Related papers: Strong confidence intervals for autoregression

Inequalities may appear in many models. They can be as simple as assuming a parameter is nonnegative, possibly a regression coefficient or a treatment effect. This paper focuses on the case that there is only one inequality and proposes a…

Conventional methods in causal effect inferencetypically rely on specifying a valid set of control variables. When this set is unknown or misspecified, inferences will be erroneous. We propose a method for inferring average causal effects…

What, if anything, should a frequentist say about a single realized confidence interval (CI) and its chance of having covered the parameter? Jerzy Neyman's original answer was to refuse any nondegenerate probability for coverage ex post…

This paper introduces new methods for constructing prediction intervals using quantile-based techniques. The procedures are developed for both classical (homoscedastic) autoregressive models and modern quantile autoregressive models. They…

We propose a new optimization framework for aleatoric uncertainty estimation in regression problems. Existing methods can quantify the error in the target estimation, but they tend to underestimate it. To obtain the predictive uncertainty…

We consider the recursive estimation of a regression functional where the explanatory variables take values in some functional space. We prove the almost sure convergence of such estimates for dependent functional data. Also we derive the…

We consider a linear regression model, with the parameter of interest a specified linear combination of the regression parameter vector. We suppose that, as a first step, a data-based model selection (e.g. by preliminary hypothesis tests or…

In this paper we consider a regression model that allows for time series covariates as well as heteroscedasticity with a regression function that is modelled nonparametrically. We assume that the regression function changes at some unknown…

In this paper an easy to implement method of stochastically weighing short and long memory linear processes is introduced. The method renders asymptotically exact size confidence intervals for the population mean which are significantly…

Empirical risk minimization is a standard principle for choosing algorithms in learning theory. In this paper we study the properties of empirical risk minimization for time series. The analysis is carried out in a general framework that…

Regularized kernel methods such as, e.g., support vector machines and least-squares support vector regression constitute an important class of standard learning algorithms in machine learning. Theoretical investigations concerning…

The asymptotic behaviour of the commonly used bootstrap percentile confidence interval is investigated when the parameters are subject to linear inequality constraints. We concentrate on the important one- and two-sample problems with data…

We discuss a general approach to building non-asymptotic confidence bounds for stochastic optimization problems. Our principal contribution is the observation that a Sample Average Approximation of a problem supplies upper and lower bounds…

Bayesian nonparametric regression under a rescaled Gaussian process prior offers smoothness-adaptive function estimation with near minimax-optimal error rates. Hierarchical extensions of this approach, equipped with stochastic variable…

This paper studies some temporal dependence properties and addresses the issue of parametric estimation for a class of state-dependent autoregressive models for nonlinear time series in which we assume a stochastic autoregressive…

Models characterized by autoregressive structure and random coefficients are powerful tools for the analysis of high-frequency, high-dimensional and volatile time series. The available literature on such models is broad, but also sectorial,…

Consider a finite sample from an unknown distribution over a countable alphabet. Unobserved events are alphabet symbols which do not appear in the sample. Estimating the probabilities of unobserved events is a basic problem in statistics…

We present an algorithm that can efficiently compute a broad class of inferences for discrete-time imprecise Markov chains, a generalised type of Markov chains that allows one to take into account partially specified probabilities and other…

Likelihood-based methods of statistical inference provide a useful general methodology that is appealing, as a straightforward asymptotic theory can be applied for their implementation. It is important to assess the relationships between…

In this paper, a new bivariate random coefficient integer-valued autoregressive process based on modified negative binomial operator with dependent innovations is proposed. Basic probabilistic and statistical properties of this model are…