共查询到20条相似文献，搜索用时 15 毫秒
1.
A Semi-parametric Regression Model with Errors in Variables 总被引：4，自引：0，他引：4
Abstract. In this paper, we consider a partial linear regression model with measurement errors in possibly all the variables. We use a method of moments and deconvolution to construct a new class of parametric estimators together with a non-parametric kernel estimator. Strong convergence, optimal rate of weak convergence and asymptotic normality of the estimators are investigated. 相似文献
2.
Aurore Delaigle 《Australian & New Zealand Journal of Statistics》2014,56(2):105-124
Estimating a curve nonparametrically from data measured with error is a difficult problem that has been studied by many authors. Constructing a consistent estimator in this context can sometimes be quite challenging, and in this paper we review some of the tools that have been developed in the literature for kernel‐based approaches, founded on the Fourier transform and a more general unbiased score technique. We use those tools to rederive some of the existing nonparametric density and regression estimators for data contaminated by classical or Berkson errors, and discuss how to compute these estimators in practice. We also review some mistakes made by those working in the area, and highlight a number of problems with an existing R package decon . 相似文献
3.
This paper is motivated by our attempt to answer a policy question: how is private health insurance take‐up in Australia affected by the income threshold at which the Medicare Levy Surcharge (MLS) kicks in? We propose a new difference deconvolution kernel estimator for the location and size of regression discontinuities. We also propose a bootstrapping procedure for estimating the confidence interval for the estimated discontinuity. Performance of the estimator is evaluated by Monte Carlo simulations before it is applied to estimating the effect of the income threshold of MLS on the take‐up of private health insurance in Australia, using contaminated data. 相似文献
4.
《Journal of nonparametric statistics》2012,24(4):415-418
Carroll et al. described a very general framework for problems involving measurement errors. The approach was based on the sieve likelihood principle where the dimension of the parameter space is allowed to grow with sample size. Thus the procedure includes many well-known estimators as special cases. In this discussion, a specific class of estimators based on B-splines will be described. It is observed that certain regularity conditions will be required to ensure the existence of the maximum likelihood estimators. 相似文献
5.
We review recent advances in modal regression studies using kernel density estimation. Modal regression is an alternative approach for investigating the relationship between a response variable and its covariates. Specifically, modal regression summarizes the interactions between the response variable and covariates using the conditional mode or local modes. We first describe the underlying model of modal regression and its estimators based on kernel density estimation. We then review the asymptotic properties of the estimators and strategies for choosing the smoothing bandwidth. We also discuss useful algorithms and similar alternative approaches for modal regression, and propose future direction in this field. This article is categorized under:
- Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory
- Statistical and Graphical Methods of Data Analysis > Nonparametric Methods
- Statistical and Graphical Methods of Data Analysis > Density Estimation
6.
Aurore Delaigle 《Revue canadienne de statistique》2007,35(1):89-104
The author considers density estimation from contaminated data where the measurement errors come from two very different sources. A first error, of Berkson type, is incurred before the experiment: the variable X of interest is unobservable and only a surrogate can be measured. A second error, of classical type, is incurred after the experiment: the surrogate can only be observed with measurement error. The author develops two nonparametric estimators of the density of X, valid whenever Berkson, classical or a mixture of both errors are present. Rates of convergence of the estimators are derived and a fully data‐driven procedure is proposed. Finite sample performance is investigated via simulations and on a real data example. 相似文献
7.
《Journal of nonparametric statistics》2012,24(8):991-1002
This paper deals with the estimation of a regression function at a fixed point in nonparametric heteroscedastic regression models with Gaussian noise. We assume that the variance of the noise depends on the regressor and on the regression function. We make use of the minimax absolute error risk taken over a Hölder class of regression functions. As the smoothness of the regression function is supposed to be unknown, we construct an adaptive kernel estimator which attains the minimax rate. More precisely, we give an asymptotic upper bound and an asymptotic lower bound for the minimax risk. 相似文献
8.
Aman Ullah 《统计学通讯:理论与方法》2013,42(5):1251-1254
This paper studies the exact density of a general nonparametric regression estimator when the errors are non-normal. The fixed design case is considered. The density function is derived by an application of the technique of Davis (1976) 相似文献
9.
《Journal of nonparametric statistics》2012,24(5):597-609
In the case of the random design nonparametric regression, the regression function estimate is produced practically by joining every two consecutive kernel estimates of regression function values by a straight line segment. Hence, it is of polygon type, and is called the kernel regression function polygon (KRFP) in this paper. The KRFP is analyzed by its asymptotic integrated mean square error (AIMSE). This AIMSE precisely quantifies both effects of the kernel function and of the distance between the points on which kernel estimates of regression function values are calculated on the KRFP. By studying the AIMSE, we have the following findings. First of all, if the distance is of smaller order in magnitude than the bandwidth used by the kernel regression function estimator, then Epanechnikov kernel is still the optimal kernel function for the KRFP. Secondly, if the distance is of the same order in magnitude as the bandwidth, then Epanechnikov kernel is no longer optimal for the KRFP. In this case, using the AIMSE of the KRFP, we obtain the optimal kernel for the KRFP over the class of two-degree polynomials by numerical calculation. As the distance increases, the computation time of the KRFP decreases. However, the resulting performance of the KRFP deteriorates, since the minimum AIMSE of the KRFP over both the bandwidth and the kernel function increases. Finally, if the distance is of larger order in magnitude than the bandwidth, then the uniform kernel is the optimal kernel function for the KRFP. 相似文献
10.
11.
Shigeru Iwata 《Econometric Reviews》2001,20(3):319-335
Since Durbin (1954) and Sargan (1958), instrumental variable (IV) method has long been one of the most popular procedures among economists and other social scientists to handle linear models with errors-in-variables. A direct application of this method to nonlinear errors-in-variables models, however, fails to yield consistent estimators.
This article restricts attention to Tobit and Probit models and shows that simple recentering and rescaling of the observed dependent variable may restore consistency of the standard IV estimator if the true dependent variable and the IV's are jointly normally distributed. Although the required condition seems rarely to be satisfied by real data, our Monte Carlo experiment suggests that the proposed estimator may be quite robust to the possible deviation from normality. 相似文献
This article restricts attention to Tobit and Probit models and shows that simple recentering and rescaling of the observed dependent variable may restore consistency of the standard IV estimator if the true dependent variable and the IV's are jointly normally distributed. Although the required condition seems rarely to be satisfied by real data, our Monte Carlo experiment suggests that the proposed estimator may be quite robust to the possible deviation from normality. 相似文献
12.
《Journal of nonparametric statistics》2012,24(8):955-971
We establish the asymptotic normality of the regression estimator in a fixed-design setting when the errors are given by a field of dependent random variables. The result applies to martingale-difference or strongly mixing random fields. On this basis, a statistical test that can be applied to image analysis is also presented. 相似文献
13.
Estimators of location and size of jumps or discontinuities in a regression function and/or its derivatives are proposed. The estimators are based on the analysis of residuals obtained from the locally weighted least squares regression. The proposed estimators adapt to both fixed and random designs. The asymptotic properties of the estimators are investigated. The method is illustrated through simulation studies. 相似文献
14.
《Journal of nonparametric statistics》2012,24(1):81-104
The beta kernel estimators are shown in Chen [S.X. Chen, Beta kernel estimators for density functions, Comput. Statist. Data Anal. 31 (1999), pp. 131–145] to be non-negative and have less severe boundary problems than the conventional kernel estimator. Numerical results in Chen [S.X. Chen, Beta kernel estimators for density functions, Comput. Statist. Data Anal. 31 (1999), pp. 131–145] further show that beta kernel estimators have better finite sample performance than some of the widely used boundary corrected estimators. However, our study finds that the numerical comparisons of Chen are confounded with the choice of the bandwidths and the quantities being compared. In this paper, we show that the performances of the beta kernel estimators are very similar to that of the reflection estimator, which does not have the boundary problem only for densities exhibiting a shoulder at the endpoints of the support. For densities not exhibiting a shoulder, we show that the beta kernel estimators have a serious boundary problem and their performances at the boundary are inferior to that of the well-known boundary kernel estimator. 相似文献
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16.
T. Senga Kiessé 《Statistics》2017,51(5):1046-1060
The discrete kernel method was developed to estimate count data distributions, distinguishing discrete associated kernels based on their asymptotic behaviour. This study investigates the class of discrete asymmetric kernels and their resulting non-consistent estimators, but this theoretical drawback of the estimators is balanced by some interesting features in small/medium samples. The role of modal probability and variance of discrete asymmetric kernels is highlighted to help better understand the performance of these kernels, in particular how the binomial kernel outperforms other asymmetric kernels. The performance of discrete asymmetric kernel estimators of probability mass functions is illustrated using simulations, in addition to applications to real data sets. 相似文献
17.
《Journal of nonparametric statistics》2012,24(2):287-303
We consider data generating mechanisms which can be represented as mixtures of finitely many regression or autoregression models. We propose nonparametric estimators for the functions characterising the various mixture components based on a local quasi maximum likelihood approach and prove their consistency. We present an EM algorithm for calculating the estimates numerically which is mainly based on iteratively applying common local smoothers and discuss its convergence properties. 相似文献
18.
《Journal of nonparametric statistics》2012,24(6):757-767
In this paper, we study the estimation of the hazard quantile function based on right censored data. Two nonparametric estimators, one based on the empirical quantile density function and the other using the kernel smoothing method, are proposed. Asymptotic properties of the kernel-based estimator are discussed. Monte Carlo simulation studies are conducted to compare the two estimators. The method is illustrated for a real data set. 相似文献
19.
《Journal of nonparametric statistics》2012,24(2):379-397
In this paper, we consider the estimation of the regression function when the interest variable is subject to random censorship and the data satisfy some dependency conditions. We show that the new estimate [defined in Guessoum, Z., and Ould Saïd, E. (2008),‘On Nonparametric Estimation of the Regression Function Under Censorship Model’, Statistics & Decisions, 26, 159–177] suitably normalised is asymptotically normally distributed and the asymptotic variance is given explicitly. An application to confidence bands is given. Some simulations are drawn to lend further support to our theoretical results and to compare finite samples sizes with different rates of censoring and dependence. 相似文献
20.
Nityananda Sarkar 《统计学通讯:理论与方法》2013,42(7):1987-2000
It is well-known in the literature on multicollinearity that one of the major consequences of multicollinearity on the ordinary least squares estimator is that the estimator produces large sampling variances, which in turn might inappropriately lead to exclusion of otherwise significant coefficients from the model. To circumvent this problem, two accepted estimation procedures which are often suggested are the restricted least squares method and the ridge regression method. While the former leads to a reduction in the sampling variance of the estimator, the later ensures a smaller mean square error value for the estimator. In this paper we have proposed a new estimator which is based on a criterion that combines the ideas underlying these two estimators. The standard properties of this new estimator have been studied in the paper. It has also been shown that this estimator is superior to both the restricted least squares as well as the ordinary ridge regression estimators by the criterion of mean sauare error of the estimator of the regression coefficients when the restrictions are indeed correct. The conditions for superiority of this estimator over the other two have also been derived for the situation when the restrictions are not correct. 相似文献