Risk Of Model Misspecification Research Articles

Model detection for semiparametric accelerated failure additive model with right-censored data.

Censored data frequently appeared in applications across a variety of different areas like epidemiology or medical research. Traditionally statistical inference on this data mechanism was based on some pre-assigned models that will suffer from the risk of model-misspecification. This article proposes a two-folded shrinkage procedure for simultaneous structure identification and variable selection of the semiparametric accelerated failure additive model with right-censored data, in which the nonparametric functions are addressed by spline approximation. Under some regularity conditions, the consistency of model structure identification is theoretically established in the sense that the proposed method can automatically separate the linear and zero components from the nonlinear ones with probability approaching to one. Detailed issues in computation and turning parameter selection are also discussed. Finally, we illustrate the proposed method by some simulation studies and two real data applications to the primary biliary cirrhosis data and skin cutaneous melanoma data.

Estimating average treatment effect on the treated via sufficient dimension reduction

In this paper, we propose to use sufficient dimension reduction (SDR) in conjunction with nonparametric techniques to estimate the average treatment effect on the treated (ATT), a parameter of common interest in causal inference. The proposed method is applicable under a general low‐dimensional structure in the data, and avoids both the risk of model misspecification and the “curse of dimensionality,” for which it often outperforms the existing parametric and nonparametric methods. We develop the theoretical properties of the proposed method, including its asymptotic normality, its asymptotic super‐efficiency, and its equivalent form as an augmented inverse probability weighting estimator. We also consider the impact of SDR estimation in the asymptotic studies. These theoretical results are further illustrated by the simulation studies at the end.

A three-parameter logistic regression model

Dose–response experiments and data analyses are often carried out according to an optimal design under a model assumption. A two-parameter logistic model is often used because of its nice mathematical properties and plausible stochastic response mechanisms. There is an extensive literature on its optimal designs and data analysis strategies. However, a model is at best a good approximation in a real-world application, and researchers must be aware of the risk of model mis-specification. In this paper, we investigate the effectiveness of the sequential ED-design, the D-optimal design, and the up-and-down design under the three-parameter logistic regression model, and we develop a numerical method for the parameter estimation. Simulations show that the combination of the proposed model and the data analysis strategy performs well. When the logistic model is correct, this more complex model has hardly any efficiency loss. The three-parameter logistic model works better than the two-parameter logistic model in the presence of model mis-specification.

Statistical Inference Based on Accelerated Failure Time Models Under Model Misspecification and Small Samples

–Accelerated failure time (AFT) models give an intuitive estimator for survival data analysis, but there is a risk of model misspecification. As a serious problem of model misspecification, the test size is likely to be far from the nominal level. Many researchers provided asymptotic corrections of various test statistics under model misspecification. However, their corrected statistics do not have good performance in small samples; in particular, they cause an inflation of test size. Although, the Bartlett adjustment is a popular approach for small-sample correction of the likelihood ratio statistic under the null hypothesis, it is impossible to derive the adjustment factor analytically under model misspecification. In this article, we proposed a robust test to model misspecification in small samples. Our proposed method is based on the Bartlett adjustment and we used the nonparametric bootstrap method to estimate the adjustment factor. We applied the proposed method to the AFT models when the error distribution and/or mean structure are misspecified in small samples. Our simulation results showed that the test size for the proposed method was close to the nominal level, although the existing methods resulted in substantial inflation of the test size. We illustrated our proposed method using two empirical examples.

A mixture model-based nonparametric approach to estimating a count distribution

The density of a mixture distribution with unknown discrete mixing distribution can be a way of finding a nonparametric estimate of a density. Comparing with a standard parametric approach that runs the risk of model misspecification and a kernel-based nonparametric approach that retains all data points for constructing a density estimate, this mixture model-based nonparametric approach that naturally circumvents these problems is very appealing to density estimation. Owing to these advantages, this approach to estimating a count distribution is considered. Estimation of a count distribution via this means necessarily involves the problem of nonparametric estimation of a discrete mixing distribution. The nonparametric estimation problem is formulated using the family of power divergences, thus offering a class of nonparametric estimators of a discrete mixing distribution. A fast algorithm is presented for computing the class of nonparametric minimum power divergence estimates with which the corresponding class of mixture model-based estimates of a count distribution can be implemented. Only the use of the probability mass function of the Poisson mixture distribution with unknown discrete mixing distribution is illustrated. The simulation results show that the mixture model-based estimators on average outperform the kernel-based estimators for uncontaminated samples of larger sizes and contaminated samples of all sizes considered.

Modelling of count data using nonparametric mixtures

Nonparametric modelling of count data is partly motivated by the fact that using parametric count models not only runs the risk of model misspecification but also is rather restrictive in terms of local approximation. Accordingly, we present a framework of using nonparametric mixtures for flexible modelling of count data. We consider the use of the least squares function in nonparametric mixture modelling and provide two algorithms for least squares fitting of nonparametric mixtures. Two illustrations of the framework are given, each with a particular nonparametric mixture. One illustration is the use of the nonparametric Poisson mixture for general modelling purposes. The other illustration is concerned with modelling of count data from some decreasing distribution, in which the Poisson mixture distribution is less appropriate, for its fitted distribution might not be a decreasing distribution. We define a mixture distribution called the discrete decreasing beta mixture distribution that always has fitted probabilities conforming with the assumption of decreasing probabilities. Through numerical studies, we demonstrate the performance of nonparametric mixtures as modelling tools.

A Note on the Identification of Dynamic Economic Models with Generalized Shock Processes

AbstractDynamic stochastic general equilibrium (DSGE) models with generalized shock processes, such as shock processes which follow a vector autoregression (VAR), have been an active area of research in recent years. Unfortunately, the structural parameters governing DSGE models are not identified when the driving process behind the model follows an unrestricted VAR. This finding implies that parameter estimates derived from recent attempts to estimate DSGE models with generalized driving processes should be treated with caution, and that there always exists a tradeoff between identification and the risk of model misspecification. However, these results also make it easier to address the issue of model misspecification by making it computationally easier to check the validity of cross‐equation restrictions.

Bias analysis and the simulation‐extrapolation method for survival data with covariate measurement error under parametric proportional odds models

It has been well known that ignoring measurement error may result in substantially biased estimates in many contexts including linear and nonlinear regressions. For survival data with measurement error in covariates, there has been extensive discussion in the literature with the focus on proportional hazards (PH) models. Recently, research interest has extended to accelerated failure time (AFT) and additive hazards (AH) models. However, the impact of measurement error on other models, such as the proportional odds model, has received relatively little attention, although these models are important alternatives when PH, AFT, or AH models are not appropriate to fit data. In this paper, we investigate this important problem and study the bias induced by the naive approach of ignoring covariate measurement error. To adjust for the induced bias, we describe the simulation-extrapolation method. The proposed method enjoys a number of appealing features. Its implementation is straightforward and can be accomplished with minor modifications of existing software. More importantly, the proposed method does not require modeling the covariate process, which is quite attractive in practice. As the precise values of error-prone covariates are often not observable, any modeling assumption on such covariates has the risk of model misspecification, hence yielding invalid inferences if this happens. The proposed method is carefully assessed both theoretically and empirically. Theoretically, we establish the asymptotic normality for resulting estimators. Numerically, simulation studies are carried out to evaluate the performance of the estimators as well as the impact of ignoring measurement error, along with an application to a data set arising from the Busselton Health Study. Sensitivity of the proposed method to misspecification of the error model is studied as well.

Nonparametric and semiparametric optimal transformations of markers

The receiver operating characteristic (ROC) curve of a likelihood-ratio function has been shown to be the highest among all transformations of continuous markers. For any sampling scheme with the same likelihoods, the induced conditional probability is derived to have the same ROC curve and is found to be more useful for inference purposes. To compromise the difficult task of high-dimensionality in fully nonparametric models and the risk of model misspecification in fully parametric ones, an appealing single-index model is also adopted in our optimization problem. Based on a nonparametric estimator of the area under the ROC curve (AUC), we develop its related inferences and provide some simple and easily checked conditions for the validity of asymptotic results. Since the optimal marker is estimated by using a semiparametric or nonparametric model, conventional theoretical approaches might be inappropriate to some circumstances. The applicability of our procedures are further demonstrated through extensive numerical experiments and data from the studies of Pima–Indian diabetes and liver disorders.

Dimension reduced kernel estimation for distribution function with incomplete data

This work focuses on the estimation of distribution functions with incomplete data, where the variable of interest Y has ignorable missingness but the covariate X is always observed. When X is high dimensional, parametric approaches to incorporate X—information is encumbered by the risk of model misspecification and nonparametric approaches by the curse of dimensionality. We propose a semiparametric approach, which is developed under a nonparametric kernel regression framework, but with a parametric working index to condense the high dimensional X—information for reduced dimension. This kernel dimension reduction estimator has double robustness to model misspecification and is most efficient if the working index adequately conveys the X—information about the distribution of Y. Numerical studies indicate better performance of the semiparametric estimator over its parametric and nonparametric counterparts. We apply the kernel dimension reduction estimation to an HIV study for the effect of antiretroviral therapy on HIV virologic suppression.