Inference in Nonlinear Regression
نویسندگان
چکیده
This paper considers inference in a standard nonlinear regression model. We show that the model is non-regular in the sense that test statistics of interest exhibit a discontinuity in their limit distribution as a function of a parameter in the model. The discontinuity occurs when the coe¢ cient of a nonlinear regressor is zero. This paper establishes the asymptotic distributions of the least squares (LS) estimator and LS-based test statistics under sequences of true parameters that drift to the point of discontinuity. Using these asymptotic distributions, we show that standard LS-based con dence intervals (CIs) based on normal critical values and subsampling CIs do not necessarily have correct asymptotic sizes and their asymptotic sizes depend on the speci c form of nonlinearity. We develop new methods to construct CIs with correct asymptotic size the latter is work in progress.
منابع مشابه
The Family of Scale-Mixture of Skew-Normal Distributions and Its Application in Bayesian Nonlinear Regression Models
In previous studies on fitting non-linear regression models with the symmetric structure the normality is usually assumed in the analysis of data. This choice may be inappropriate when the distribution of residual terms is asymmetric. Recently, the family of scale-mixture of skew-normal distributions is the main concern of many researchers. This family includes several skewed and heavy-tailed d...
متن کاملNonlinear Analysis of Nonlinearly Loaded Dipole Antenna in the Frequency Domain Using Fuzzy Inference
In this paper, inference model is proposed so as to analyze nonlinearly loaded dipole antenna. In modeling process, linear and nonlinear behavior of the problem is saved as simple and unchanged membership functions and the effect of incident wave on the induced voltage at different harmonies are then extracted easily. Consequently the model achieved is more efficient than previous studies using...
متن کاملThe Optimal Construction of Instruments in Nonlinear Regression: Implications for Gmm Inference
Interpreted as an instrumental variables estimator, nonlinear least squares constructs its instruments optimally from the explanatory variables using the nonlinear specification of the regression function. This has implications for the use of GMM estimators in nonlinear regression models, including systems of nonlinear regressions, where the explanatory variables are exogenous or predetermined ...
متن کاملImproved Inference for Moving Average Disturbances in Nonlinear Regression Models
This paper proposes an improved likelihood-based method to test for first-order moving average in the disturbances of nonlinear regression models. The proposed method has a third-order distributional accuracy which makes it particularly attractive for inference in small sample sizes models. Compared to commonly used first-order methods such as likelihood ratio and Wald tests which rely on large...
متن کاملADAPTIVE NEURO-FUZZY INFERENCE SYSTEM AND STEPWISE REGRESSION FOR COMPRESSIVE STRENGTH ASSESSMENT OF CONCRETE CONTAINING METAKAOLIN
In the current study two methods are evaluated for predicting the compressive strength of concrete containing metakaolin. Adaptive neuro-fuzzy inference system (ANFIS) model and stepwise regression (SR) model are developed as a reliable modeling method for simulating and predicting the compressive strength of concrete containing metakaolin at the different ages. The required data in training an...
متن کاملBayesian Regression Tree Models for Causal Inference: Regularization, Confounding, and Heterogeneous Effects
This paper develops a semi-parametric Bayesian regression model for estimating heterogeneous treatment effects from observational data. Standard nonlinear regression models, which may work quite well for prediction, can yield badly biased estimates of treatment effects when fit to data with strong confounding. Our Bayesian causal forests model avoids this problem by directly incorporating an es...
متن کامل