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AbstractTime series models (TSMs) are used to forecast events based on verified historical data that are widely applied to describe natural and social phenomena. The spectral density function (SDF) of the TSM has the benefit to determine trends, periodic patterns and behavior of observable events and is used in degree of memory (DOM) which is used to identify independent and dependent structures. Therefore, paying attention to the estimator of SDF (SDE) is the cornerstone and desired goal in the statistical properties of TSMs. This paper gives a novel perspective for improving the SDE then dependency structure of TSMs by integrating clustering and sequential analysis. The accuracy of the lag window estimator (LWE) and periodogram estimator (PE), which are commonly used as SDEs in practice, is examined both with and without integrating the new proposed technique in order to figure out the efficacy of the new technique. Several circumstances, including independent and dependent data structures, TSMs with long and short DOMs, different numbers of clusters, and different dataset sizes, are used to carry out the investigation. The main findings indicate that: (i) The SDEs (PE and LWE) perform better when combined with the new proposed technique than when used alone. (ii) Using the new technique in conjunction with the SDEs results in absolutely perfect estimators for independent processes. (iii) High efficiency estimators for short memory TSMs arise when the new proposed technique is combined with the SDEs in the dependent processes; however, high efficiency in long memory TSMs (LMTSMs) is not guaranteed. (iv) Using the new technique, the correlation estimator behavior between SDEs and frequencies improves significantly with increasing DOM values of LMTSMs. (v) By applying the new technique for LMTSMs, the DOM estimator provides results indicating significant dependence. This study demonstrates that there are other efficient ways to improve the estimator than estimate techniques. [ABSTRACT FROM AUTHOR]

AbstractThis paper aims to simulate conditional samples for generalized linear models and to show their use in goodness of fit. The particular case of the natural exponential family with quadratic variance function and categorical covariates is studied. The conditional samples are drawn from the conditional distribution having conditioned on a sufficient statistic. A procedure that uses the Rao-Blackwell estimate for the cumulative distribution function is employed. The performance of the proposed procedure is shown through a simulation study and the analysis of a data set. [ABSTRACT FROM AUTHOR]

The randomness of the biases of parameter estimates, residuals and some variables is seldom considered for calculating covariance matrix of parameter estimates in total least squares (TLS) iterative algorithm. There are few studies on the precision estimation with the approximate probability distribution method of function in the TLS. In order to get more reasonable precision information for the TLS adjustment, the derivative-free Sterling interpolation method is introduced and implemented. The errors-in-variables (EIV) model and its TLS algorithm are introduced. The TLS iterative algorithm is combined with the Sterling interpolation, and two kinds of schemes for calculating biases of the TLS parameter estimates and approximate mean squared error matrix are designed. The method is used to four examples: line fitting model, coordinate transformation model, auto-regression model and variation function model. Comparing the results with the scaled unscented transformation (SUT) method, the feasibility and effectiveness of the Sterling interpolation method in the TLS precision estimation are verified. The Sterling interpolation method has fewer parameters than the SUT method, and it is simpler to implement. And the scheme two in this paper can be applied to the case where some matrix elements are nonlinear functions of the observation. The application of the precision estimation is expanded by this method, and the theory for precision estimation of TLS is further improved. [ABSTRACT FROM AUTHOR]

Gibbs samplings is a Markov Chain Monte Carlo technique for estimating conditional probabilities in Bayesian networks. A major problem of Gibbs sampling is the dependency of the generated chain of samples. Thus the estimates are biased unless the initial value of the chain is drawn from the target distribution. One elegant method to overcome the initial bias is regenerative samplings. We reported elsewhere the "stationary minorization condition" that makes any Markov Chain Monte Carlo technique regenerative. In this paper, we show how this condition can be easily met in the simulations of any Bayesian network. [ABSTRACT FROM AUTHOR]

Few studies have been conducted on the precision estimation of weighted total least squares (WTLS) by using the approximate function probability distribution method. And the existing Monte Carlo method needs to simulate a lot, the amount of calculation is large and the results obtained are uncertain. In order to further improve the total least squares precision estimation theory, this paper introduces the Jackknife method into Geomatics data processing. Combining the Jackknife method and WTLS method, the delete-1 Jackknife method and delete-d Jackknife method are proposed. The biases and standard deviations or covariance of parameter estimations are calculated by these proposed methods. And the specific steps of the precision estimation of these two methods are given. Applying these methods to the linear regression model and the coordinate transformation model, and comparing with the approximate function method and the Monte Carlo method, we can see that the Jackknife methods for precision estimation can obtain more stable and reasonable precision results and are very adaptive. In order to get more reasonable precision results, the Jackknife method does spend much more time over total least squares when the amount of the observed data is large. But compared with Monte Carlo method, it can reduce the amount of calculation and improve the computational efficiency. The method in this paper could provide an idea for further study on the precision estimation for total least squares. [ABSTRACT FROM AUTHOR]

Functional polynomial multiple-index model which includes the functional linear model, functional quadratic model and functional single index model as the special cases is considered. In this paper we propose an iterative technique to estimate the link function and polynomial coefficients nonparametrically. Simulations show that the proposed methods have good prediction performances. The proposed model is also illustrated with tecator data. [ABSTRACT FROM AUTHOR]

In this paper, we propose modified spline estimators for nonparametric regression models with right-censored data, especially when the censored response observations are converted to synthetic data. Efficient implementation of these estimators depends on the set of knot points and an appropriate smoothing parameter. We use three algorithms, the default selection method (DSM), myopic algorithm (MA), and full search algorithm (FSA), to select the optimum set of knots in a penalized spline method based on a smoothing parameter, which is chosen based on different criteria, including the improved version of the Akaike information criterion (AICc), generalized cross validation (GCV), restricted maximum likelihood (REML), and Bayesian information criterion (BIC). We also consider the smoothing spline (SS), which uses all the data points as knots. The main goal of this study is to compare the performance of the algorithm and criteria combinations in the suggested penalized spline fits under censored data. A Monte Carlo simulation study is performed and a real data example is presented to illustrate the ideas in the paper. The results confirm that the FSA slightly outperforms the other methods, especially for high censoring levels. [ABSTRACT FROM AUTHOR]

In this paper, we briefly overview different zero-inflated probability distributions. We compare the performance of the estimates of Poisson, Generalized Poisson, ZIP, ZIGP and ZINB models through Mean square error (MSE), bias and Standard error (SE) when the samples are generated from ZIP distribution. We propose a new estimator referred to as probability estimator (PE) of inflation parameter of ZIP distribution based on moment estimator (ME) of the mean parameter and compare its performance with ME andmaximum likelihood estimator (MLE) through a simulation study.We use the PE along with ME and MLE to fit ZIP distribution to various zero-inflated datasets and observe that the results do not differ significantly. We recommend using PE in place of MLE since it is easy to calculate and the simulation study in this paper demonstrates that the PE performs as good as MLE irrespective of the sample size. [ABSTRACT FROM AUTHOR]

This paper presents a robust version of partial residuals technique to estimate parametric and nonparametric components in semiparametric partially linear model. The robust estimation of the parametric component is constructed by using an M-estimation after eliminating the effect of the nonparametric component on both the response and covariates based on the pseudo data. Finally, the nonparametric component is estimated robustly by using the residuals from the obtained M-estimation of the parametric component. Simulation studies and a real data analysis illustrate that the proposed estimator performs better than the existing estimations when outliers in the dataset or errors with heavy tails. [ABSTRACT FROM AUTHOR]

This paper considers the estimation of parameters of AR(p) models for time series witht-distribution via EM-based algorithms. The paper develops asymptotic properties for the estimation to show that the estimators are efficient. Also testing theory for the estimators is considered. The robustness of the estimators and various tests to deviations from an assumed model is investigated. The study shows that the algorithms have equal estimation efficiency even if the error distribution is miss-specified or perturbed by outliers. Interestingly, the estimators from these algorithms performed better than that of the Modified Maximum Likelihood (MML) considered in Tiku et al. (2000). [ABSTRACT FROM AUTHOR]

This paper is concerned with the Bayesian estimation parameters of the stochastic SIR (Susceptible-Infective-Removed) epidemic model from the trajectory data. Specifically, the data from the count of both infectives and susceptibles is assumed to be available on some time grid as the epidemic progresses. The diffusion approximation of the appropriate jump process is then used to estimate missing data between every pair of observation times. If the time step of imputations is small enough, we derive the posterior distributions of the infection and recovery rates using the Milstein scheme. The paper also presents Markov-chain Monte Carlo (MCMC) simulation that demonstrates that the method provides accurate estimates, as illustrated by the synthetic data from SIR epidemic model and the real data. [ABSTRACT FROM AUTHOR]

In this paper, a one-stage multiple comparison procedures with the average for exponential location parameters based on the doubly censored sample under heteroscedasticity is proposed. These intervals can be used to identify a subset which includes all no-worse-than-the-average treatments in an experimental design and to identify better-than-the-average, worse-than-the-average and not-much-different-from-the-average products in agriculture, emerging market, pharmaceutical industries. The critical values are tabulated in a table for practical use. A simulation study on the confidence length and coverage probabilities is done. At last, an example of comparing four drugs in the treatment of leukemia is given to demonstrate the proposed procedures. [ABSTRACT FROM AUTHOR]

In the field of computer virus, a growing number of mathematical models have been published during the last decade. In this paper, we consider several estimation methods under two parametric models, the random constant scanning model and the nonhomogeneous random scanning model, to propose a comparison of the estimators’ performances based on the simulation of random populations. We conclude our work with an application of the different estimation methods to a real data set of worm propagation. [ABSTRACT FROM AUTHOR]

Different longitudinal study designs require different statistical analysis methods and different methods of sample size determination. Statistical power analysis is a flexible approach to sample size determination for longitudinal studies. However, different power analyses are required for different statistical tests which arises from the difference between different statistical methods. In this paper, the simulation-based power calculations ofF-tests with Containment, Kenward-Roger or Satterthwaite approximation of degrees of freedom are examined for sample size determination in the context of a special case of linear mixed models (LMMs), which is frequently used in the analysis of longitudinal data. Essentially, the roles of some factors, such as variance–covariance structure of random effects [unstructured UN or factor analytic FA0], autocorrelation structure among errors over time [independent IND, first-order autoregressive AR1 or first-order moving average MA1], parameter estimation methods [maximum likelihood ML and restricted maximum likelihood REML] and iterative algorithms [ridge-stabilized Newton-Raphson and Quasi-Newton] on statistical power of approximateF-tests in the LMM are examined together, which has not been considered previously. The greatest factor affecting statistical power is found to be the variance–covariance structure of random effects in the LMM. It appears that the simulation-based analysis in this study gives an interesting insight into statistical power of approximateF-tests for fixed effects in LMMs for longitudinal data. [ABSTRACT FROM AUTHOR]

The maximum likelihood (MLE), the weighted maximum likelihood (WMLE), and the maximum a posteriori (MAP or BMLE) have been widely used to estimate ability parameters in item response theory (IRT), and their precisions and biases have been studied and compared. Multidimensional IRT (MIRT) has been shown to provide better subscore estimates in both paper-and-pencil and computer adaptive tests; thus, it is very important to have an accurate score estimate for the MIRT model. The purpose of this article is to compare the performances of the three estimation methods in the MIRT framework for tests of mixed item types that have both dichotomous and polytomously scored items, and for tests of mixed structured items (simple structured and complex structured). It is found that all three methods perform well for all conditions. For all models studied (one-, two-, three-, and four- dimensional model), WMLE has smaller BIAS and higher reliabilities, but larger RMSE and SE. WMLE and MLE are closer to each other than to BMLE. However, for higher dimensions, BMLE is recommended, especially when there are correlations between the dimensions. [ABSTRACT FROM AUTHOR]

This paper considers the constant-partially accelerated life tests for series system products, where dependent M-O bivariate exponential distribution is assumed for the components. Based on progressive type-II censored and masked data, the maximum likelihood estimates for the parameters and acceleration factors are obtained by using the decomposition approach. In addition, this method can also be applied to the Bayes estimates, which are too complex to obtain as usual way. Finally, a Monte Carlo simulation study is carried out to verify the accuracy of the methods under different masking probabilities and censoring schemes. [ABSTRACT FROM AUTHOR]

Testing homogeneity of multivariate normal mean vectors under an order restriction when the covariance matrices are unknown, arbitrary positive definite and unequal are considered. This problem of testing has been studied to some extent, for example, by Kulatunga and Sasabuchi (1984) when the covariance matrices are known and also Sasabuchi et al. (2003) and Sasabuchi (2007) when the covariance matrices are unknown but common. In this paper, a test statistic is proposed and because of the main advantage of the bootstrap test is that it avoids the derivation of the complex null distribution analytically, a bootstrap test statistic is derived and since the proposed test statistic is location invariance the bootstrapp-value defined logical and some steps are presented to estimate it. Our numerical studies via Monte Carlo simulation show that the proposed bootstrap test can correctly control the type I error rates. The power of the test for some of thep-dimensional normal distributions is computed by Monte Carlo simulation. Also, the null distribution of test statistic is estimated using kernel density. Finally, the bootstrap test is illustrated using a real data. [ABSTRACT FROM AUTHOR]

In this paper, we propose a value-at-risk (VaR) estimation technique based on a new stochastic volatility model with leverage effect, nonconstant conditional mean and jump. In order to estimate the model parameters and latent state variables, we integrate the particle filter and adaptive Markov Chain Monte Carlo (MCMC) algorithms to develop a novel adaptive particle MCMC (A-PMCMC) algorithm. Comprehensive simulation experiments based on three stock indices and two foreign exchange time series show effectiveness of the proposed A-PMCMC algorithm and the VaR estimation technique. [ABSTRACT FROM AUTHOR]

In this paper, we focus on exact inference for exponential distribution under multiple Type-I censoring, which is a general form of Type-I censoring and represents that the units are terminated at different times. The maximum likelihood estimate of mean parameter is calculated. Further, the distribution of maximum likelihood estimate is derived and it yields an exact lower confidence limit for the mean parameter. Based on a simulation study, we conclude that the exact limit outperforms the bootstrap limit in terms of the coverage probability and average limit. Finally, a real dataset is analyzed for illustration. [ABSTRACT FROM AUTHOR]

This paper adopts a Bayesian strategy for generalized ridge estimation for high-dimensional regression. We also consider significance testing based on the proposed estimator, which is useful for selecting regressors. Both theoretical and simulation studies show that the proposed estimator can simultaneously outperform the ordinary ridge estimator and the LSE in terms of the mean square error (MSE) criterion. The simulation study also demonstrates the competitive MSE performance of our proposal with the Lasso under sparse models. We demonstrate the method using the lung cancer data involving high-dimensionalmicroarrays. [ABSTRACT FROM AUTHOR]

In this paper, we propose a lower bound based smoothed quasi-Newton algorithm for computing the solution paths of the group bridge estimator in linear regression models. Our method is based on the quasi-Newton algorithm with a smoothed group bridge penalty in combination with a novel data-driven thresholding rule for the regression coefficients. This rule is derived based on a necessary KKT condition of the group bridge optimization problem. It is easy to implement and can be used to eliminate groups with zero coefficients. Thus, it reduces the dimension of the optimization problem. The proposed algorithm removes the restriction of groupwise orthogonal condition needed in coordinate descent and LARS algorithms for group variable selection. Numerical results show that the proposed algorithm outperforms the coordinate descent based algorithms in both efficiency and accuracy. [ABSTRACT FROM AUTHOR]

Two classes of methods properly account for clustering of data: design-based methods and model-based methods. Estimates from both methods have been shown to be approximately equal with large samples. However, both classes are known to produce biased standard error estimates with small samples. This paper compares the bias of standard errors and statistical power of marginal effects for generalized estimating equations (a design-based method) and generalized/linear mixed effects models (model-based methods) with small sample sizes via a simulation study. Provided that the distributional assumptions are met, model-based methods produced the least-biased standard error estimates and greater relative statistical power. [ABSTRACT FROM PUBLISHER]

In many cyclical processes it is of interest to have a system for on-line detection of turning points. This could be detection of the turns in leading economic indicators in order to predict the next turn of the business cycle. In natural family planning we want to detect the peak in the human menstrual cycle in order to predict the most fertile phase. Another example is detection of an influenza outbreak, by monitoring the weekly reports of the number of patients showing influenza-like symptoms. The methodology of statistical surveillance is used here to construct alarm systems, consisting of an alarm statistic and an alarm limit. At each time point a new observation becomes available and the alarm system is used to make a decision as to whether the turning point has occurred or not. The same methodology is used in control charts. Optimal alarm systems are based on the likelihood ratio, the ratio between the likelihood functions for the in-control process and the out-of-control process. The optimal likelihood ratio method for surveillance is based on the assumption that the parametric model for the cyclical process is known. This rather strong assumption can be avoided by using an approximation, the maximum likelihood ratio method, where a non-parametric estimation procedure is used. The estimation is made using only monotonicity restrictions, no parametric restrictions are placed on the cycles. Hereby, mis-specification of the parameters is avoided and thus we are sure that the false alarms are really controlled at the nominal level. The aim of this paper is to evaluate how two likelihood ratio based methods for on-line detection(the likelihood ratio method and the maximum likelihood ratio method) react to different assumption about the intensity, i.e., different assumption regarding how often we can expect a turn. Information about the previous intensity of the change point process is included in the methods by the empirical density of the change point times. This paper compares the performances of the likelihood ratio method and the maximum likelihood ratio method, when an empirical intensity is used(based on a bell shaped density) and when a constant intensity is used. In addition, these methods are compared and evaluated for the situation when no information about the time of the turn is used. The results of the study in this paper show that the likelihood ratio method with the empirical intensity works well except for early turns, when the time until detection is very long. For early turns the likelihood ratio method with a constant intensity without any information about the intensity, gives quicker detection. The maximum likelihood ratio method with the empirical intensity only works well for those turning point times that are the most likely according to the empirical density. Early turns take a long time to detect and late alarms have low predictive value. For the maximum likelihood ratio approach, the constant intensity gives the shortest expected delay and high predictive values. [ABSTRACT FROM AUTHOR]

Standard Shewhart &Xmacr; control charts with estimated control limits are widely used in practice. There are four ways to estimate the standard deviation σ generally, as which we call the average range, the average sample standard deviation, the pooled sample standard deviation and the average absolute deviation, respectively. We give three new estimators which are based on median in order to estimate standard deviation in this paper, and we get their means through simulated computation. The simulated results are then used to discuss their properties when the data is from a ε-contaminated normal distribution. At last, we simulate the in-control and outof-control average run lengths of Shewhart &Xmacr; control charts when the process standard deviation is estimated by seven different ways including three absolute deviations to median mentioned in the paper. [ABSTRACT FROM AUTHOR]

This paper presents a new random weighting-based adaptive importance resampling method to estimate the sampling distribution of a statistic. A random weighting-based cross-entropy procedure is developed to iteratively calculate the optimal resampling probabilityweights by minimizing the Kullback-Leibler distance between the optimal importance resampling distribution and a family of parameterized distributions. Subsequently, the random weighting estimation of the sampling distribution is constructed from the obtained optimal importance resampling distribution. The convergence of the proposed method is rigorously proved. Simulation and experimental results demonstrate that the proposed method can effectively estimate the sampling distribution of a statistic. [ABSTRACT FROM AUTHOR]

It is well-known that under fairly conditions linear regression becomes a powerful statistical tool. In practice, however, some of these conditions are usually not satisfied and regression models become ill-posed, implying that the application of traditional estimation methods may lead to non-unique or highly unstable solutions. Addressing this issue, in this paper a new class of maximum entropy estimators suitable for dealing with ill-posed models, namely for the estimation of regression models with small samples sizes affected by collinearity and outliers, is introduced. The performance of the new estimators is illustrated through several simulation studies. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present new likelihood based goodness-of-fit tests for the two-parameter Weibull distribution. These tests consist in nesting the Weibull distribution in three-parameter generalized Weibull families and testing the value of the third parameter by using the Wald, score, and likelihood ratio procedures. We simplify the usual likelihood based tests by getting rid of the nuisance parameters, using three estimation methods. The proposed tests are not asymptotic. A comprehensive comparison study is presented. Among a large range of possible GOF tests, the best ones are identified. The results depend strongly on the shape of the underlying hazard rate. [ABSTRACT FROM AUTHOR]

This paper develops the Bayesian estimation for the Birnbaum–Saunders distribution based on Type-II censoring in the simple step stress–accelerated life test with power law accelerated form. Maximum likelihood estimates are obtained and Gibbs sampling procedure is used to get the Bayesian estimates for shape parameter of Birnbaum–Saunders distribution and parameters of power law–accelerated model. Asymptotic normality method and Markov Chain Monte Carlo method are employed to construct the corresponding confidence interval and highest posterior density interval at different confidence level, respectively. At last, the results are compared by using Monte Carlo simulations, and a numerical example is analyzed for illustration. [ABSTRACT FROM AUTHOR]

In this paper, we consider estimating the benchmark dose in a dose–response study with right-censored lifetime data, where the benchmark dose is the dose corresponding to a specific benchmark response, which is related to the probability that the lifetime of a subject receiving the dose is too short. Under the Cox or Weibull extension proportional hazards model, simultaneous lower confidence limits on the benchmark dose are developed. We further conduct a Monte Carlo study to investigate the performance of the proposed lower confidence limits. Finally, a real dataset is illustrated to demonstrate the application of the proposed procedures. [ABSTRACT FROM AUTHOR]

In bioinformatics application, the estimation of the starting and ending points of drop-down in the longitudinal data is important. One possible approach to estimate such change times is to use the partial spline model with change points. In order to use estimate change time, the minimum operator in terms of a smoothing parameter has been widely used, but we showed that the minimum operator causes large MSE of change point estimates. In this paper, we proposed the summation operator in terms of a smoothing parameter, and our simulation study showed that the summation operator gives smaller MSE for estimated change points than the minimum one. We also applied the proposed approach to the experiment data, blood flow during photodynamic cancer therapy. [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]

This paper addresses the issue of state estimation in nonlinear systems in the presence of non-Gaussian and bounded noises, under which the interval analysis based estimation is introduced as an auxiliary approach of generic particle filter (PF). This yields the so-called Set-Membership aided particle filter (SMPF). Unlike the mature alternatives of generic particle filter, the proposal distribution of SMPF approximates the posterior probability density function (PDF), not only on the numerical value but also on the definition-domain, and the performance analysis on the proposed alternative is proven through detailed formulations. In addition, contrasting simulations under SMPF and other mature alternatives also validate the effectiveness of SMPF. [ABSTRACT FROM AUTHOR]

System characteristics of a redundant repairable system with two primary units and one standby are studied from a Bayesian viewpoint with different types of priors assumed for unknown parameters, in which the coverage factor is the same for an operating unit failure as that for a standby unit failure. Times to failure and times to repair of the operating and standby units are assumed to follow exponential distributions. When times to failure and times to repair with uncertain parameters, a Bayesian approach is adopted to evaluate system characteristics. Monte Carlo simulation is used to derive the posterior distribution for the mean time to system failure and the steady-state availability. Some numerical experiments are performed to illustrate the results derived in this paper. [ABSTRACT FROM AUTHOR]

In a two-variable regression model setup, we examine in this paper the effects of trimming and winsorization and dichotomization of the independent variable on the regression estimates and the efficiency of the regression estimation. These results have direct implications in the accounting literature when dealing with the effects of analyst forecast errors on stock returns. [ABSTRACT FROM AUTHOR]

This paper examines a version of the tests of P. M. Robinson for testing unit roots and other fractionally integrated hypotheses in the context of autocorrelated disturbances. We use Monte Carlo simulations to examine the finite-sample behaviour of the tests when the disturbances follow AR(1) processes. Using the asymptotic critical values of the normal distribution, we show that the power of the tests is extremely low in some cases. Finite-sample critical values were then computed and the problem still persists unless we calculate these critical values for specific values of the AR parameters. An empirical application, illustrating this problem, is also carried out at the end of the article. [ABSTRACT FROM AUTHOR]

The X¯ and S (or R) control charts are most commonly used in practice for monitoring the process mean and variance, respectively. A method for detecting changes in the process mean or variance is to obtain a stopping time at which the control charts issue a signal. The potential delay in generating a signal from the control charts calls for the change point estimation combined with control charts. In this paper, when X¯ and S control charts issue a signal, a maximum likelihood joint estimator of the change point is suggested considering simultaneous change in the process mean and variance. The use of the proposed estimator is illustrated with an example. [ABSTRACT FROM AUTHOR]

Despite of its lasting popularity, the application of the exact Wilcoxon–Mann–Whitney (WMW) test has never been free of inappropriateness or unnecessary inefficiency in practice. The goal of this paper is to exemplify some modifications that can be conducted to the application of the exact WMW test in small sample cases to achieve more precise and more powerful estimations and tests. At first, we propose a modified procedure to replace the current generalized Hodges–Lehmann procedure in Proc-StatXact 5® to correctly derive the exact WMW test based interval estimates for the shift parameter in the presence of ties. We then propose a variance adjustment for the exact WMW test to achieve more powerful exact test as the variance adjusted WMW statistic has less discrete distribution than the conventionally unadjusted WMW statistic. We find that the proposed variance adjusted exact method is noticeably less conservative than the conventional exact WMW method, especially when ties in observation are not very heavy. [ABSTRACT FROM AUTHOR]

Suppose that the lifetimes of the first ri items to fail in a random sample of size ni (type-II censoring) at stress vi, , are distributed according to a finite mixture model. The components of the model may represent different causes of failure and include, among others, the Weibull, compound Weibull, Pareto, power function, Gompertz and compound Gompertz distributions. In this paper, the Bayes estimates of the parameters, reliability and hazard rate functions are computed by using an approximate form due to Tierney and Kadane [Tierney, L., Kadane, J. B. (1986). Accurate approximations for posterior moments and marginal densities. J. Am. Statist. Assoc. 81:82–86]. A special attention is paid to a mixture of two Weibull components where the mean squared errors of the Bayes estimators are compared with their maximum likelihood counterparts via a simulation study. [ABSTRACT FROM AUTHOR]

In practical application, the observed data could be a symmetric or asymmetric model due to the interference of the contamination. Thus, a proper asymmetric truncation needs to be made to avoid the outliers. In this paper, an adaptive choice of trimming proportions for symmetric and asymmetric distributions are presented. Three stages are included for processing, these are: (1) compute the tail length of skewness of the observed data, (2) classify the observed data using tail length and skewness, and map to the pre-calculated trimmed proportions table, (3) compute the trimmed mean. The simulation results show that the proposed estimator has a low bias and standard deviation for location estimation of the mean in simulated random sample with outliers. [ABSTRACT FROM AUTHOR]

It is well known that prior application of GLS detrending, as advocated by Elliot et al. [Elliot, G., Rothenberg, T., Stock, J. (1996). Efficient tests for an autoregressive unit root. Econometrica 64:813–836], can produce a significant increase in power to reject the unit root null over that obtained from a conventional OLS-based Dickey and Fuller [Dickey, D., Fuller, W. (1979). Distribution of the estimators for autoregressive time series with a unit root. J. Am. Statist. Assoc. 74:427–431] testing equation. However, this paper employs Monte Carlo simulation to demonstrate that this increase in power is not necessarily obtained when breaks occur in either level or trend. It is found that neither OLS nor GLS-based tests are robust to level or trend breaks, their size and power properties both deteriorating as the break size increases. [ABSTRACT FROM AUTHOR]

Constrained M (CM) estimates of multivariate location and scatter [Kent, J. T., Tyler, D. E. (1996). Constrained M-estimation for multivariate location and scatter. Ann. Statist. 24:1346–1370] are defined as the global minimum of an objective function subject to a constraint. These estimates combine the good global robustness properties of the S estimates and the good local robustness properties of the redescending M estimates. The CM estimates are not explicitly defined. Numerical methods have to be used to compute the CM estimates. In this paper, we give an algorithm to compute the CM estimates. Using the algorithm, we give a small simulation study to demonstrate the capability of the algorithm finding the CM estimates, and also to explore the finite sample behavior of the CM estimates. We also use the CM estimators to estimate the location and scatter parameters of some multivariate data sets to see the performance of the CM estimates dealing with the real data sets that may contain outliers. [ABSTRACT FROM AUTHOR]

The existence of outliers in a sample is an obvious problem which can become worse when the usual bootstrap is applied, because some resamples may have a higher contamination level than the initial sample. Bootstrapping using robust estimators may be a solution to this problem. However, in many instances, this will not be enough because it can lead to several complications, such as: (i) the breakdown point for the whole procedure may be small even when based on an estimator with a high breakdown point; (ii) mathematical difficulties; (iii) very high computation time. In this paper, we suggest a modification of the bootstrap procedure in order to solve these problems which consists of forming each bootstrap sample by resampling with different probabilities so that the potentially more harmful observations have smaller probabilities of selection. The aim is to protect the whole procedure against a given number of arbitrary outliers. As an illustration, we consider point and interval estimation for the correlation coefficient. We use Monte Carlo methods to compare this method with another robust bootstrap procedure, the winsorized bootstrap, recently suggested by Singh [Singh, K. (1998). Breakdown theory for bootstrap quantiles. [ABSTRACT FROM AUTHOR]

In this paper we use a one-stage procedure described by Chen [Chen, S. Y. (2001). One-stage and two-stage statistical inference under heteroscedasticity. Commun. Statist. Simulation Computat. 30(4):991–1009] for testing the equality of normal means against an ordered alternative in one-way layout when variances are unknown and unequal. Tables of percentage points and the power under a specific alternative needed for implementation are given. The relationship between the one-stage and the two-stage test procedures is discussed. Comparison between the new procedure and the range test [Chen, S. Y. (2000). One-sided range test for testing against an ordered alternative under heteroscedasticity. Commun. Statist. Simulation Computat. 29(4): 1255–1272] by simulation study is also given. [ABSTRACT FROM AUTHOR]

In traditional Response Surface Methods (RSM), running a first order experimental design is usually followed by a steepest ascent search using the vector of parameter estimates as an approximation to the gradient. In the presence of variability in the responses, there is a need for a stopping rule to determine the optimal point in the search direction. Two formal stopping rules have been proposed in the literature, Myers and Khuri's (MK) stopping rule and Del Castillo's Recursive Parabolic Rule (RPR). The first rule requires the specification of an initial guess on the number of steps required to reach the optimum, while the performance of the second rule has only been studied for quadratic responses. This paper proposes some modifications to the recursive parabolic rule in order to increase its robustness for non-quadratic responses. The modifications consist of using only a fraction of the experiments made along the search, the estimation of all the parameters in the parabolic model, and the utilization of a coding convention for the regressors. The performance of the two rules, together with classical rules of stopping after 1, 2 or 3 consecutive drops in the response, are studied through simulation under non-quadratic and non-normally distributed responses. We show, by example, that the new rule is easy to use in practice, keeping one of the main attractions of this RSM technique. It was observed that the original recursive parabolic rule stops before the optimum under non-quadratic behavior, while the modified parabolic rule and the MK rule perform satisfactorily under most of the simulated conditions. [ABSTRACT FROM AUTHOR]

In this paper, resampling methods, namely the jackknife and the bootstrap, are considered for bias evaluation and correction of maximum partial likelihood estimators. A complete set of Monte Carlo simulations compare the proposed approaches with formulae recently proposed for bias correction to order n−1. The results indicate a competitive performance for these methods. [ABSTRACT FROM AUTHOR]

The generally most powerful unconditional exact test for testing independence in a 2 × 2 multinomial trial is Barnard's test, but at present it is impossible to apply in samples of even moderate size. Alternatively, it can be used as an asymptotic method. This paper evaluates 10 different approximations (as well as 48 others not included here) under the criterion that the optimal approximation is the one which produces a p-value that differs from the exact test by less than a given quantity. The best method is the one based on Pirie and Hamdan's chi-squared statistics –  = {|N11N22 − N12N21| − 0.5}2(N − 1)/{N1•N2•N•1N•2} – which is valid, for ordinary significances and one(two)tailed-tests, if the minimum expected quantity E is larger than or equal to 2.5 (1.5). However, when the test is valid it may fail between 1% and 5% of times (the failures are sometimes liberal and others are conservative). If one wants to avoid failure, E will have to be rather more than 9. (Present computation capacity does not allow us to determine the exact amount.) [ABSTRACT FROM AUTHOR]

In this paper the ingestion and subsequent metabolism of a drug in a given individual, are investigated through the use of compartmental models. An adaptive formulation of the widely used extended Kalman filter (EKF) has been derived in order to solve the resulting nonlinear estimation problem at the output of the compartments. The adaptive EKF employs a forgetting factor to emphasize artificially the effect of current data by exponentially weighting the observations. The dependence of EKF's performance on the selection of appropriate values of the arbitrary matrices, the measurement covariance R and the process noise covariance Q has been demonstrated through simulations. With the appropriate choice of the matrices the EKF provides a very useful tool for online estimation of both the state and the parameters. [ABSTRACT FROM AUTHOR]

Burdick and Larsen (1) compared the Gui et al. (2) Modified Large-Sample and the Satterthwaite methods for constructing approximate confidence interval for the ratio δ = σ²[sub α]/σ²[sub β] + σ²[sub αβ] + σ²[sub ε];) in a classical gauge Ramp;R study. In this paper, we provide results showing that both methods can fail by a large margin to maintain the nominal confidence level when used to estimate small values of δ. We discuss the implications of these findings and suggest a simple and apparently effective alternative to these methods for estimating δ. [ABSTRACT FROM AUTHOR]

This paper has developed a new robust Shewhart-type control chart for monitoring the location of a bivariate process and examine its behavior based on the Hodges-Lehamnn and Shamos-Bickel-Lehmann estimators. A numerical example is given to illustrate the use of the proposed method. Its performance is investigated using a simulation study. [ABSTRACT FROM AUTHOR]

This paper concerns maximum likelihood estimation for the semiparametric shared gamma frailty model; that is the Cox proportional hazards model with the hazard function multiplied by a gamma random variable with mean 1 and variance θ. A hybrid ML-EM algorithm is applied to 26 400 simulated samples of 400 to 8000 observations with Weibull hazards. The hybrid algorithm is much faster than the standard EM algorithm, faster than standard direct maximum likelihood (ML, Newton Raphson) for large samples, and gives almost identical results to the penalised likelihood method in S-PLUS 2000. When the true value θ[sub 0] of θ is zero, the estimates of θ are asymptotically distributed as a 50-50 mixture between a point mass at zero and a normal random variable on the positive axis. When θ[sub 0] > 0, the asymptotic distribution is normal. However, for small samples, simulations suggest that the estimates of θ are approximately distributed as an x - (100 - x)% mixture, 0 ≤ x ≤ 50, between a point mass at zero and a normal random variable on the positive axis even for θ[sub 0] > 0. In light of this, p-values and confidence intervals need to be adjusted accordingly. We indicate an approximate method for carrying out the adjustment. [ABSTRACT FROM AUTHOR]