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Consider a linear regression model and suppose that our aim is to find a confidence interval for a specified linear combination of the regression parameters. In practice, it is common to perform a Durbin-Watson pretest of the null…
We propose a new statistical test for the residual autocorrelation in ARX adaptive tracking. The introduction of a persistent excitation in the adaptive tracking control allows us to build a bilateral statistical test based on the…
In statistics, the Durbin-Watson test is always employed to detect the presence of serial correlation of residuals from a least squares regression analysis. However, the Durbin-Watson statistic is only suitable for ordered time or spatial…
We propose a two-sample test for high-dimensional means that requires neither distributional nor correlational assumptions, besides some weak conditions on the moments and tail properties of the elements in the random vectors. This…
We consider linear models with scalar responses and covariates from a separable Hilbert space. The aim is to detect change points in the error distribution, based on sequential residual empirical distribution functions. Expansions for those…
Testing independence among a number of (ultra) high-dimensional random samples is a fundamental and challenging problem. By arranging $n$ identically distributed $p$-dimensional random vectors into a $p \times n$ data matrix, we investigate…
A simple test is proposed for examining the correctness of a given completely specified response function against unspecified general alternatives in the context of univariate regression. The usual diagnostic tools based on residuals plots…
Hypothesis about the parallelism of the regression lines in R multivariate simple linear models are studied in this paper. Tests on common intercept and sets of lines intersected at a fixed value, are also developed. An application in an…
Testing the independence between random vectors is a fundamental problem in statistics. Distance correlation, a recently popular dependence measure, is universally consistent for testing independence against all distributions with finite…
For the last two decades, high-dimensional data and methods have proliferated throughout the literature. Yet, the classical technique of linear regression has not lost its usefulness in applications. In fact, many high-dimensional…
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…
The behavior of the power function of autocorrelation tests such as the Durbin-Watson test in time series regressions or the Cliff-Ord test in spatial regression models has been intensively studied in the literature. When the correlation…
Model checking plays an important role in linear regression as model misspecification seriously affects the validity and efficiency of regression analysis. In practice, model checking is often performed by subjectively evaluating the plot…
We develop tests for high-dimensional covariance matrices under a generalized elliptical model. Our tests are based on a central limit theorem (CLT) for linear spectral statistics of the sample covariance matrix based on self-normalized…
High-dimensional auto-regressive models provide a natural way to model influence between $M$ actors given multi-variate time series data for $T$ time intervals. While there has been considerable work on network estimation, there is limited…
This paper develops some theory of the Dyson equation for correlated linearizations and uses it to solve a problem on asymptotic deterministic equivalent for the test error in random features regression. The theory developed for the…
We propose a general, modular method for significance testing of groups (or clusters) of variables in a high-dimensional linear model. In presence of high correlations among the covariables, due to serious problems of identifiability, it is…
This paper studies the high-dimensional mixed linear regression (MLR) where the output variable comes from one of the two linear regression models with an unknown mixing proportion and an unknown covariance structure of the random…
Hypothesis testing in the linear regression model is a fundamental statistical problem. We consider linear regression in the high-dimensional regime where the number of parameters exceeds the number of samples ($p> n$). In order to make…
Fitting high-dimensional statistical models often requires the use of non-linear parameter estimation procedures. As a consequence, it is generally impossible to obtain an exact characterization of the probability distribution of the…