Related papers: Inference for a Special Bilinear Time Series Model
This paper investigates the quasi-maximum likelihood inference including estimation, model selection and diagnostic checking for linear double autoregressive (DAR) models, where all asymptotic properties are established under only…
This paper develops an asymptotic likelihood theory for triangular arrays of stationary Gaussian time series depending on a multidimensional unknown parameter. We give sufficient conditions for the associated sequence of statistical models…
We consider an integer-valued time series $Y=(Y_t)_{t\in\Z}$ where the models after a time $k^*$ is Poisson autoregressive with the conditional mean that depends on a parameter $\theta^*\in\Theta\subset\R^d$. The structure of the process…
Our paper deals with inferring simulator-based statistical models given some observed data. A simulator-based model is a parametrized mechanism which specifies how data are generated. It is thus also referred to as generative model. We…
We propose a method for inference in generalised linear mixed models (GLMMs) and several extensions of these models. First, we extend the GLMM by allowing the distribution of the random components to be non-Gaussian, that is, assuming an…
We propose a new class of univariate nonstationary time series models, using the framework of modulated time series, which is appropriate for the analysis of rapidly-evolving time series as well as time series observations with missing…
Misclassification of binary responses, if ignored, may severely bias the maximum likelihood estimators (MLE) of regression parameters. For such data, a binary regression model incorporating misclassification probabilities is extensively…
In many applications it is desirable to infer coarse-grained models from observational data. The observed process often corresponds only to a few selected degrees of freedom of a high-dimensional dynamical system with multiple time scales.…
This paper develops asymptotic theory for estimation of parameters in regression models for binomial response time series where serial dependence is present through a latent process. Use of generalized linear model (GLM) estimating…
Generalized linear models (GLMs) are fundamental tools for statistical modeling, with maximum likelihood estimation (MLE) serving as the classical approach for parameter inference. While MLE performs well for canonical GLMs, it can become…
We analyze the properties of arguably the simplest bilinear stochastic multiplicative process, proposed as a model of financial returns and of other complex systems combining both nonlinearity and multiplicative noise. By construction, it…
This study explores the estimation of parameters in a matrix-valued linear regression model, where the $T$ responses $(Y_t)_{t=1}^T \in \mathbb{R}^{n \times p}$ and predictors $(X_t)_{t=1}^T \in \mathbb{R}^{m \times q}$ satisfy the…
Let $\{X_n\}_{n=0}^{\infty}$ be a stationary real-valued time series with unknown distribution. Our goal is to estimate the conditional expectation of $X_{n+1}$ based on the observations $X_i$, $0\le i\le n$ in a strongly consistent way.…
In this paper, we address the identification problem for the systems characterized by linear time-invariant dynamics with bilinear observation models. More precisely, we consider a suitable parametric description of the system and formulate…
This paper deals with nonparametric maximum likelihood estimation for Gaussian locally stationary processes. Our nonparametric MLE is constructed by minimizing a frequency domain likelihood over a class of functions. The asymptotic behavior…
Inference for mechanistic models is challenging because of nonlinear interactions between model parameters and a lack of identifiability. Here we focus on a specific class of mechanistic models, which we term stable differential equations.…
This paper is concerned with estimation and inference for ultrahigh dimensional partially linear single-index models. The presence of high dimensional nuisance parameter and nuisance unknown function makes the estimation and inference…
Bilinear dynamical systems are ubiquitous in many different domains and they can also be used to approximate more general control-affine systems. This motivates the problem of learning bilinear systems from a single trajectory of the…
We consider the problem of inference for non-stationary time series with heavy-tailed error distribution. Under a time-varying linear process framework we show that there exists a suitable local approximation by a stationary process with…
Unnormalized (or energy-based) models provide a flexible framework for capturing the characteristics of data with complex dependency structures. However, the application of standard Bayesian inference methods has been severely limited…