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1.
Heteroscedasticity checks for regression models 总被引:1,自引:0,他引:1
For checking on heteroscedasticity in regression models, a unified approach is proposed to constructing test statistics in
parametric and nonparametric regression models. For nonparametric regression, the test is not affected sensitively by the
choice of smoothing parameters which are involved in estimation of the nonparametric regression function. The limiting null
distribution of the test statistic remains the same in a wide range of the smoothing parameters. When the covariate is one-dimensional,
the tests are, under some conditions, asymptotically distribution-free. In the high-dimensional cases, the validity of bootstrap
approximations is investigated. It is shown that a variant of the wild bootstrap is consistent while the classical bootstrap
is not in the general case, but is applicable if some extra assumption on conditional variance of the squared error is imposed.
A simulation study is performed to provide evidence of how the tests work and compare with tests that have appeared in the
literature. The approach may readily be extended to handle partial linear, and linear autoregressive models. 相似文献
2.
3.
A Frisch-Newton Algorithm for Sparse Quantile Regression 总被引:3,自引:0,他引:3
RogerKoenker PinNg 《应用数学学报(英文版)》2005,21(2):225-236
Recent experience has shown that interior-point methods using a log barrier approach are far superior to classical simplex methods for computing solutions to large parametric quantile regression problems. In many large empirical applications, the design matrix has a very sparse structure. A typical example is the classical fixed-effect model for panel data where the parametric dimension of the model can be quite large, but the number of non-zero elements is quite small. Adopting recent developments in sparse linear algebra we introduce a modified version of the Prisch-Newton algorithm for quantile regression described in Portnoy and Koenker~([28]). The new algorithm substantially reduces the storage (memory) requirements and increases computational speed. The modified algorithm also facilitates the development of nonparametric quantile regression methods. The pseudo design matrices employed in nonparametric quantile regression smoothing are inherently sparse in both the fidelity and roughness penalty components. Exploiting the sparse structure of these problems opens up a whole range of new possibilities for multivariate smoothing on large data sets via ANOVA-type decomposition and partial linear models. 相似文献
4.
Yu Ryan Yue Paul L. Speckman Dongchu Sun 《Annals of the Institute of Statistical Mathematics》2012,64(3):577-613
Adaptive smoothing has been proposed for curve-fitting problems where the underlying function is spatially inhomogeneous.
Two Bayesian adaptive smoothing models, Bayesian adaptive smoothing splines on a lattice and Bayesian adaptive P-splines,
are studied in this paper. Estimation is fully Bayesian and carried out by efficient Gibbs sampling. Choice of prior is critical
in any Bayesian non-parametric regression method. We use objective priors on the first level parameters where feasible, specifically
independent Jeffreys priors (right Haar priors) on the implied base linear model and error variance, and we derive sufficient
conditions on higher level components to ensure that the posterior is proper. Through simulation, we demonstrate that the
common practice of approximating improper priors by proper but diffuse priors may lead to invalid inference, and we show how
appropriate choices of proper but only weakly informative priors yields satisfactory inference. 相似文献
5.
6.
This paper addresses the problem of modelling time series with nonstationarity from a finite number of observations. Problems encountered with the time varying parameters in regression type models led to the smoothing techniques. The smoothing methods basically rely on the finiteness of the error variance, and thus, when this requirement fails, particularly when the error distribution is heavy tailed, the existing smoothing methods due to [1], are no longer optimal. In this paper, we propose a penalized minimum dispersion method for time varying parameter estimation when a regression model generated by an infinite variance stable process with characteristic exponent α ε (1, 2). Recursive estimates are evaluated and it is shown that these estimates for a nonstationary process with normal errors is a special case. 相似文献
7.
We developed two kernel smoothing based tests of a parametric mean-regression model against a nonparametric alternative when the response variable is right-censored. The new test statistics are inspired by the synthetic data and the weighted least squares approaches for estimating the parameters of a (non)linear regression model under censoring. The asymptotic critical values of our tests are given by the quantiles of the standard normal law. The tests are consistent against fixed alternatives, local Pitman alternatives and uniformly over alternatives in Hölder classes of functions of known regularity. 相似文献
8.
Xiaohui Yuan Tianqing Liu Nan Lin Baoxue Zhang 《Journal of multivariate analysis》2010,101(10):2420-2433
Many statistical models, e.g. regression models, can be viewed as conditional moment restrictions when distributional assumptions on the error term are not assumed. For such models, several estimators that achieve the semiparametric efficiency bound have been proposed. However, in many studies, auxiliary information is available as unconditional moment restrictions. Meanwhile, we also consider the presence of missing responses. We propose the combined empirical likelihood (CEL) estimator to incorporate such auxiliary information to improve the estimation efficiency of the conditional moment restriction models. We show that, when assuming responses are strongly ignorable missing at random, the CEL estimator achieves better efficiency than the previous estimators due to utilization of the auxiliary information. Based on the asymptotic property of the CEL estimator, we also develop Wilks’ type tests and corresponding confidence regions for the model parameter and the mean response. Since kernel smoothing is used, the CEL method may have difficulty for problems with high dimensional covariates. In such situations, we propose an instrumental variable-based empirical likelihood (IVEL) method to handle this problem. The merit of the CEL and IVEL are further illustrated through simulation studies. 相似文献
9.
In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the local linear technique and the averaged method,the initial estimates of the coefficient functions are given.Second step,based on the initial estimates,the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure.The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions.Two simulated examples show that the procedure is effective. 相似文献
10.
We consider the use ofB-spline nonparametric regression models estimated by the maximum penalized likelihood method for extracting information from
data with complex nonlinear structure. Crucial points inB-spline smoothing are the choices of a smoothing parameter and the number of basis functions, for which several selectors
have been proposed based on cross-validation and Akaike information criterion known as AIC. It might be however noticed that
AIC is a criterion for evaluating models estimated by the maximum likelihood method, and it was derived under the assumption
that the ture distribution belongs to the specified parametric model. In this paper we derive information criteria for evaluatingB-spline nonparametric regression models estimated by the maximum penalized likelihood method in the context of generalized
linear models under model misspecification. We use Monte Carlo experiments and real data examples to examine the properties
of our criteria including various selectors proposed previously. 相似文献
11.
Forecasting concentrations of air pollutants by logarithm support vector regression with immune algorithms 总被引:2,自引:0,他引:2
Kuo-Ping LinPing-Feng Pai Shun-Ling Yang 《Applied mathematics and computation》2011,217(12):5318-5327
The need to minimize the potential impact of air pollutants on humans has made the accurate prediction of concentrations of air pollutants a crucial subject in environmental research. Support vector regression (SVR) models have been successfully employed to solve time series problems in many fields. The use of SVR models for forecasting concentrations of air pollutants has not been widely investigated. Data preprocessing procedures and the parameter selection of SVR models can radically influence forecasting performance. This study proposes a support vector regression with logarithm preprocessing procedure and immune algorithms (SVRLIA) model which takes advantage of the structural risk minimization of SVR models, the data smoothing of preprocessing procedures, and the optimization of immune algorithms, in order to more accurately forecast concentrations of air pollutants. Three pollutants, namely particulate matter (PM10), nitrogen oxide, (NOx), and nitrogen dioxide (NO2), are collected and examined to determine the feasibility of the developed SVRLIA model. Experimental results reveal that the SVRLIA model can accurately forecast concentrations of air pollutants. 相似文献
12.
Antonis A Michis 《The Journal of the Operational Research Society》2015,66(5):832-844
This article proposes a wavelet smoothing method to improve conditional forecasts generated from linear regression sales response models. The method is applied to the forecasted values of the predictors to remove forecast errors and thereby improve the overall forecasting performance of the models. Eight empirical studies are presented in which the purpose was to forecast detergent sales in the Netherlands, and wavelet smoothing was compared with a moving average and a band-pass filter. All methods were found to improve forecasts. Wavelet smoothing provided the best results when applied on highly volatile marketing time series. In contrast, it was less effective when applied on highly aggregated and smooth time series. An advantage of wavelets is that they are flexible enough to allow for data characteristics like abrupt changes, spikes and cyclical changes that are usually associated with price changes and promotions. 相似文献
13.
Rob J. Hyndman Muhammad Akram Blyth C. Archibald 《Annals of the Institute of Statistical Mathematics》2008,60(2):407-426
We discuss the admissible parameter space for some state space models, including the models that underly exponential smoothing
methods. We find that the usual parameter restrictions (requiring all smoothing parameters to lie between 0 and 1) do not
always lead to stable models. We also find that all seasonal exponential smoothing methods are unstable as the underlying
state space models are neither reachable nor observable. This instability does not affect the forecasts, but does corrupt
the state estimates. The problem can be overcome with a simple normalizing procedure. Finally we show that the admissible
parameter space of a seasonal exponential smoothing model is much larger than that for a basic structural model, leading to
better forecasts from the exponential smoothing model when there is a rapidly changing seasonal pattern. 相似文献
14.
Quantile regression has received a great deal of attention as an important tool for modeling statistical quantities of interest other than the conditional mean. Varying coefficient models are widely used to explore dynamic patterns among popular models available to avoid the curse of dimensionality. We propose a support vector quantile regression model with varying coefficients and its two estimation methods. One uses the quadratic programming, and the other uses the iteratively reweighted least squares procedure. The proposed method can be applied easily and effectively to estimating the nonlinear regression quantiles depending on the high-dimensional vector of smoothing variables. We also present the model selection method that employs generalized cross validation and generalized approximate cross validation techniques for choosing the hyperparameters, which affect the performance of the proposed model. Numerical studies are conducted to illustrate the performance of the proposed model. 相似文献
15.
This paper proposes statistical procedures to check if a real-valued covariate X has an effect on a functional response Y(t). A non-parametric kernel regression is considered to estimate the influence of X on Y(t) and two test statistics based on residual sums of squares and smoothing residuals are proposed. Their acceptance levels
are determined by means of permutations. The lack-of-fit test for a class of parametric models is then discussed as a consequence
of the no effect procedure. Monte Carlo simulations provide an insight into the level and the power of the no effect tests.
A study of atmospheric radiation illustrates the behavior of the proposed methods in practice. 相似文献
16.
John Hughes 《Journal of computational and graphical statistics》2013,22(3):733-755
Non-Gaussian spatial data are common in many fields. When fitting regressions for such data, one needs to account for spatial dependence to ensure reliable inference for the regression coefficients. The two most commonly used regression models for spatially aggregated data are the automodel and the areal generalized linear mixed model (GLMM). These models induce spatial dependence in different ways but share the smoothing approach, which is intuitive but problematic. This article develops a new regression model for areal data. The new model is called copCAR because it is copula-based and employs the areal GLMM’s conditional autoregression (CAR). copCAR overcomes many of the drawbacks of the automodel and the areal GLMM. Specifically, copCAR (1) is flexible and intuitive, (2) permits positive spatial dependence for all types of data, (3) permits efficient computation, and (4) provides reliable spatial regression inference and information about dependence strength. An implementation is provided by R package copCAR, which is available from the Comprehensive R Archive Network, and supplementary materials are available online. 相似文献
17.
Summary Additive models of the type y=f
1(x
1)+...+f
p(x
p)+ε where f
j
, j=1,..,p, have unspecified functional form, are flexible statistical regression models which can be used to characterize nonlinear
regression effects. One way of fitting additive models is the expansion in B-splines combined with penalization which prevents
overfitting. The performance of this penalized B-spline (called P-spline) approach strongly depends on the choice of the amount
of smoothing used for components f
j
. In particular for higher dimensional settings this is a computationaly demanding task. In this paper we treat the problem
of choosing the smoothing parameters for P-splines by genetic algorithms. In several simulation studies this approach is compared
to various alternative methods of fitting additive models. In particular functions with different spatial variability are
considered and the effect of constant respectively local adaptive smoothing parameters is evaluated. 相似文献
18.
The non-parametric estimation of average causal effects in observational studies often relies on controlling for confounding covariates through smoothing regression methods such as kernel, splines or local polynomial regression. Such regression methods are tuned via smoothing parameters which regulates the amount of degrees of freedom used in the fit. In this paper we propose data-driven methods for selecting smoothing parameters when the targeted parameter is an average causal effect. For this purpose, we propose to estimate the exact expression of the mean squared error of the estimators. Asymptotic approximations indicate that the smoothing parameters minimizing this mean squared error converges to zero faster than the optimal smoothing parameter for the estimation of the regression functions. In a simulation study we show that the proposed data-driven methods for selecting the smoothing parameters yield lower empirical mean squared error than other methods available such as, e.g., cross-validation. 相似文献
19.
Christine H. Müller 《Journal of multivariate analysis》2005,95(1):153-181
We investigate depth notions for general models which are derived via the likelihood principle. We show that the so-called likelihood depth for regression in generalized linear models coincides with the regression depth of Rousseeuw and Hubert (J. Amer. Statist. Assoc. 94 (1999) 388) if the dependent observations are appropriately transformed. For deriving tests, the likelihood depth is extended to simplicial likelihood depth. The simplicial likelihood depth is always a U-statistic which is in some cases not degenerated. Since the U-statistic is degenerated in the most cases, we demonstrate that nevertheless the asymptotic distribution of the simplicial likelihood depth and thus asymptotic α-level tests for general types of hypotheses can be derived. The tests are distribution-free. We work out the method for linear and quadratic regression. 相似文献
20.
本文探讨具有不同光滑变量的变系数模型的建模、估计和估计的渐近性.首先,从实际出发建立模型;然后,使用局部线性方法给出模型中未知函数的初始估计,再使用平均方法,给出它们的平均估计;进—步,给出这些平均估计的渐近正态性.两个模拟例子说明这一估计方法是有效的. 相似文献