In this paper, we apply the empirical likelihood method to heteroscedastic partially linear errors-in-variables model. For the cases of known and unknown error variances, the two different empirical log-likelihood ratios for the parameter of interest are constructed. If the error variances are...

In this paper, we construct a nonparametric regression quantile estimator by using the local linear fitting for left-truncated data, and establish the Bahadur-type representation and asymptotic normality of the proposed estimator when the observations form a stationary α-mixing sequence....

Summary In this paper, we discuss the global L 2 error of the nonlinear wavelet estimators of the density function in the Besov space B s pq , when the survival times form a stationary α-mixing sequence, and prove that the nonlinear wavelet estimators can achieve the optimal rate of...

Let {X <Subscript> n </Subscript>,n≥1} be a strictly stationary sequence of negatively associated random variables with the marginal probability density function f(x), the recursive kernel estimate of f(x) is defined by [InlineMediaObject not available: see fulltext.] where h <Subscript> n </Subscript> is a sequence of positive bandwidths...</subscript></subscript>

In a recent paper by Chen (in press) the limit law of the iterated logarithm for the partial sums of i.i.d. real-valued random variables has been established. In this note we look at the corresponding problem in Banach space setting. Let (B,‖⋅‖) be a real separable Banach space with...

In this paper we define a kernel estimator of the conditional density for a left-truncated and right-censored model based on the generalized product-limit estimator of the conditional distributed function. Under the observations with multivariate covariates form a stationary α-mixing sequence,...

This article is concerned with the estimating problem of heteroscedastic partially linear errors-in-variables models. We derive the asymptotic normality for estimators of the slope parameter and the nonparametric component in the case of known error variance with stationary <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\alpha $$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi mathvariant="italic">α</mi> </math> </EquationSource>...</equationsource></equationsource></inlineequation>