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This paper considers the uniform strong consistency of the kernel estimator of the error cumulative distribution function (CDF) in the first-order autoregressive model. The classical Glivenko–Cantelli Theorem is extended to the residual based kernel smooth CDF estimator in the autoregressive model. [ABSTRACT FROM AUTHOR]

When a conditional distribution has an infinite variance, commonly employed kernel smoothing methods such as local polynomial estimators for the conditional mean admit non-normal limiting distributions (Hall et al., 2002). This complicates the related inference as the conventional tests and confidence intervals based on asymptotic normality are no longer applicable, and the standard bootstrap method often fails. By utilizing the middle part of data nonparametrically and the tail parts parametrically based on extreme value theory, this paper proposes a new estimation method for conditional means, resulting in asymptotically normal estimators even when the conditional distribution has infinite variance. Consequently the standard bootstrap method could be employed to construct, for example, confidence intervals regardless of the tail heaviness. The same idea can be applied to estimating the difference between a conditional mean and a conditional median, which is a useful measure in data exploratory analysis. [ABSTRACT FROM AUTHOR]

We introduce the smooth total variation distance as a natural choice to establish equivalence. We propose asymptotic and bootstrap-based tests for which asymptotic optimality is shown. The finite sample performance is studied by simulations. Then we apply tests to real data sets. [ABSTRACT FROM AUTHOR]

We study random series priors for estimating a functional parameter f ∈ L 2 [ 0 , 1 ] . We show that with a series prior with random truncation, Gaussian coefficients, and inverse gamma multiplicative scaling, it is possible to achieve posterior contraction at optimal rates and adaptation to arbitrary degrees of smoothness. We present general results that can be combined with existing rate of contraction results for various nonparametric estimation problems. We give concrete examples for signal estimation in white noise and drift estimation for a one-dimensional SDE. [ABSTRACT FROM AUTHOR]

We study the efficiency of two estimators of quantile difference with left truncated and right censored data. Based on deficiency, the performances of the estimators are compared. The theoretical results and numerical studies show that the smoothed estimator is more efficient. [ABSTRACT FROM AUTHOR]

In this paper the ridge regression (RR) diagnostic method of Walker and Brich (1988) is applied to the ridge semiparametric regression model (RSPRM). We propose case deletion formulas to detect influential points. Furthermore, a real data set is analysed. [ABSTRACT FROM AUTHOR]

We propose a new test for covariate-threshold caused change point in quantile regression with random censoring, based on partial subgradient. Critical values are obtained using wild bootstrap samples, where induced smoothing method is used to estimate the conditional density. [ABSTRACT FROM AUTHOR]

Abstract: Cohen et al. (2007) introduced the concept of a smooth multiple testing procedure and suggested a method for smoothing traditional stepwise procedures. We propose an alternative way of smoothing, which has some advantages over the CKS method. [Copyright &y& Elsevier]

Abstract: Smoothing methods for density estimators struggle when the shape of the reference density differs markedly from the actual density. We propose a bootstrap bandwidth selector where no reference distribution is used. It performs reliably in difficult cases and asymptotically outperforms well known automatic bandwidths. [Copyright &y& Elsevier]

Abstract: This note uses the established connection between the local-EM and EMS algorithms to explore methods for smoothing mismeasured data. Implementations of local-EM are developed for several forms of censored and/or mismeasured data and their connections with other methods explored. [Copyright &y& Elsevier]

Abstract: We obtain the rate of complete convergence for maximums of moving average sums of martingale difference fields in -uniformly smooth Banach spaces, and extend Marcinkiewicz–Zygmund strong laws. Our results extend the results of , , and some other ones. [Copyright &y& Elsevier]

Abstract: Consider a linear regression model. describe the smoothly clipped absolute deviation (SCAD) point estimator of the regression parameter vector. To gain insight into the properties of this estimator, they consider an orthonormal design matrix and focus on the estimation of a specified component of this vector. They show that the SCAD point estimator has three attractive properties. We answer the question: to what extent can an interval estimator, centred on the SCAD estimator, have similar attractive properties? [Copyright &y& Elsevier]

Abstract: This paper focuses on nonparametric regression estimation for the parameters of a discrete or continuous distribution, such as the Poisson or Gamma distributions, when anomalous data are present. The proposal is a natural extension of robust methods developed in the setting of parametric generalized linear models. Robust estimators bounding either large values of the deviance or of the Pearson residuals are introduced and their asymptotic behaviour is derived. Through a Monte Carlo study, for the Poisson and Gamma distributions, the finite properties of the proposed procedures are investigated and their performance is compared with that of the classical ones. A resistant cross-validation method to choose the smoothing parameter is also considered. [Copyright &y& Elsevier]

Abstract: Regression analysis of the odds ratios for sparse data has received a lot of attention. However, existing works are restricted to the parametric case, and a parametric model may be a misspecification, which may lead to biased and inefficient estimators. Little attention is received for nonparametric regression analysis of the odds ratios. Based on kernel smoothing techniques, we propose two simple estimators of the log odds-ratio function for sparse data. Large sample properties of the estimators are derived, and the methods proposed are evaluated through simulation. [Copyright &y& Elsevier]

Abstract: The quantity deficiency which was proposed by is used to compare different statistical procedures. In this article, the deficiency of the sample quantile estimator with respect to the kernel quantile estimator for left truncated and right censored (LTRC) data in the sense of Hodges and Lehmann is considered. We also give the optimal bandwidth for the kernel quantile estimator. Monte Carlo studies are conducted to illustrate our results. [Copyright &y& Elsevier]

Abstract: One major goal in clinical applications of multi-state models is the estimation of transition probabilities. In a recent paper, introduce a substitute for the Aalen–Johansen estimator in the case of a non-Markov illness–death model. The idea behind their estimator is to weight the data by the Kaplan–Meier weights pertaining to the distribution of the total survival time of the process. In this paper we propose a modification of estimator based on presmoothing. Consistency is established. We investigate the finite sample performance of the new estimator through simulations. Data from a study on colon cancer are used for illustration purposes. [Copyright &y& Elsevier]

Abstract: We prove a functional central limit theorem for the volume of the excursion sets generated by a stationary and associated random field with smooth realizations. [Copyright &y& Elsevier]

Abstract: We propose and study a kernel estimator of a density in which the kernel is adapted to the data but not fixed. The smoothing procedure is followed by a location-scale transformation to reduce bias and variance. The new method naturally leads to an adaptive choice of the smoothing parameters which avoids asymptotic expansions. [Copyright &y& Elsevier]

Abstract: Two-sample point prediction is considered for a two-parameter exponential distribution. Several point predictors such as the best unbiased predictor, best invariant predictor and maximum likelihood predictor are obtained for future order statistics on the basis of observed record values in two cases: where the location parameter is known and unknown. These predictors are compared in the sense of their mean squared prediction errors. Finally, some numerical results are given to illustrate the proposed procedures. [ABSTRACT FROM AUTHOR]

Abstract: We consider the smoothing probabilities of hidden Markov model (HMM). We show that under fairly general conditions for HMM, the exponential forgetting still holds, and the smoothing probabilities can be well approximated with the ones of double-sided HMM. This makes it possible to use ergodic theorems. As an application we consider the pointwise maximum a posteriori segmentation, and show that the corresponding risks converge. [ABSTRACT FROM AUTHOR]

Abstract: This paper proposes an empirical likelihood method to estimate the parameters of infinite variance autoregressive (IVAR) models and to construct confidence regions for the parameters. Simulation studies suggest that in small sample case, the empirical likelihood confidence regions may be more accurate than the confidence regions constructed by the normal approximation based on the self-weighted LAD estimator proposed by . [Copyright &y& Elsevier]

Abstract: Intermediate quantiles play an important role in the statistics of extremes with particular applications in risk management. For interval estimation of quantiles, proposed the so-called smoothed empirical likelihood method. In this paper, we apply the method in to construct confidence intervals for an intermediate quantile by deriving the corresponding Wilks Theorem. [Copyright &y& Elsevier]

Abstract: We consider nonparametric estimation of a smooth function of one variable. Global selection procedures cannot sufficiently account for local sparseness of the covariate nor can they adapt to local curvature of the regression function. We propose a new method for selecting local smoothing parameters which takes into account sparseness and adapts to local curvature. A Bayesian type argument provides an initial smoothing parameter which adapts to the local sparseness of the covariate and provides the basis for local bandwidth selection procedures which further adjust the bandwidth according to the local curvature of the regression function. Simulation evidence indicates that the proposed method can result in reduction of both pointwise mean squared error and integrated mean squared error. [Copyright &y& Elsevier]

Abstract: The adaptive varying-coefficient partially linear regression (AVCPLR) model is proposed by combining the nonparametric regression model and varying-coefficient regression model with different smoothing variables. It can be seen as a generalization of the varying-coefficient partially linear regression model, and it is also an example of a generalized structured model as defined by Mammen and Neilsen [Mammen, E., Nielsen, J.P., 2003. Generalised structured models. Biometrika 90, 551–566]. Based on the local linear technique and the marginal integrated method, the initial estimators of these unknown functions are obtained, each of which has big variance. To decrease the variances of these initial estimators, the one-step backfitting technique proposed by Linton [Linton, O.B., 1997. Efficient estimation of additive nonparametric regression models. Biometrika 82, 93–100] is used to obtain the efficient estimators of all unknown functions for the AVCPLR model, and their asymptotic normalities are studied. Two simulated examples are given to illustrate the AVCPLR model and the proposed estimation methodology. [Copyright &y& Elsevier]

Abstract: For spatio-temporal regression models with observations taken regularly in time but irregularly over space, we investigate the effect of spatial smoothing on the reduction of variance in estimating both parametric and nonparametric regression functions. The processes concerned are stationary in time but may be nonstationary over space. Our study indicates that under the infill asymptotic framework, the existence of the so-called nugget effect in either regressor process or noise process is necessary for spatial smoothing to reduce the estimation variance. In particular the nugget effect in the regressor process may lead to a faster convergence rate in estimating nonparametric regression functions. [Copyright &y& Elsevier]

Abstract: In this note we show that, from a conventional viewpoint, there are particularly close parallels between optimal-kernel-choice problems in non-parametric deconvolution, and their better-understood counterparts in density estimation and regression. However, other aspects of these problems are distinctly different, and this property leads us to conclude that “optimal” kernels do not give satisfactory performance when applied to deconvolution. This unexpected result stems from the fact that standard side conditions, which are used to ensure that the familiar kernel-choice problem has a unique solution, do not have statistically beneficial implications for deconvolution estimators. In consequence, certain “sub-optimal” kernels produce estimators that enjoy both greater efficiency and greater visual smoothness. [Copyright &y& Elsevier]

Kernel density estimators have been studied in great detail. In this note a new family of kernels, depending on a parameter c , is obtained by kernel-smoothing an initial kernel density estimator. Under certain conditions, we show that nonparametric density estimators based on such kernels outperform the initial estimator in terms of minimized asymptotic mean integrated squared error and in kernel efficiency. [ABSTRACT FROM AUTHOR]