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There is no general exact analysis for the class of generalized mixed models, and asymptotic procedures are widely used. Importantly, under small sample conditions equivalent asymptotic procedures can yield conflicting inference when applied to the same data set [Aubin, E. C. Q., Cordeiro, G. M. (2000). Bartlett-corrected tests for normal linear models when the covariance matrix is nonscalar. Commun. Statist.—Theory Methods 29:2405–2426]. For the classical likelihood ratio test (LRT), Bartlett’s [Bartlett, M. S. (1937). Properties of sufficiency and statistical tests. Proc. R. Soc. London. Ser. A, Math. Phys. Sci. 160(901):268–282] correction may be used to yield improved small sample performance. Zucker et al. [Zucker, D. M., Lieberman, O., Manor, O. (2000). Improved small sample inference in the mixed linear model: Bartlett correction and adjusted likelihood. J. R. Statist. Soc., Ser. B 62:827–838] proposed and investigated methods for improved small sample inference in the mixed linear model using refined LRTs. The refinements included the use of a Bartlett correction and the Cox–Reid adjusted likelihood [Cox, D. R., Reid, N. (1987). Approximations to noncentral distributions. Can. J. Statist. 15(2):105–114], which using simulation studies (under a random-line model, and a two-period, four-treatment crossover design) were shown to yield Type I error rates very close to the nominal level. An alternative approach which has also been shown [Kowalchuk, R., Keselman, H. (2001). The analysis of repeated measurements with mixed-model Kenward Roger's adjusted F-tests. Paper presented at the Annual Meeting of the American Educational Research Association, Seattle, Washington] to have improved performance characteristics is a procedure involving t and F statistics for tests of fixed effects with modified degrees of freedom calculations detailed by Kenward and Roger [Kenward, M. G., Roger, J. H. (1997). Small sample inference for fixed effects from restricted maximum likelihood. Biometrics 53:983–997]. However, to date there has been no direct comparison of the Bartlett modified likelihood ratio and Kenward Roger procedures. This paper provides the results from a Monte Carlo simulation study examining the Type I error control and power profiles of modified likelihood ratio procedures including those described in Zucker et al. and proposed by Kenward and Roger for tests of fixed effect parameters in mixed linear models with data simulated from small sample unbalanced repeated measures designs, followed by results from a real data example. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of estimating the scale parameter of the inverse Rayleigh distribution based on general progressively Type-II censored samples and progressively Type-II censored samples. The pivotal quantity method is used to derive the estimator of the scale parameter. Besides, considering that the maximum likelihood estimator is tough to obtain for this distribution, we derive an explicit estimator of the scale parameter by approximating the likelihood equation with Taylor expansion. The interval estimation is also studied based on pivotal inference. Then we conduct Monte Carlo simulations and compare the performance of different estimators. We demonstrate that the pivotal inference is simpler and more effective. The further application of the pivotal quantity method is also discussed theoretically. Finally, two real data sets are analyzed using our methods. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to develop the approximate Bayes estimation of the five-dimensional vector of the parameters and reliability function of a mixture of two inverse Weibull distributions (MTIWD) under Type-2 censoring. Usually, the posterior distribution is complicated under the scheme of Type-2 censoring and the integrals that are involved cannot be obtained in a simple explicit form. In this study, we use Lindley's [Approximate Bayesian method, Trabajos Estadist. 31 (1980), pp. 223–237] approximate form of Bayes estimation in the case of an MTIWD under Type-2 censoring. Later, we calculate the estimated risks (ERs) of the Bayes estimates and compare them with the corresponding ERs of the maximum-likelihood estimates through Monte Carlo simulation. Finally, we analyse a real data set using the findings. [ABSTRACT FROM AUTHOR]

When simulating discrete-time approximations of solutions of stochastic differential equations (SDEs), in particular martingales, numerical stability is clearly more important than some higher order of convergence. Discrete-time approximations of solutions of SDEs with multiplicative noise, similar to the Black–Scholes model, are widely used in simulation in finance. The stability criterion presented in this paper is designed to handle both scenario simulation and Monte Carlo simulation, i.e. both strong and weak approximations. Methods are identified that have the potential to overcome some of the numerical instabilities experienced when using the explicit Euler scheme. This is of particular importance in finance, where martingale dynamics arise frequently and the diffusion coefficients are often multiplicative. Stability regions for a range of schemes are visualized and analysed to provide a methodology for a better understanding of the numerical stability issues that arise from time to time in practice. The result being that schemes that have implicitness in the approximations of both the drift and the diffusion terms exhibit the largest stability regions. Most importantly, it is shown that by refining the time step size one can leave a stability region and may face numerical instabilities, which is not what one is used to experiencing in deterministic numerical analysis. [ABSTRACT FROM AUTHOR]

Log-location-scale distributions are widely used parametric models that have fundamental importance in both parametric and semiparametric frameworks. The likelihood equations based on a Type II censored sample from location-scale distributions do not provide explicit solutions for the para-meters. Statistical software is widely available and is based on iterative methods (such as, Newton Raphson Algorithm, EM algorithm etc.), which require starting values near the global maximum. There are also many situations that the specialized software does not handle. This paper provides a method for determining explicit estimators for the location and scale parameters by approximating the likelihood function, where the method does not require any starting values. The performance of the proposed approximate method for the Weibull distribution and Log-Logistic distributions is compared with those based on iterative methods through the use of simulation studies for a wide range of sample size and Type II censoring schemes. Here we also examine the probability coverages of the pivotal quantities based on asymptotic normality. In addition, two examples are given. [ABSTRACT FROM AUTHOR]

This article assumes the goal of proposing a simulation-based theoretical model comparison methodology with application to two time series road accident models. The model comparison exercise helps to quantify the main differences and similarities between the two models and comprises of three main stages: (1) simulation of time series through a true model with predefined properties; (2) estimation of the alternative model using the simulated data; (3) sensitivity analysis to quantify the effect of changes in the true model parameters on alternative model parameter estimates through analysis of variance, ANOVA. The proposed methodology is applied to two time series road accident models: UCM (unobserved components model) and DRAG (Demand for Road Use, Accidents and their Severity). Assuming that the real data-generating process is the UCM, new datasets approximating the road accident data are generated, and DRAG models are estimated using the simulated data. Since these two methodologies are usually assumed to be equivalent, in a sense that both models accurately capture the true effects of the regressors, we are specifically addressing the modeling of the stochastic trend, through the alternative model. Stochastic trend is the time-varying component and is one of the crucial factors in time series road accident data. Theoretically, it can be easily modeled through UCM, given its modeling properties. However, properly capturing the effect of a non-stationary component such as stochastic trend in a stationary explanatory model such as DRAG is challenging. After obtaining the parameter estimates of the alternative model (DRAG), the estimates of both true and alternative models are compared and the differences are quantified through experimental design and ANOVA techniques. It is observed that the effects of the explanatory variables used in the UCM simulation are only partially captured by the respective DRAG coefficients. This a priori, could be due to multicollinearity but the results of both simulation of UCM data and estimating of DRAG models reveal that there is no significant static correlation among regressors. Moreover, in fact, using ANOVA, it is determined that this regression coefficient estimation bias is caused by the presence of the stochastic trend present in the simulated data. Thus, the results of the methodological development suggest that the stochastic component present in the data should be treated accordingly through a preliminary, exploratory data analysis. [ABSTRACT FROM PUBLISHER]

Based on progressively type-II censored data, the problem of estimating unknown parameters and reliability function of a two-parameter generalized half-normal distribution is considered. Maximum likelihood estimates are obtained by applying expectation-maximization algorithm. Since they do not have closed forms, approximate maximum likelihood estimators are proposed. Several Bayesian estimates with respect to different symmetric and asymmetric loss functions such as squared error, LINEX and general entropy are calculated. The Lindley approximation method is applied to determine Bayesian estimates. Monte Carlo simulations are performed to compare the performances of the different methods. Finally, one real data set is analysed. [ABSTRACT FROM PUBLISHER]

In this article we present a new variance reduction technique for estimating the Value-at-Risk (VaR) of a portfolio of various securities via Monte Carlo (MC) simulation. The technique can be applied for any type of distribution of the risk factors, no matter if light- or heavy-tailed. It consists of a particular variant of importance sampling where the change of measure is obtained by using an approximation to an optimal importance sampling density. Any approximation of the portfolio loss function (such as the popular Delta–Gamma approximation) can be used. An in-depth numerical study in the case of risk factors with light-tailed distributions exhibits a great variance reduction when estimating the probability of large portfolio losses outperforming other known methods. [ABSTRACT FROM PUBLISHER]

This article proposes a fast approximation for the small sample bias correction of the iterated bootstrap. The approximation adapts existing fast approximation techniques of the bootstrapp-value and quantile functions to the problem of estimating the bias function. We show an optimality result which holds under general conditions not requiring an asymptotic pivot. Monte Carlo evidence, from the linear instrumental variable model and the nonlinear GMM, suggest that in addition to its computational appeal and success in reducing the mean and median bias in identified models, the fast approximation provides scope for bias reduction in weakly identified configurations. [ABSTRACT FROM AUTHOR]

This article studies seven different tests of normality. The tests in question are Kolmogorov-Smirnov, Anderson-Darling, Kuiper, Jarque-Bera, Cramer von Mises, Shapiro-Wilk, and Vasicek. Each test is described and power comparisons are made by using Monte Carlo computations under various alternatives. The results are discussed and interpreted separately. [ABSTRACT FROM AUTHOR]

Waisman has obtained the direct correlation function (DCF) for the Yukawa fluid using the mean spherical approximation (MSA). Although his result has been used to obtain the thermodynamic functions of this fluid, the resultant radial distribution function (RDF) has not been calculated. In this study, the RDF is calculated by obtaining the Laplace transforms of the DCF and RDF of this fluid by analytic integration. These Laplace transforms are then converted to Fourier transforms that can be inverted numerically. Results are reported for a value of the decay parameter (z = 1.8) that mimics a Lennard-Jones (LJ) 12-6 fluid and for z = 5, which has been used in perturbation theory. For the cases studied, the RDF at contact is greater for the Yukawa fluid than for the hard-sphere fluid and increases monotonically with decreasing temperature. At low densities, the difference between the hard-sphere and LJ-like Yukawa RDFs is appreciable. However, at high densities this difference is much smaller. The dependence on temperature is stronger for z = 5 than for z = 1.8. A comparison of the MSA results with simulation results is made. The agreement of the MSA results with simulation is good except near contact where the MSA contact value always lies below the MC result. [ABSTRACT FROM AUTHOR]

The Fisher information matrix summarizes the amount of information in the data relative to the quantities of interest. There are many applications of the information matrix in modeling, systems analysis, and estimation, including confidence region calculation, input design, prediction bounds, and "noninformative" priors for Bayesian analysis. This article reviews some basic principles associated with the information matrix, presents a resampling-based method for computing the information matrix together with some new theory related to efficient implementation, and presents some numerical results. The resampling-based method relies on an efficient technique for estimating the Hessian matrix, introduced as part of the adaptive ("second-order") form of the simultaneous perturbation stochastic approximation (SPSA) optimization algorithm. [ABSTRACT FROM AUTHOR]

We develop a likelihood-ratio based procedure for testing for a change in the hazard rate of the patients' survival distribution when the patients enter the trial at random times. We show that the profile log-likelihood ratio process converges weakly to a non-stationary Gaussian process and obtain the upper percentiles of the supremum of the limiting process using an approximation for the tail distribution of the supremum of the Ornstein–Uhlenbeck process. We also discuss the power of the test. [ABSTRACT FROM AUTHOR]

Focuses on a single map of the spread of an innovation produced from a Monte Carlo simulation which is equivalent from the viewpoint of sampling theory to a random sample size on drawn from the set of all possible maps. Recommended practice in the simulation of diffusion; Rationale for repetitive simulation which lies in the statistical behavior of the sampling process.