Parameter estimation in a verhulst stochastic model

Summary Maximum likelihood estimation is a well-known statistical tool. When applied to the study of dynamical continuous-time phenomena, it requires some specific assumptions. In this paper we discuss some properties of the maximum likelihood estimator for a stochastic Verhulst model and we show some simulation results on the behaviour of the corresponding discrete estimator.     

Statistical inference for a relaxation index of stochastic dominance under density ratio model

Stochastic dominance is usually used to rank random variables by comparing their distributions, so it is widely applied in economics and finance. In actual applications, complete stochastic dominance is too demanding to meet, so relaxation indexes of stochastic dominance have attracted more attention. The π index, the biggest gap between two distributions, can be a measure of the degree of deviation from complete dominance. The traditional estimation method is to use the empirical distribution functions to estimate it. Considering the populations under comparison are generally of the same nature, we can link the populations through density ratio model under certain condition. Based on this model, we propose a new estimator and establish its statistical inference theory. Simulation results show that the proposed estimator substantially improves estimation efficiency and power of the tests and coverage probabilities satisfactorily match the confidence levels of the tests, which show the superiority of the proposed estimator. Finally we apply our method to a real example of the Chinese household incomes.     

The analysis of partially-censored date from a fitst-order semi-markov model

This paper describes a Fortran program for analyzing partially-censored data from a firstorder semi-Markov model. Nonparametric maximum likelihood estimates and estimates of their corresponding covariance matrices are computed based on the results of Lagakos, Sornmer and Zelen (1978). The program can be applied to data arising from a wide array of multistate stochastic processes. The program's required input and output are discussed and illustrated using the data from a recent lung cancer clinical trial.     

A stochastic variant of the EM algorithm to fit mixed (discrete and continuous) longitudinal data with nonignorable missingness

Abstract

In longitudinal studies data are collected on the same set of units for more than one occasion. In medical studies it is very common to have mixed Poisson and continuous longitudinal data. In such studies, for different reasons, some intended measurements might not be available resulting in a missing data setting. When the probability of missingness is related to the missing values, the missingness mechanism is termed nonrandom. The stochastic expectation-maximization (SEM) algorithm and the parametric fractional imputation (PFI) method are developed to handle nonrandom missingness in mixed discrete and continuous longitudinal data assuming different covariance structures for the continuous outcome. The proposed techniques are evaluated using simulation studies. Also, the proposed techniques are applied to the interstitial cystitis data base (ICDB) data.     

Preservation properties of stochastic orders by transformation to the transmuted-G model

Abstract

The transmuted-G model is a useful technique to construct some new distributions by adding a parameter. This paper considers stochastic comparisons in the transmuted-G family with different parameters and different baseline distributions in the sense of the usual stochastic, shifted stochastic, proportional stochastic and shifted proportional stochastic orders. Also, we present a necessary and sufficient condition for existence of the moments of the transmuted-G model and then we obtain some bounds for the survival and aging intensity functions of the transmuted-G model conditioned on its parameter and its baseline distribution.     

Simultaneous Modelling of Survival and Longitudinal Data with an Application to Repeated Quality of Life Measures

In biomedical studies, interest often focuses on the relationship between patients characteristics or some risk factors and both quality of life and survival time of subjects under study. In this paper, we propose a simultaneous modelling of both quality of life and survival time using the observed covariates. Moreover, random effects are introduced into the simultaneous models to account for dependence between quality of life and survival time due to unobserved factors. EM algorithms are used to derive the point estimates for the parameters in the proposed model and profile likelihood function is used to estimate their variances. The asymptotic properties are established for our proposed estimators. Finally, simulation studies are conducted to examine the finite-sample properties of the proposed estimators and a liver transplantation data set is analyzed to illustrate our approaches.     

Using a correlated probit model approximation to estimate the variance for binary matched pairs

A correlated probit model approximation for conditional probabilities (Mendell and Elston 1974) is used to estimate the variance for binary matched pairs data by maximum likelihood. Using asymptotic data, the bias of the estimates is shown to be small for a wide range of intra-class correlations and incidences. This approximation is also compared with other recently published, or implemented, improved approximations. For the small sample examples presented, it shows a substantial advantage over other approximations. The method is extended to allow covariates for each observation, and fitting by iteratively reweighted least squares.     

Application of 'delete = replace' to deletion diagnostics for variance component estimation in the linear mixed model

Summary.  'Delete = replace' is a powerful and intuitive modelling identity. This paper extends previous work by stating and proving the identity in more general terms and extending its application to deletion diagnostics for estimates of variance components obtained by restricted maximum likelihood estimation for the linear mixed model. We present a new, fast, transparent and approximate computational procedure, arising as a by-product of the fitting process. We illustrate the effect of the deletion of individual observations, of 'subjects' and of arbitrary subsets. Central to the identity and its application is the conditional residual.     

Exact and stochastic nonlinear constrained estimation in the conditional poisson log-linear model

A minimum chi-square estimator of the conditional Poisson log-linear model parameters subject to exact and stochastic nonlinear constraints is defined. The Wald test is used to evaluate the exact and stochastic constraints.     

Effects of omitting a covariate in poisson models when the data are balanced

The authors show that for balanced data, the estimates of effects of interest and of their standard errors are unaffected when a covariate is removed from a multiplicative Poisson model. As they point out, this is not verified in the analogous linear model, nor in the logistic model. In the first case, only the estimated coefficients remain the same, while in the second case, both the estimated effects and their standard errors can change.     

GMM estimation of a realized stochastic volatility model: A Monte Carlo study

This article investigates alternative generalized method of moments (GMM) estimation procedures of a stochastic volatility model with realized volatility measures. The extended model can accommodate a more general correlation structure. General closed form moment conditions are derived to examine the model properties and to evaluate the performance of various GMM estimation procedures under Monte Carlo environment, including standard GMM, principal component GMM, robust GMM and regularized GMM. An application to five company stocks and one stock index is also provided for an empirical demonstration.     

On computing estimates of a change-point in the Weibull regression hazard model

The hazard function describes the instantaneous rate of failure at a time t, given that the individual survives up to t. In applications, the effect of covariates produce changes in the hazard function. When dealing with survival analysis, it is of interest to identify where a change point in time has occurred. In this work, covariates and censored variables are considered in order to estimate a change-point in the Weibull regression hazard model, which is a generalization of the exponential model. For this more general model, it is possible to obtain maximum likelihood estimators for the change-point and for the parameters involved. A Monte Carlo simulation study shows that indeed, it is possible to implement this model in practice. An application with clinical trial data coming from a treatment of chronic granulomatous disease is also included.     

Additional comparisons of designs to estimate variance components in a two-way classification model

In this paper, the research of Muse and Anderson is extended to include additional comparisons of designs, featuring planned unbalance, for the estimation of variance components in a two-way cross classification model. Their results are extended to Include the following: (i) a small sample study of the original off-diagonal (OD) design and (ii) an asymptotic maximum likelihood investigation of three modifica-tions of the balanced diagonal rectangles (BD) design and one modification of the 01) design to permit the estimation of row, column, interaction and error variance components. Also a general iterative least.     

Exact and Approximate Distributions of the Maximum Likelihood Estimate in a Simple Factor Analysis Model

We study a factor analysis model with two normally distributed observations and one factor. In the case when the errors have equal variance, the maximum likelihood estimate of the factor loading is given in closed form. Exact and approximate distributions of the maximum likelihood estimate are considered. The exact distribution function is given in a complex form that involves the incomplete Beta function. Approximations to the distribution function are given for the cases of large sample sizes and small error variances. The accuracy of the approximations is discussed     

Estimation and tests of hypotheses for the initial mean and covariance in the kalman filter model

Kalman filtering techniques are widely used by engineers to recursively estimate random signal parameters which are essentially coefficients in a large-scale time series regression model. These Bayesian estimators depend on the values assumed for the mean and covariance parameters associated with the initial state of the random signal. This paper considers a likelihood approach to estimation and tests of hypotheses involving the critical initial means and covariances. A computationally simple convergent iterative algorithm is used to generate estimators which depend only on standard Kalman filter outputs at each successive stage. Conditions are given under which the maximum likelihood estimators are consistent and asymptotically normal. The procedure is illustrated using a typical large-scale data set involving 10-dimensional signal vectors.     

Fairness of the national health service in Italy: a bivariate correlated random effects model

The primary purpose of this paper is to comprehensively assess households’ burden due to health payments. Starting from the fairness approach developed by the World Health Organization, we analyse the burden of healthcare payments on Italian households by modeling catastrophic payments and impoverishment due to healthcare expenditures. For this purpose, we propose to extend the analysis of fairness in financing contribution through a generalized linear mixed models by introducing a bivariate correlated random effects model, where association between the outcomes is modeled through individual- and outcome-specific latent effects which are assumed to be correlated. We discuss model parameter estimation in a finite mixture context. By using such model specification, the fairness of the Italian national health service is investigated.     

Identifiability and bias reduction in the skew-probit model for a binary response

The skew-probit link function is one of the popular choices for modelling the success probability of a binary variable with regard to covariates. This link deviates from the probit link function in terms of a flexible skewness parameter. For this flexible link, the identifiability of the parameters is investigated. Next, to reduce the bias of the maximum likelihood estimator of the skew-probit model we propose to use the penalized likelihood approach. We consider three different penalty functions, and compare them via extensive simulation studies. Based on the simulation results we make some practical recommendations. For the illustration purpose, we analyse a real dataset on heart-disease.     

The unconditional distributions of the OLS,TSLS and LIML estimators in a simple structural equations model

The exact distributions of the standard estimators of the structural coe?cients in a linear structural equations model conditional on the exogenous variables have been shown to have some unexpected and quirky features. Since the argument for conditioning on exogenous (ancillary) variables has been weakened over the past 20 years by the discovery of an “ancillarity paradox,” it is natural to wonder whether such finite sample properties are in fact due to conditioning on the exogenous variables. This article studies the exact distributions of the ordinary least squares (OLS), two-stage least squares (TSLS), and limited information maximum likelihood (LIML) estimators of the structural coe?cients in a linear structural equation without conditioning on the exogenous variables.