Estimation in Linear Models

Estimating ultrasonic time of flight using envelope and quasi maximum likelihood method for damage detection and assessment

Estimating and simulating Weibull models of risk or price durations: An application to ACD models

In this paper a quasi maximum likelihood method for estimating a low order model of a flexible vehicle has been developed and demonstrated. The quasi maximum likelihood method uses a large number of sensors to estimate the parameters and covariance in a method consistent with the maximum likelihood filter-error method. The cost function has been defined in a frequency domain to improve computational efficiency and to enable estimation of an unstable plant. The method has been demonstrated using flight data from the National Aeronautics and Space Administration X-56A Multi-Utility Technology Testbed flex wing tests, which include unstable flutter modes. The method was able to effectively estimate the frequency and damping of the dynamics of the aircraft and generate a transfer function that is useful for control system evaluations.

This article introduces a discrete‐time fractional stochastic volatility model (FSV) based on fractional Gaussian noise. The new model includes the standard stochastic volatility model as a special case and has the same limit as the fractional integrated stochastic volatility (FISV) model, which is the continuous‐time fractional Ornstein–Uhlenbeck process. A simulated maximum likelihood method, which maximizes the time‐domain log‐likelihood function calculated by the importance sampling technique, and a frequency‐domain quasi maximum likelihood method (or quasi Whittle) are employed to estimate the model parameters. Simulation studies suggest that, while both estimation methods can accurately estimate the model, the simulated maximum likelihood method outperforms the quasi Whittle method. As an illustration, we fit the FSV and FISV models with the proposed estimation techniques to the S&P 500 composite index over a sample period spanning 45 years.

An alternative quasi likelihood approach, Bayesian analysis and data-based inference for model specification

Current methods used to analyze time to event data either rely on highly parametric assumptions which result in biased estimates of parameters which are purely chosen out of convenience, or are highly unstable because they ignore the global constraints of the true model. By using Targeted Maximum Likelihood Estimation (TMLE) one may consistently estimate parameters which directly answer the statistical question of interest. Targeted Maximum Likelihood Estimators are substitution estimators, which rely on estimating the underlying distribution. However, unlike other substitution estimators, the underlying distribution is estimated specifically to reduce bias in the estimate of the parameter of interest. We will present here an extension of TMLE for observational time to event data, the Collaborative Targeted Maximum Likelihood Estimator (C-TMLE) for the treatment specific survival curve. Through the use of a simulation study we will show that this method improves on commonly used methods in both robustness and efficiency. In fact, we will show that in certain situations the C-TMLE produces estimates whose mean square error is lower than the semi-parametric efficiency bound. We will also demonstrate that a semi-parametric efficient substitution estimator (TMLE) outperforms a semi-parametric efficient non-substitution estimator (the Augmented Inverse Probability Weighted estimator) in sparse data situations. Lastly, we will show that the bootstrap is able to produce valid 95 percent confidence intervals in sparse data situations, while influence curve based inference breaks down.

In this paper, we introduce the Panel Buffered Threshold Spatial Durbin model, which builds upon the idea of hysteresis. This model extends the Panel Threshold Spatial Durbin model, recently proposed by Wei et al., and offers an alternative to address the issue of sudden jumps between regimes in their model. Parameter estimation is performed using two straightforward approaches: the two-stage least squares method and the quasi-maximum likelihood method. Additionally, we develop a linearity test. We analyze the performance of the proposed estimation and testing procedures through a simulation study. Finally, we present an empirical application that explores the interactions between R&D expenditure, trade, GDP per capita, and their effects on patent applications.

Semiparametric estimation for count data through weighted distributions

Efficient estimation for partially linear varying coefficient models when coefficient functions have different smoothing variables

The derivation of the likelihood function for binary data from two types of main study/validation study designs where model covariates are measured with error is elaborated. Rather than limiting consideration to a restricted family of models with convenient mathematical properties, we suggest that empirical considerations, customized to the data at hand, should drive model choices. The joint likelihood function for the main study, in which the covariates are measured with error, and the validation study, in which they are not, is maximized, and estimation and inference proceeds using standard theory. Although the choice of the measurement error model is driven by empirical considerations, the relatively small validation study sizes typically seen may lead to misspecification, resulting in bias in estimation and inference about exposure-disease relationships. By using a nonparametric form for the measurement error model, the resulting semi-parametric methods suggested by Robins, Rotnitzky, and Zhao (1994, Journal of the American Statistical Association 89, 864-866) and Robins, Hsieh, and Newey (1995, Journal of the Royal Statistical Society, Series B 57, 409-424) are free from bias due to misspecification of the measurement error model, trading efficiency for robustness as usual. These fully and semi-parametric methods are illustrated with a detailed example from a main study/validation study of the health effects of occupational exposure to chemotherapeutics among pharmacists (Valanis et al., 1993, American Journal of Hospital Pharmacy 50, 455-462). A constant, prevalence ratio model for common binary events, with gamma covariate measurement error, is derived and empirically verified by the available data. A careful reanalysis of the data, taking measurement error fully into account, leads to a threefold increase in the log relative risk and no loss of statistical power. The semi-parametric estimates are consistent with the parametric results, providing reassurance that important bias due to misspecification of the measurement error model is unlikely.

When modeling multilevel data, it is important to accurately represent the interdependence of observations within clusters. Ignoring data clustering may result in parameter misestimation. However, it is not well established to what degree parameter estimates are affected by model misspecification when applying missing data techniques (MDTs) to incomplete multilevel data. We compare the performance of three MDTs with incomplete hierarchical data. We consider the impact of imputation model misspecification on the quality of parameter estimates by employing multiple imputation under assumptions of a normal model (MI/NM) with two-level cross-sectional data when values are missing at random on the dependent variable at rates of 10%, 30%, and 50%. Five criteria are used to compare estimates from MI/NM to estimates from MI assuming a linear mixed model (MI/LMM) and maximum likelihood estimation to the same incomplete data sets. With 10% missing data (MD), techniques performed similarly for fixed-effects estimates, but variance components were biased with MI/NM. Effects of model misspecification worsened at higher rates of MD, with the hierarchical structure of the data markedly underrepresented by biased variance component estimates. MI/LMM and maximum likelihood provided generally accurate and unbiased parameter estimates but performance was negatively affected by increased rates of MD.

In maximum likelihood estimation, the real but unknown innovation distribution is often replaced by a nonparametric estimate, and thus the estimation procedure becomes semiparametric. These semiparametric approaches generally involve two steps: the first step that incorporate an initial estimate of the model parameter to produce a residual sample, and the second step that uses the residuals to estimate the likelihood, which is subsequently maximized to obtain the final estimate of the model parameter. Therefore, the characteristics of the initial input estimator may be carried over to the final semiparametric estimator, and the performance of the semiparametric estimator will be impaired if the input estimate is deficient. In this article we have studied a onestep semiparametric estimator where no initial input is necessary. The estimation procedure is illustrated via a generalized autoregressive conditional heteroskedasticity (GARCH) model. Asymptotic properties of the estimator are established, and finite sample performance of the estimator is evaluated via simulation. The results suggest that the proposed one-step semiparametric estimator avoids significant drawbacks of its two-step counterparts. (JEL: C02, C22, C51)

Recurrent events, including cardiovascular events, are commonly observed in biomedical studies. Understanding the effects of various treatments on recurrent events and investigating the underlying mediation mechanisms by which treatments may reduce the frequency of recurrent events are crucial tasks for researchers. Although causal inference methods for recurrent event data have been proposed, they cannot be used to assess mediation. This study proposed a novel methodology of causal mediation analysis that accommodates recurrent outcomes of interest in a given individual. A formal definition of causal estimands (direct and indirect effects) within a counterfactual framework is given, and empirical expressions for these effects are identified. To estimate these effects, a semiparametric estimator with triple robustness against model misspecification was developed. The proposed methodology was demonstrated in a real-world application. The method was applied to measure the effects of two diabetes drugs on the recurrence of cardiovascular disease and to examine the mediating role of kidney function in this process.

I consider the problem of estimating an additive partially linear model using general series estimation methods with polynomial and splines as two leading cases. I show that the finite‐dimensional parameter is identified under weak conditions. I establish the root‐n‐normality result for the finite‐dimensional parameter in the linear part of the model and show that it is asymptotically more efficient than a semiparametric estimator that ignores the additive structure. When the error is conditional homoskedastic, my finite‐dimensional parameter estimator reaches the semiparametric efficiency bound. Efficient estimation when the error is conditional heteroskedastic is also discussed.

Overall Rates and Sample Selection: Inferring HIV Prevalence from a Selected Sample