as needed. An example is included to illustrate the methodology.     

A modification of the Box–Meyer method for finding the active factors in screening experiments

Screening experiments are conducted to identify a few active factors among a large number of factors. For the objective of identifying active factors, Box and Meyer provided an innovative approach, the Box–Meyer method (BMM). With the use of means models, we propose a modification of the BMM in this paper. Compared with the original BMM, the modified BMM (MBMM) can circumvent the problem that the original BMM runs into, namely that it may fail to identify some active factors due to the ignorance of higher order interactions. Furthermore, the number of explanatory variables in the MBMM is smaller. Therefore, the computational complexity is reduced. Finally, three examples with different types of designs are used to demonstrate the wide applicability of the MBMM.     

A comparison of the Hosmer–Lemeshow,Pigeon–Heyse,and Tsiatis goodness-of-fit tests for binary logistic regression under two grouping methods

Algebraic relationships between Hosmer–Lemeshow (HL), Pigeon–Heyse (J²), and Tsiatis (T) goodness-of-fit statistics for binary logistic regression models with continuous covariates were investigated, and their distributional properties and performances studied using simulations. Groups were formed under deciles-of-risk (DOR) and partition-covariate-space (PCS) methods. Under DOR, HL and T followed reported null distributions, while J² did not. Under PCS, only T followed its reported null distribution, with HL and J² dependent on model covariate number and partitioning. Generally, all had similar power. Of the three, T performed best, maintaining Type-I error rates and having a distribution invariant to covariate characteristics, number, and partitioning.     

Optimal design of repetitive group sampling plans for Weibull and gamma distributions with applications and comparison to the Birnbaum–Saunders distribution

In this paper, we propose a multiple deferred state repetitive group sampling plan which is a new sampling plan developed by incorporating the features of both multiple deferred state sampling plan and repetitive group sampling plan, for assuring Weibull or gamma distributed mean life of the products. The quality of the product is represented by the ratio of true mean life and specified mean life of the products. Two points on the operating characteristic curve approach is used to determine the optimal parameters of the proposed plan. The plan parameters are determined by formulating an optimization problem for various combinations of producer's risk and consumer's risk for both distributions. The sensitivity analysis of the proposed plan is discussed. The implementation of the proposed plan is explained using real-life data and simulated data. The proposed plan under Weibull distribution is compared with the existing sampling plans. The average sample number (ASN) of the proposed plan and failure probability of the product are obtained under Weibull, gamma and Birnbaum–Saunders distributions for a specified value of shape parameter and compared with each other. In addition, a comparative study is made between the ASN of the proposed plan under Weibull and gamma distributions.