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Register a new userH-relative error estimation approach for multiplicative regression model with random effect
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Added by
Zimu Chen
Publication date
2017
fields
Mathematical Statistics
and research's language is
English
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Relative error approaches are more of concern compared to absolute error ones such as the least square and least absolute deviation, when it needs scale invariant of output variable, for example with analyzing stock and survival data. An h-relative error estimation method via the h-likelihood is developed to avoid heavy and intractable integration for a multiplicative regression model with random effect. Statistical properties of the parameters and random effect in the model are studied. To estimate the parameters, we propose an h-relative error computation procedure. Numerical studies including simulation and real examples show the proposed method performs well.
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A product relative error estimation method for single index regression model is proposed as an alternative to absolute error methods, such as the least square estimation and the least absolute deviation estimation. It is scale invariant for outcome and covariates in the model. Regression coefficients are estimated via a two-stage procedure and their statistical properties such as consistency and normality are studied. Numerical studies including simulation and a body fat example show that the proposed method performs well.
Model uncertainty quantification is an essential component of effective data assimilation. Model errors associated with sub-grid scale processes are often represented through stochastic parameterizations of the unresolved process. Many existing Stochastic Parameterization schemes are only applicable when knowledge of the true sub-grid scale process or full observations of the coarse scale process are available, which is typically not the case in real applications. We present a methodology for estimating the statistics of sub-grid scale processes for the more realistic case that only partial observations of the coarse scale process are available. Model error realizations are estimated over a training period by minimizing their conditional sum of squared deviations given some informative covariates (e.g. state of the system), constrained by available observations and assuming that the observation errors are smaller than the model errors. From these realizations a conditional probability distribution of additive model errors given these covariates is obtained, allowing for complex non-Gaussian error structures. Random draws from this density are then used in actual ensemble data assimilation experiments. We demonstrate the efficacy of the approach through numerical experiments with the multi-scale Lorenz 96 system using both small and large time scale separations between slow (coarse scale) and fast (fine scale) variables. The resulting error estimates and forecasts obtained with this new method are superior to those from two existing methods.
A least product relative error criterion is proposed for multiplicative regression models. It is invariant under scale transformation of the outcome and covariates. In addition, the objective function is smooth and convex, resulting in a simple and uniquely defined estimator of the regression parameter. It is shown that the estimator is asymptotically normal and that the simple plugging-in variance estimation is valid. Simulation results confirm that the proposed method performs well. An application to body fat calculation is presented to illustrate the new method.
In this paper, we built a new nonparametric regression estimator with the local linear method by using the mean squared relative error as a loss function when the data are subject to random right censoring. We establish the uniform almost sure consistency with rate over a compact set of the proposed estimator. Some simulations are given to show the asymptotic behavior of the estimate in different cases.
Multilevel regression and poststratification (MRP) is a flexible modeling technique that has been used in a broad range of small-area estimation problems. Traditionally, MRP studies have been focused on non-causal settings, where estimating a single population value using a nonrepresentative sample was of primary interest. In this manuscript, MRP-style estimators will be evaluated in an experimental causal inference setting. We simulate a large-scale randomized control trial with a stratified cluster sampling design, and compare traditional and nonparametric treatment effect estimation methods with MRP methodology. Using MRP-style estimators, treatment effect estimates for areas as small as 1.3$%$ of the population have lower bias and variance than standard causal inference methods, even in the presence of treatment effect heterogeneity. The design of our simulation studies also requires us to build upon a MRP variant that allows for non-census covariates to be incorporated into poststratification.
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