Distance-based estimation under progressive type-i interval censoring

In the present paper a mixed approach is proposed for the simultaneously estimation of regression and correlation structure parameters in multivariate probit models using generalized estimating equations for the former and pseudo-score equations for the latter. The finite sample properties of the corresponding estimators are compared to estimators proposed by Qu, Williams, Beck and Medendorp (1992) and Qu, Piedmonte and Williams (1994) using generalized estimating equations for both sets of parameters via a Monte Carlo experiment. As a `reference' estimator for an equicorrelation model, the maximum likelihood (ML) estimator of the random effects probit model is calculated. The results show the mixed approach to be the most robust approach in the sense that the number of datasets for which the corresponding estimates converged was largest relative to the other two approaches. Furthermore, the mixed approach led to the most efficient non-ML estimators and to very efficient estimators for regression and correlation structure parameters relative to the ML estimator if individual covariance matrices were used.

Estimation of the female labor supply models by Heckman’s two-step estimator and the maximum likelihood estimator

Estimation of Markov regime-switching regression models with endogenous switching

Latent growth models (LGMs) are an application of structural equation modeling and frequently used in developmental and clinical research to analyze change over time in longitudinal outcomes. Maximum likelihood (ML), the most common approach for estimating LGMs, can fail to converge or may produce biased estimates in complex LGMs especially in studies with modest samples. Bayesian estimation is a logical alternative to ML for LGMs, but there is a lack of research providing guidance on when Bayesian estimation may be preferable to ML or vice versa. This study compared the performance of Bayesian versus ML estimators for LGMs by evaluating their accuracy via Monte Carlo (MC) simulations. For the MC study, longitudinal data sets were generated and estimated using LGM via both ML and Bayesian estimation with three different priors, and parameter recovery across the two estimators was evaluated to determine their relative performance. The findings suggest that ML estimation is a reasonable choice for most LGMs, unless it fails to converge, which can occur with limiting data situations (i.e., just a few time points, no covariate or outcome, modest sample sizes). When models do not converge using ML, we recommend Bayesian estimation with one caveat that the influence of the priors on estimation may have to be carefully examined, per recent recommendations on Bayesian modeling for applied researchers.

It is well known that, in misspecified parametric models, the maximum likelihood estimator (MLE) is consistent for the pseudo-true value and has an asymptotically normal sampling distribution with “sandwich” covariance matrix. Also, posteriors are asymptotically centered at the MLE, normal, and of asymptotic variance that is, in general, different than the sandwich matrix. It is shown that due to this discrepancy, Bayesian inference about the pseudo-true parameter value is, in general, of lower asymptotic frequentist risk when the original posterior is substituted by an artificial normal posterior centered at the MLE with sandwich covariance matrix. An algorithm is suggested that allows the implementation of this artificial posterior also in models with high dimensional nuisance parameters which cannot reasonably be estimated by maximizing the likelihood.

The binary logistic regression model (LRM) is practical in situations when the response variable (RV) is dichotomous. The maximum likelihood estimator (MLE) is generally considered to estimate the LRM parameters. However, in the presence of multicollinearity (MC), the MLE is not the correct choice due to its inflated standard deviation (SD) and standard errors (SE) of the estimates. To combat MC, commonly used biased estimators, i.e., the Ridge estimators (RE) and Liu estimators (LEs), are preferred. However, most of the time, the traditional LE attains a negative value for its Liu parameter (LP), which is considered to be a major drawback. Therefore, to overcome this issue, we proposed a new adjusted LE for the binary LRM. Owing to numerical evaluation purposes, Monte Carlo simulation (MCS) study is performed under different conditions where bias and mean squared error are the performance criteria. Findings showed the superiority of our proposed estimator in comparison with the other estimation methods due to the existence of high but imperfect multicollinearity, which clearly means that it is consistent when the regressors are multicollinear. Furthermore, the findings demonstrated that whenever there is MC, the MLE is not the best choice. Finally, a real application is being considered to be evidence for the advantage of the intended estimator. The MCS and the application findings pointed out that the considered adjusted LE for the binary logistic regression model is a more efficient estimation method whenever the regressors are highly multicollinear.

This paper proposes a method that uses mean square error (MSE) and model confidence set (MCS) as the loss function of back‐propagation neural network (BPNN), aiming to train and find a generalized autoregressive conditional heteroskedastic (GARCH) model that has the best forecasting performance of a time series. Combining MSE and the p‐value of MCS can not only estimate better parameters for the GARCH models but also find the best GARCH model to forecast the volatility of a time series. Meanwhile, we divide a time series into several parts and use each part as the input of the BPNN. Through the BPNN, each part of the time series will be turned into several forecasting values. These values will be used to calculate the MSE and the p‐value of MCS, which will then be used to update the parameters of the BPNN. In the end, we use MCS to choose the best GARCH model among the trained GARCH models and compare this method with maximum likelihood estimation (MLE) and the generalized least squares estimation (GLS). The result shows that the p‐value of MCS of the best model estimated by this method is higher than the p‐value of MCS of the best model estimated by MLE and GLS. According to the theory of MCS, a model that has a larger p‐value does have a better forecasting performance. The method proposed by this paper can provide a potential application of neural network in GARCH model forecasting and estimation.

In this article, we consider the estimation of the stress-strength reliability parameter for the inverse Lindley distribution based on lower record values. The maximum likelihood estimator and its asymptotic distribution are obtained. An approximate classical confidence interval, as well as two bootstrap-type confidence intervals for the reliability parameter are derived. The Bayesian inference for the parameter has been considered using Tierney and Kadane’s approximation method, as well as two Monte Carlo methods, namely the Metropolis-Hastings and importance sampling techniques under both symmetric and asymmetric loss functions. Besides, the Chen and Shao shortest width credible intervals are constructed for the stress-strength parameter. A simulation study and a real data example are conducted to explore and compare the performances of the presented results.

This paper presents a novel framework for maximum likelihood (ML) estimation in skew-t factor analysis (STFA) models in the presence of missing values or nonresponses. As a robust extension of the ordinary factor analysis model, the STFA model assumes a restricted version of the multivariate skew-t distribution for the latent factors and the unobservable errors to accommodate non-normal features such as asymmetry and heavy tails or outliers. An EM-type algorithm is developed to carry out ML estimation and imputation of missing values under a missing at random mechanism. The practical utility of the proposed methodology is illustrated through real and synthetic data examples.

ABSTRACTIn this article, we propose mixtures of skew Laplace normal (SLN) distributions to model both skewness and heavy-tailedness in the neous data set as an alternative to mixtures of skew Student-t-normal (STN) distributions. We give the expectation–maximization (EM) algorithm to obtain the maximum likelihood (ML) estimators for the parameters of interest. We also analyze the mixture regression model based on the SLN distribution and provide the ML estimators of the parameters using the EM algorithm. The performance of the proposed mixture model is illustrated by a simulation study and two real data examples.

In this paper, we offer generalized exponentiated gamma distribution. We consider the maximum likelihood and Bayesian estimators of unknown parameters and propose Markov chain Monte Carlo (MCMC) method to generate samples from the posterior distribution. The mean square error of estimations is computed and comparisons are made using Monte Carlo simulation. Key words: Maximum likelihood estimator, Bayesian estimator, squared error loss function, generalized exponentiated gamma distribution.

In this work, we addressed parameter estimation and prediction in the high-dimensional sparse logistic regression model through both Monte Carlo simulations and application to real data. We applied two well-known penalized maximum likelihood (ML) methods (LASSO and aLASSO) for variable screening. There may exist overfitting from LASSO or underfitting from aLASSO, making ML estimators based on these models inefficient. Hence, after performing variable selection, we proposed post-selection improved estimation based on linear shrinkage, pretest, and James-Stein shrinkage strategies, which efficiently combine overfitted and underfitted ML estimators. Regardless of the correctness in the variable selection stage, the proposed estimators were shown to be more efficient than the classical ML estimators, which were severely affected by inappropriate variable selection.

Estimation and Inference for Linear Panel Data Models under Misspecification when Both N and T are Large

We consider the problem of maximum likelihood estimation of logistic sinusoidal regression models and develop some asymptotic theory including the consistency and joint rates of convergence for the maximum likelihood estimators. The key techniques build upon a synthesis of the results of Walker and Song and Li for the widely studied sinusoidal regression model and on making a connection to a result of Radchenko. Monte Carlo simulations are also presented to demonstrate the finite-sample performance of the estimators

Bayesian estimation of the mixture of Burr Type-XII distributions using doubly censored data