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This paper discusses asymptotic distributions of various estimators of the underlying parameters in some regression models with long memory (LM) Gaussian design and nonparametric heteroscedastic LM moving average errors. In the simple linear regression model, the first-order asymptotic distribution of the least square estimator of the slope parameter is observed to be degenerate. However, in the second order, this estimator is $n^{1/2}$-consistent and asymptotically normal for $h+H<3/2$; nonnormal otherwise, where $h$ and $H$ are LM parameters of design and error processes, respectively. The finite-dimensional asymptotic distributions of a class of kernel type estimators of the conditional variance function $sigma^2(x)$ in a more general heteroscedastic regression model are found to be normal whenever $H<(1+h)/2$, and non-normal otherwise. In addition, in this general model, $log(n)$-consistency of the local Whittle estimator of $H$ based on pseudo residuals and consistency of a cross validation type estimator of $sigma^2(x)$ are established. All of these findings are then used to propose a lack-of-fit test of a parametric regression model, with an application to some currency exchange rate data which exhibit LM.
For the class of Gauss-Markov processes we study the problem of asymptotic equivalence of the nonparametric regression model with errors given by the increments of the process and the continuous time model, where a whole path of a sum of a determinis
We consider the problem of choosing between several models in least-squares regression with heteroscedastic data. We prove that any penalization procedure is suboptimal when the penalty is a function of the dimension of the model, at least for some t
We deal with a general class of extreme-value regression models introduced by Barreto- Souza and Vasconcellos (2011). Our goal is to derive an adjusted likelihood ratio statistic that is approximately distributed as c{hi}2 with a high degree of accur
We study the asymptotic properties of bridge estimators in sparse, high-dimensional, linear regression models when the number of covariates may increase to infinity with the sample size. We are particularly interested in the use of bridge estimators
This paper deals with the estimation of hidden periodicities in a non-linear regression model with stationary noise displaying cyclical dependence. Consistency and asymptotic normality are established for the least-squares estimates.