Asymptotic results for parametric estimation in inadequate two phases regression models

We study the asymptotic properties, consistency, asymptotic normality, of the least squares estimator in a non linear regression problem. The model uses a parametric class Л of functions, but we do not assume that the unknown function belongs to that class. Л is here a class of continuous functions with a discontinuity in the first derivative. The problem of making a choice between two classes of that type is also studied.     

Least absolute value estimation in regression models: an annotated bibliography

This paper presents a comprehensive listing of articles on least absolute value (LAV) estimation as applied to linear and non-linear regression models and in systems of equations. References to the LAV method as applied in approximation theory are also included. Annotations describing the content of each article follow each reference.     

Testing for a change point in linear regression models

In this paper, the Schwarz Information Criterion (SIC) is proposed to locate a change point in the simple linear regression model, as well as in the multiple linear regression model. The method is then applied to a financial data set, and a change point is successfully detected.     

Asymptotic results for estimation and testing variances in regression models

Usually the variance of independent observations resulting from a linear or a nonlinear relationship is estimated by the Least-Squares residual estimator. In this paper its asymptotic properties are investigated. Further the asymptotic behaviour of tests for one-sided hypotheses on the variance is studied. The paper splits into two parts, the first one concerned with linear and the second one with nonlinear models.     

A test for abrupt change in hazard regression models with Weibull baselines

We develop a likelihood ratio test for an abrupt change point in Weibull hazard functions with covariates, including the two-piece constant hazard as a special case. We first define the log-likelihood ratio test statistic as the supremum of the profile log-likelihood ratio process over the interval which may contain an unknown change point. Using local asymptotic normality (LAN) and empirical measure, we show that the profile log-likelihood ratio process converges weakly to a quadratic form of Gaussian processes. We determine the critical values of the test and discuss how the test can be used for model selection. We also illustrate the method using the Chronic Granulomatous Disease (CGD) data.     

A cubic smoothing spline based lack of fit test for nonlinear regression models

The use of a statistic based on cubic spline smoothing is considered for testing nonlinear regression models for lack of fit. The statistic is defined to be the Euclidean squared norm of the smoothed residual vector obtained from fitting the nonlinear model, The asymptotic distribution of the statistic is derived under suitable smooth local alternatives and a numerical example is presented.     

Local composite quantile regression estimation of time-varying parameter vector for multidimensional time-inhomogeneous diffusion models

This paper is dedicated to the study of the composite quantile regression (CQR) estimations of time-varying parameter vectors for multidimensional diffusion models. Based on the local linear fitting for parameter vectors, we propose the local linear CQR estimations of the drift parameter vectors, and verify their asymptotic biases, asymptotic variances and asymptotic normality. Moreover, we discuss the asymptotic relative efficiency (ARE) of the local linear CQR estimations with respect to the local linear least-squares estimations. We obtain that the local estimations that we proposed are much more efficient than the local linear least-squares estimations. Simulation studies are constructed to show the performance of the estimations proposed.     

Second-order least squares estimation of censored regression models

This paper proposes the second-order least squares estimation, which is an extension of the ordinary least squares method, for censored regression models where the error term has a general parametric distribution (not necessarily normal). The strong consistency and asymptotic normality of the estimator are derived under fairly general regularity conditions. We also propose a computationally simpler estimator which is consistent and asymptotically normal under the same regularity conditions. Finite sample behavior of the proposed estimators under both correctly and misspecified models are investigated through Monte Carlo simulations. The simulation results show that the proposed estimator using optimal weighting matrix performs very similar to the maximum likelihood estimator, and the estimator with the identity weight is more robust against the misspecification.     

Structural changes in multivariate regression models

This study generalizes the work of chin choy and Broemeling (1980) who investigated the change in the regression parameters of univariate linear models.

The marginal posterior distributions of the change point, the regression matrices,and the precision matrix are found with the use of a proper multivariate normal-Wishart distribution for the parameters of the model.

A numerical study is undertaken in order to gain some insight into the effect that changes in sample size and certain parameter values have on these marginal posterior distributions.     

On cusp location estimation for perturbed dynamical systems

We consider the problem of parameter estimation in the case of observation of the trajectory of the diffusion process. We suppose that the drift coefficient has a singularity of cusp type and that the unknown parameter corresponds to the position of the point of the cusp. The asymptotic properties of the maximum likelihood estimator and Bayesian estimators are described in the asymptotic of small noise, that is, as the diffusion coefficient tends to zero. The consistency, limit distributions, and the convergence of moments of these estimators are established.     

Regularized robust estimation in binary regression models

In this paper, we investigate robust parameter estimation and variable selection for binary regression models with grouped data. We investigate estimation procedures based on the minimum-distance approach. In particular, we employ minimum Hellinger and minimum symmetric chi-squared distances criteria and propose regularized minimum-distance estimators. These estimators appear to possess a certain degree of automatic robustness against model misspecification and/or for potential outliers. We show that the proposed non-penalized and penalized minimum-distance estimators are efficient under the model and simultaneously have excellent robustness properties. We study their asymptotic properties such as consistency, asymptotic normality and oracle properties. Using Monte Carlo studies, we examine the small-sample and robustness properties of the proposed estimators and compare them with traditional likelihood estimators. We also study two real-data applications to illustrate our methods. The numerical studies indicate the satisfactory finite-sample performance of our procedures.     

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.     

Error variance function estimation in nonparametric regression models

In this article, a new class of variance function estimators is proposed in the setting of heteroscedastic nonparametric regression models. To obtain a variance function estimator, the main proposal is to smooth the product of the response variable and residuals as opposed to the squared residuals. The asymptotic properties of the proposed methodology are investigated in order to compare its asymptotic behavior with that of the existing methods. The finite sample performance of the proposed estimator is studied through simulation studies. The effect of the curvature of the mean function on its finite sample behavior is also discussed.     

Generalized least squares estimation of multivariate nonlinear models with missing data

The method of estimated generalized least squares estimation of multiple response models is extended to the randomly missing date case. This estimation procedure is computationally simply when there are many missing data but the number of distinct patterns of missing data for the response vectors is small. The consistency and asymptotic normality of the proposed estimators are established.     

Quantile regression estimation for distortion measurement error data

We study the quantile estimation methods for the distortion measurement error data when variables are unobserved and distorted with additive errors by some unknown functions of an observable confounding variable. After calibrating the error-prone variables, we propose the quantile regression estimation procedure and composite quantile estimation procedure. Asymptotic properties of the proposed estimators are established, and we also investigate the asymptotic relative efficiency compared with the least-squares estimator. Simulation studies are conducted to evaluate the performance of the proposed methods, and a real dataset is analyzed as an illustration.     

Contributions to-asymptotic theory in regression models with linear covariance structure 1

Asymptotic results are .presented- for estimating the parameters in variance-components models both with linear and with nonlinear regression functions.     

On the first order regression procedure of estimation for incomplete regression models

This article discusses some properties of the first order regression method for imputation of missing values on an explanatory variable in linear regression model and presents an estimation strategy based on hypothesis testing. This work was carried out before Professor V.K. Srivastava passed away in 2001. The author is grateful to the referees for their illuminating comments on an earlier draft of this paper.     

Variance estimation in nonparametric regression with jump discontinuities

Variance estimation is an important topic in nonparametric regression. In this paper, we propose a pairwise regression method for estimating the residual variance. Specifically, we regress the squared difference between observations on the squared distance between design points, and then estimate the residual variance as the intercept. Unlike most existing difference-based estimators that require a smooth regression function, our method applies to regression models with jump discontinuities. Our method also applies to the situations where the design points are unequally spaced. Finally, we conduct extensive simulation studies to evaluate the finite-sample performance of the proposed method and compare it with some existing competitors.