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For nonparametric inference about a function, multiscale testing procedures resolve the need for bandwidth selection and achieve asymptotically optimal detection performance against a broad range of alternatives. However, critical values…
This paper investigates the two-step estimation of a high dimensional additive regression model, in which the number of nonparametric additive components is potentially larger than the sample size but the number of significant additive…
Asymptotic methods for hypothesis testing in high-dimensional data usually require the dimension of the observations to increase to infinity, often with an additional condition on its rate of increase compared to the sample size. On the…
In high-dimensional linear models, the sparsity assumption is typically made, stating that most of the parameters are equal to zero. Under the sparsity assumption, estimation and, recently, inference have been well studied. However, in…
In this article, we investigate the asymptotic properties of Bayesian multiple testing procedures under general dependent setup, when the sample size and the number of hypotheses both tend to infinity. Specifically, we investigate strong…
We consider the problem of testing the hypothesis that the parameter of linear regression model is 0 against an s-sparse alternative separated from 0 in the l2-distance. We show that, in Gaussian linear regression model with p < n, where p…
Classical two-sample permutation tests for equality of distributions have exact size in finite samples, but they fail to control size for testing equality of parameters that summarize each distribution. This paper proposes permutation tests…
This paper explores hypothesis testing for the parametric forms of the mean and variance functions in regression models under diverging-dimension settings. To mitigate the curse of dimensionality, we introduce weighted residual empirical…
This paper considers the problem of testing whether there exists a non-negative solution to a possibly under-determined system of linear equations with known coefficients. This hypothesis testing problem arises naturally in a number of…
In this paper new tests for the independence of two high-dimensional vectors are investigated. We consider the case where the dimension of the vectors increases with the sample size and propose multivariate analysis of variance-type…
Several hypothesis testing methods have been proposed to validate the assumption of isotropy in spatial point patterns. A majority of these methods are characterised by an unknown distribution of the test statistic under the null hypothesis…
We develop non-asymptotically justified methods for hypothesis testing about the $p-$dimensional coefficients $\theta^{*}$ in (possibly nonlinear) regression models. Given a function $h:\,\mathbb{R}^{p}\mapsto\mathbb{R}^{m}$, we consider…
By means of two simple convexity arguments we are able to develop a general method for proving consistency and asymptotic normality of estimators that are defined by minimisation of convex criterion functions. This method is then applied to…
Linear ARCH (LARCH) processes were introduced by Robinson [J. Econometrics 47 (1991) 67--84] to model long-range dependence in volatility and leverage. Basic theoretical properties of LARCH processes have been investigated in the recent…
In this paper, we build upon the asymptotic theory for GARCH processes, considering the general class of augmented GARCH($p$, $q$) processes. Our contribution is to complement the well-known univariate asymptotics by providing a joint…
We consider parameter estimation, hypothesis testing and variable selection for partially time-varying coefficient models. Our asymptotic theory has the useful feature that it can allow dependent, nonstationary error and covariate…
In this paper, we study inference for high-dimensional data characterized by small sample sizes relative to the dimension of the data. In particular, we provide an infinite-dimensional framework to study statistical models that involve…
This paper analyses the use of bootstrap methods to test for parameter change in linear models estimated via Two Stage Least Squares (2SLS). Two types of test are considered: one where the null hypothesis is of no change and the alternative…
We set up a formal framework to characterize encompassing of nonparametric models through the L2 distance. We contrast it to previous literature on the comparison of nonparametric regression models. We then develop testing procedures for…
This paper introduces a likelihood ratio (LR)-type test that possesses the robustness properties of \(C(\alpha)\)-type procedures in an extremum estimation setting. The test statistic is constructed by applying separate adjustments to the…