Related papers: A two-stage estimation procedure for non-linear st…
In fitting a mixture of linear regression models, normal assumption is traditionally used to model the error and then regression parameters are estimated by the maximum likelihood estimators (MLE). This procedure is not valid if the normal…
Traditionally, spline or kernel approaches in combination with parametric estimation are used to infer the linear coefficient (fixed effects) in a partially linear mixed-effects model for repeated measurements. Using machine learning…
We propose a two-stage penalized least squares method to build large systems of structural equations based on the instrumental variables view of the classical two-stage least squares method. We show that, with large numbers of endogenous…
The additive partially linear model (APLM) combines the flexibility of nonparametric regression with the parsimony of regression models, and has been widely used as a popular tool in multivariate nonparametric regression to alleviate the…
In this paper, different strands of literature are combined in order to obtain algorithms for semi-parametric estimation of discrete choice models that include the modelling of unobserved heterogeneity by using mixing distributions for the…
Latent variable (LV) models are widely used in psychological research to investigate relationships among unobservable constructs. When one-stage estimation of the overall LV model is challenging, two-stage factor score regression (FSR)…
This paper focuses on the system identification of an important class of nonlinear systems: linearly parameterized nonlinear systems, which enjoys wide applications in robotics and other mechanical systems. We consider two system…
A non linear regression approach which consists of a specific regression model incorporating a latent process, allowing various polynomial regression models to be activated preferentially and smoothly, is introduced in this paper. The model…
State-space models are ubiquitous in the statistical literature since they provide a flexible and interpretable framework for analyzing many time series. In most practical applications, the state-space model is specified through a…
Differential graphical models are designed to represent the difference between the conditional dependence structures of two groups, thus are of particular interest for scientific investigation. Motivated by modern applications, this…
The problem of estimating a linear functional based on observational data is canonical in both the causal inference and bandit literatures. We analyze a broad class of two-stage procedures that first estimate the treatment effect function,…
An algorithm for non-stationary spatial modelling using multiple secondary variables is developed. It combines Geostatistics with Quantile Random Forests to give a new interpolation and stochastic simulation algorithm. This paper introduces…
A Two-Stage approach is described that literally "straighten outs" any potentially nonlinear relationship between a y-outcome variable and each of p = 2 or more potential x-predictor variables. The y-outcome is then predicted from all p of…
We develop estimation and inference methods for a stylized macroeconomic model with potentially multiple behavioural equilibria, where agents form expectations using a constant-gain learning rule. We first show geometric ergodicity of the…
Real-time nonlinear Bayesian filtering algorithms are overwhelmed by data volume, velocity and increasing complexity of computational models. In this paper, we propose a novel ensemble based nonlinear Bayesian filtering approach which only…
We introduce the Locally Linear Latent Variable Model (LL-LVM), a probabilistic model for non-linear manifold discovery that describes a joint distribution over observations, their manifold coordinates and locally linear maps conditioned on…
We present a method of parameter estimation for large class of nonlinear systems, namely those in which the state consists of output derivatives and the flow is linear in the parameter. The method, which solves for the unknown parameter by…
We study the parameter estimation method for linear regression models with possibly skewed stable distributed errors. Our estimation procedure consists of two stages: first, for the regression coefficients, the Cauchy quasi-maximum…
Measurement error is ubiquitous in many variables - from blood pressure recordings in physiology to intelligence measures in psychology. Structural equation models (SEMs) account for the process of measurement by explicitly distinguishing…
Statistical and structural modeling represent two distinct approaches to data analysis. In this paper, we propose a set of novel methods for combining statistical and structural models for improved prediction and causal inference. Our first…