Statistical estimation for partially linear error-in-variable models with error-prone covariates

Motivated by a heart disease data, we propose a new partially linear error-in-variable models with error-prone covariates, in which mismeasured covariate appears in the noparametric part and the covariates in the parametric part are not observed, but ancillary variables are available. In this case, we first calibrate the linear covariates, and then use the least-square method and the local linear method to estimate parametric and nonparametric components. Also, under certain conditions the asymptotic distributions of proposed estimates are obtained. Simulated and real examples are conducted to illustrate our proposed methodology.     

Nonparametric estimation of varying coefficient error-in-variable models with validation sampling

In this paper, varying coefficient models are investigated with the response and covariate prone to measurement error. Without specifying any error structure equation, four estimators of the coefficient function vector are proposed by using the local linear kernel smoothing technique and also proved to be asymptotically normal. The data-driven bandwidth selection method is discussed. Simulation examples are conducted to evaluate the proposed estimation methods.     

Bayesian estimation for first-order autoregressive model with explanatory variables

In this article, we develop a Bayesian analysis in autoregressive model with explanatory variables. When σ² is known, we consider a normal prior and give the Bayesian estimator for the regression coefficients of the model. For the case σ² is unknown, another Bayesian estimator is given for all unknown parameters under a conjugate prior. Bayesian model selection problem is also being considered under the double-exponential priors. By the convergence of ρ-mixing sequence, the consistency and asymptotic normality of the Bayesian estimators of the regression coefficients are proved. Simulation results indicate that our Bayesian estimators are not strongly dependent on the priors, and are robust.     

Robust estimation for zero-inflated poisson autoregressive models based on density power divergence

In this study, we consider a robust estimation for zero-inflated Poisson autoregressive models using the minimum density power divergence estimator designed by Basu et al. [Robust and efficient estimation by minimising a density power divergence. Biometrika. 1998;85:549–559]. We show that under some regularity conditions, the proposed estimator is strongly consistent and asymptotically normal. The performance of the estimator is evaluated through Monte Carlo simulations. A real data analysis using New South Wales crime data is also provided for illustration.     

Robust estimation and variable selection for varying-coefficient single-index models based on modal regression

ABSTRACT

In this paper, we propose a new efficient and robust penalized estimating procedure for varying-coefficient single-index models based on modal regression and basis function approximations. The proposed procedure simultaneously solves two types of problems: separation of varying and constant effects and selection of variables with non zero coefficients for both non parametric and index components using three smoothly clipped absolute deviation (SCAD) penalties. With appropriate selection of the tuning parameters, the new method possesses the consistency in variable selection and the separation of varying and constant coefficients. In addition, the estimators of varying coefficients possess the optimal convergence rate and the estimators of constant coefficients and index parameters have the oracle property. Finally, we investigate the finite sample performance of the proposed method through a simulation study and real data analysis.     

Double-smoothed drift estimation of jump-diffusion model

In this paper, we consider the non parametric drift estimation for the jump-diffusion model. We employ the double-smoothed non parametric method, and establish the strong consistency and asymptotic normality for estimator.     

Bayes sequential estimation for a time-transformed exponential model

A problem of Bayesian sequential estimating an unknown parameter of a time-transformed exponential model is considered. It is supposed that the loss associated with the error of estimation is weighted squared or precautionary and the cost of observing the process is a function of time and the number of observations. Bayes sequential procedures for estimating the unknown parameter are presented.     

A target distribution model for nonparametric density estimation

In this paper a model is proposed which represents a wide class of continuous distributions. It is shown how the parameters of this model can be estimated leading to a distribution estimator and a corresponding density estimator. An important property of this estimator is that it can be structured to reflect a priori knowledge of the unknown distribution.

Finally, some examples are shown and some comparisons made with kernel and orthogonal series estimators.     

Robust parameter estimation of regression model with AR(p) error terms

In this article, we consider a linear regression model with AR(p) error terms with the assumption that the error terms have a t distribution as a heavy-tailed alternative to the normal distribution. We obtain the estimators for the model parameters by using the conditional maximum likelihood (CML) method. We conduct an iteratively reweighting algorithm (IRA) to find the estimates for the parameters of interest. We provide a simulation study and three real data examples to illustrate the performance of the proposed robust estimators based on t distribution.     

Efficient estimation in a nonlinear counting-process regression model

Suppose we observe i.i.d. copies of X, C, Y, where X is a counting process, C is a censoring process talcing only values 0 and 1, and Y is a covariate process. Assume that the intensity process of X is of the form C(s)a(s, Y(s)) with a unknown, but that the distribution of X, C, Y is unspecified otherwise. McKeague and Utikal proposed an estimator for the doubly cumulative hazard f f a(s, y) ds dy and determined its asymptotic distribution. We show that the estimator is regular and efficient in the sense of a Hájek-Inagaki convolution theorem for partially specified models.     

Parameter estimation for a deformable template model

In recent years, a number of statistical models have been proposed for the purposes of high-level image analysis tasks such as object recognition. However, in general, these models remain hard to use in practice, partly as a result of their complexity, partly through lack of software. In this paper we concentrate on a particular deformable template model which has proved potentially useful for locating and labelling cells in microscope slides Rue and Hurn (1999). This model requires the specification of a number of rather non-intuitive parameters which control the shape variability of the deformed templates. Our goal is to arrange the estimation of these parameters in such a way that the microscope user's expertise is exploited to provide the necessary training data graphically by identifying a number of cells displayed on a computer screen, but that no additional statistical input is required. In this paper we use maximum likelihood estimation incorporating the error structure in the generation of our training data.     

E-Bayesian estimation for the proportional hazard rate model based on record values

In this article, a new parameter estimation method, named E-Bayesian method, is considered to obtain the estimates of the unknown parameter and reliability function based on record values. The maximum likelihood, Bayesian, E-Bayesian, and hierarchical Bayesian estimates of the unknown parameter and reliability function are obtained when the underlying distribution belongs to the proportional hazard rate model. The Bayesian estimates are obtained based on squared error and linear-exponential loss functions. The previously obtained some relations for the E-Bayesian estimates are improved. The relationship between E-Bayesian and hierarchical Bayesian estimations are obtained under the same loss functions. The comparison of the derived estimates are carried out by using Monte Carlo simulations. Real data are analyzed for an illustration of the findings.     

Simultaneous estimation of number of signals and signal parameters of superimposed sinusoidal model: A robust sequential bivariate M-periodogram approach

Accurate estimation of the parameters of superimposed sinusoidal signals is an important problem in digital signal processing and time series analysis. In this article, we propose a simultaneous estimation procedure for estimation of the number of signals and signal parameters. The proposed sequential method is based on a robust bivariate M-periodogram and uses the orthogonal structure of the superimposed sinusoidal model for sequential estimation. Extensive simulations and data analysis show that the proposed method has a high degree of frequency resolution capability and can provide robust and efficient estimates of the number of signals and signal parameters.     

Quasi-minimax estimation in the general linear regression model

This paper is mainly concerned with minimax estimation in the general linear regression model y=Xβ+ε$y=X\beta +\epsilon$ under ellipsoidal restrictions on the parameter space and quadratic loss function. We confine ourselves to estimators that are linear in the response vector y  . The minimax estimators of the regression coefficient β$\beta$ are derived under homogeneous condition and heterogeneous condition, respectively. Furthermore, these obtained estimators are the ridge-type estimators and mean dispersion error (MDE) superior to the best linear unbiased estimator b=(X^′W^-1X)^-1X^′W^-1y$b=(X^{\prime }{W}^{-1}X{)}^{-1}{X}^{\prime }{W}^{-1}y$ under some conditions.     

Density estimation under the koziol-green model of censoring by penalized likelihood methods

We propose two density estimators of the survival distribution in the setting of the Koziol-Green random-censoring model. The estimators are obtained by maximum-penalized-likelihood methods, and we provide an algorithm for their numerical evaluation. We establish the strong consistency of the estimators in the Hellinger metric, the L_p-norms, p= 1,2, ∞, and a Sobolev norm, under mild conditions on the underlying survival density and the censoring distribution.     

Targeted estimation of state occupation probabilities for the non-Markov illness-death model

We use semi-parametric efficiency theory to derive a class of estimators for the state occupation probabilities of the continuous-time irreversible illness-death model. We consider both the setting with and without additional baseline information available, where we impose no specific functional form on the intensity functions of the model. We show that any estimator in the class is asymptotically linear under suitable assumptions about the estimators of the intensity functions. In particular, the assumptions are weak enough to allow the use of data-adaptive methods, which is important for making the identifying assumption of coarsening at random plausible in realistic settings. We suggest a flexible method for estimating the transition intensity functions of the illness-death model based on penalized Poisson regression. We apply this method to estimate the nuisance parameters of an illness-death model in a simulation study and a real-world application.     

Empirical study of robust estimation methods for PAR models with application to the air quality area

Abstract

This paper compares three estimators for periodic autoregressive (PAR) models. The first is the classical periodic Yule-Walker estimator (YWE). The second is a robust version of YWE (RYWE) which uses the robust autocovariance function in the periodic Yule-Walker equations, and the third is the robust least squares estimator (RLSE) based on iterative least squares with robust versions of the original time series. The daily mean particulate matter concentration (PM10) data is used to illustrate the methodologies in a real application, that is, in the Air Quality area.     

Semiparametric estimation of employment duration models

There are a variety of economic areas, such as studies of employment duration and of the durability of capital goods, in which data on important variables typically are censored. The standard techinques for estimating a model from censored data require the distributions of unobservable random components of the model to be specified a priori up to a finite set of parameters, and misspecification of these distributions usually leads to inconsistent parameter estimates. However, economic theory rarely gives guidance about distributions and the standard estimation techniques do not provide convenient methods for identifying distributions from censored data. Recently, several distribution-free or semiparametric methods for estimating censored regression models have been developed. This paper presents the results of using two such methods to estimate a model of employment duration. The paper reports the operating characteristics of the semiparametric estimators and compares the semiparametric estimates with those obtained from a standard parametric model.