Related papers: Testing convex hypotheses on the mean of a Gaussia…
We propose a general method for constructing confidence intervals and statistical tests for single or low-dimensional components of a large parameter vector in a high-dimensional model. It can be easily adjusted for multiplicity taking…
In this paper, we introduce the notion of Gaussian processes indexed by probability density functions for extending the Mat\'ern family of covariance functions. We use some tools from information geometry to improve the efficiency and the…
We propose generalized resubstitution error estimators for regression, a broad family of estimators, each corresponding to a choice of empirical probability measures and loss function. The usual sum of squares criterion is a special case…
Heteroscedasticity testing is of importance in regression analysis. Existing local smoothing tests suffer severely from curse of dimensionality even when the number of covariates is moderate because of use of nonparametric estimation. In…
In this note a general a Cauchy-type mean value theorem for the ratio of functional determinants is offered. It generalizes Cauchy's and Taylor's mean value theorems as well as other classical mean value theorems.
We consider the nonparametric regression problem with multiple predictors and an additive error, where the regression function is assumed to be coordinatewise nondecreasing. We propose a Bayesian approach to make an inference on the…
It has been a long history in testing whether a mean vector with a fixed dimension has a specified value. Some well-known tests include the Hotelling $T^2$-test and the empirical likelihood ratio test proposed by Owen [Biometrika 75 (1988)…
High-dimensional mean vector testing problem for two or more groups remain a very active research area. In these setting, traditional tests are not applicable because they involve the inversion of rank deficient group covariance matrix. In…
Recently, several authors have re-examined the power of the classical F-test in linear regression in a `large-p, large-n' framework (cf. Zhong and Chen (2011), Wang and Cui (2013)). They highlight the loss of power as the number of…
While there exists several inferential methods for analyzing functional data in factorial designs, there is a lack of statistical tests that are valid (i) in general designs, (ii) under non-restrictive assumptions on the data generating…
This paper develops a method for estimating parameters of a vector autoregression (VAR) observed in white noise. The estimation method assumes the noise variance matrix is known and does not require any iterative process. This study…
Consider the Gaussian vector model with mean value {\theta}. We study the twin problems of estimating the number |{\theta}|_0 of non-zero components of {\theta} and testing whether |{\theta}|_0 is smaller than some value. For testing, we…
In this article, we propose a new class of consistent tests for $p$-variate normality. These tests are based on the characterization of the standard multivariate normal distribution, that the Hessian of the corresponding cumulant generating…
Though Gaussian graphical models have been widely used in many scientific fields, relatively limited progress has been made to link graph structures to external covariates. We propose a Gaussian graphical regression model, which regresses…
Regression is one of the most commonly used statistical techniques. However, testing regression systems is a great challenge because of the absence of test oracle in general. In this paper, we show that Metamorphic Testing is an effective…
This paper is motivated by the comparison of genetic networks based on microarray samples. The aim is to test whether the differences observed between two inferred Gaussian graphical models come from real differences or arise from…
We study hypothesis testing for penalized estimators in settings where the full marginal distribution of a multivariate response is difficult to specify, such as longitudinal data with correlated measurements or high-dimensional…
Consider a nonparametric regression model with one-sided errors and regression function in a general H\"older class. We estimate the regression function via minimization of the local integral of a polynomial approximation. We show uniform…
In the paper, we introduce the generalized convex function on fractal sets of real line numbers and study the properties of the generalized convex function. Based on these properties, we establish the generalized Jensen inequality and…
Invariant and equivariant models incorporate the symmetry of an object to be estimated (here non-parametric regression functions $f : \mathcal{X} \rightarrow \mathbb{R}$). These models perform better (with respect to $L^2$ loss) and are…