共查询到20条相似文献,搜索用时 15 毫秒
1.
Philip T. Reiss R. Todd Ogden 《Journal of the Royal Statistical Society. Series B, Statistical methodology》2009,71(2):505-523
Summary. Spline-based approaches to non-parametric and semiparametric regression, as well as to regression of scalar outcomes on functional predictors, entail choosing a parameter controlling the extent to which roughness of the fitted function is penalized. We demonstrate that the equations determining two popular methods for smoothing parameter selection, generalized cross-validation and restricted maximum likelihood, share a similar form that allows us to prove several results which are common to both, and to derive a condition under which they yield identical values. These ideas are illustrated by application of functional principal component regression, a method for regressing scalars on functions, to two chemometric data sets. 相似文献
2.
C. C. Holmes & B. K. Mallick 《Journal of the Royal Statistical Society. Series B, Statistical methodology》2001,63(1):3-17
We present a Bayesian analysis of a piecewise linear model constructed by using basis functions which generalizes the univariate linear spline to higher dimensions. Prior distributions are adopted on both the number and the locations of the splines, which leads to a model averaging approach to prediction with predictive distributions that take into account model uncertainty. Conditioning on the data produces a Bayes local linear model with distributions on both predictions and local linear parameters. The method is spatially adaptive and covariate selection is achieved by using splines of lower dimension than the data. 相似文献
3.
In the context of the partially linear semiparametric model examined by Robinson (1988), we show that root-n-consisten estimation results established using kernel and series methods can also be obtained by using k-nearest-neighbor (k-nn) method. 相似文献
4.
In the context of the partially linear semiparametric model examined by Robinson (1988), we show that root-n-consisten estimation results established using kernel and series methods can also be obtained by using k-nearest-neighbor (k-nn) method. 相似文献
5.
Dayanand N. Naik 《统计学通讯:理论与方法》2013,42(6):2225-2232
In this article we suggest multivariate kurtosis as a statistic for detection of outliers in a multivariate linear regression model. The statistic has some local optimality properties. 相似文献
6.
Consider a partially linear regression model with an unknown vector parameter β, an unknown functiong(·), and unknown heteroscedastic error variances. In this paper we develop an asymptotic semiparametric generalized least
squares estimation theory under some weak moment conditions. These moment conditions are satisfied by many of the error distributions
encountered in practice, and our theory does not require the number of replications to go to infinity. 相似文献
7.
Yaowu Zhang 《Journal of Statistical Computation and Simulation》2017,87(11):2115-2127
Inspired by a primary hypertension study was conducted by Chinese government in the Inner Mongolia Autonomous Region, we introduce partially linear models with multivariate responses to evaluate the simultaneous effects of modifiable risk factors on both the systolic and the diastolic blood pressures. We propose a class of weighted profile least-squares approaches to estimate both the parametric and the nonparametric components of the multivariate partially linear models. We also investigate how the weight matrix affects the resultant estimation efficiency. We illustrate our proposals through simulations and an analysis of the primary hypertension data. Our analysis provides strong evidence that the obesity is indeed an important risk factor predisposing to primary hypertension even after adjusting for the ageing effect. 相似文献
8.
Partially linear additive model is useful in statistical modelling as a multivariate nonparametric fitting technique. This paper considers statistical inference for the semiparametric model in the presence of multicollinearity. Based on the profile least-squares (PL) approach and Liu estimation method, we propose a PL Liu estimator for the parametric component. When some additional linear restrictions on the parametric component are available, the corresponding restricted Liu estimator for the parametric component is constructed. The properties of the proposed estimators are derived. Some simulations are conducted to assess the performance of the proposed procedures and the results are satisfactory. Finally, a real data example is analysed. 相似文献
9.
This paper proposes nonparametric estimation methods for functional linear semiparametric quantile regression, where the conditional quantile of the scalar responses is modelled by both scalar and functional covariates and an additional unknown nonparametric function term. The slope function is estimated using the functional principal component basis and the nonparametric function is approximated by a piecewise polynomial function. The asymptotic distribution of the estimators of slope parameters is derived and the global convergence rate of the quantile estimator of unknown slope function is established under suitable norm. The asymptotic distribution of the estimator of the unknown nonparametric function is also established. Simulation studies are conducted to investigate the finite-sample performance of the proposed estimators. The proposed methodology is demonstrated by analysing a real data from ADHD-200 sample. 相似文献
10.
J.M. Muñoz Pichardo J. Muñoz García J.M. Fernández Ponce M.D. Jiménez Garnero 《统计学通讯:理论与方法》2013,42(3):529-547
In this paper we obtain several influence measures for the multivariate linear general model through the approach proposed by Muñoz-Pichardo et al. (1995), which is based on the concept of conditional bias. An interesting charasteristic of this approach is that it does not require any distributional hypothesis. Appling the obtained results to the multivariate regression model, we obtain some measures proposed by other authors. Nevertheless, on the results obtained in this paper, we emphasize two aspects. First, they provide a theoretical foundation for measures proposed by other authors for the mul¬tivariate regression model. Second, they can be applied to any linear model that can be formulated as a particular case of the multivariate linear general model. In particular, we carry out an application to the multivariate analysis of covariance. 相似文献
11.
Semiparametric models provide a more flexible form for modeling the relationship between the response and the explanatory variables. On the other hand in the literature of modeling for the missing variables, canonical form of the probability of the variable being missing (p) is modeled taking a fully parametric approach. Here we consider a regression spline based semiparametric approach to model the missingness mechanism of nonignorably missing covariates. In this model the relationship between the suitable canonical form of p (e.g. probit p) and the missing covariate is modeled through several splines. A Bayesian procedure is developed to efficiently estimate the parameters. A computationally advantageous prior construction is proposed for the parameters of the semiparametric part. A WinBUGS code is constructed to apply Gibbs sampling to obtain the posterior distributions. We show through an extensive Monte Carlo simulation experiment that response model coefficent estimators maintain better (when the true missingness mechanism is nonlinear) or equivalent (when the true missingness mechanism is linear) bias and efficiency properties with the use of proposed semiparametric missingness model compared to the conventional model. 相似文献
12.
ABSTRACTIn this paper, shrinkage ridge estimator and its positive part are defined for the regression coefficient vector in a partial linear model. The differencing approach is used to enjoy the ease of parameter estimation after removing the non parametric part of the model. The exact risk expressions in addition to biases are derived for the estimators under study and the region of optimality of each estimator is exactly determined. The performance of the estimators is evaluated by simulated as well as real data sets. 相似文献
13.
José M. R. Murteira 《统计学通讯:理论与方法》2013,42(24):7367-7375
ABSTRACTThis note presents an approximation to multivariate regression models which is obtained from a first-order series expansion of the multivariate link function. The proposed approach yields a variable-addition approximation of regression models that enables a multivariate generalization of the well-known goodness-of-link specification test, available for univariate generalized linear models. Application of this general methodology is illustrated with models of multinomial discrete choice and multivariate fractional data, in which context it is shown to lead to well-established approximation and testing procedures. 相似文献
14.
In this paper, we study the estimation and inference for a class of semiparametric mixtures of partially linear models. We prove that the proposed models are identifiable under mild conditions, and then give a PL–EM algorithm estimation procedure based on profile likelihood. The asymptotic properties for the resulting estimators and the ascent property of the PL–EM algorithm are investigated. Furthermore, we develop a test statistic for testing whether the non parametric component has a linear structure. Monte Carlo simulations and a real data application highlight the interest of the proposed procedures. 相似文献
15.
Hadi Emami 《统计学通讯:理论与方法》2020,49(8):1793-1800
AbstractIn this article we develop the minimax estimation approach of general linear models to the semiparametric linear models when the parameters are simultaneously constrained by an ellipsoid and linear restrictions. Combining sample information and prior constraints the minimax estimator is obtained and compared with partially least square estimator by theoretical and simulation methods. 相似文献
16.
Generalized linear models (GLMs) are widely studied to deal with complex response variables. For the analysis of categorical dependent variables with more than two response categories, multivariate GLMs are presented to build the relationship between this polytomous response and a set of regressors. Traditional variable selection approaches have been proposed for the multivariate GLM with a canonical link function when the number of parameters is fixed in the literature. However, in many model selection problems, the number of parameters may be large and grow with the sample size. In this paper, we present a new selection criterion to the model with a diverging number of parameters. Under suitable conditions, the criterion is shown to be model selection consistent. A simulation study and a real data analysis are conducted to support theoretical findings. 相似文献
17.
In objective Bayesian model selection, a well-known problem is that standard non-informative prior distributions cannot be used to obtain a sensible outcome of the Bayes factor because these priors are improper. The use of a small part of the data, i.e., a training sample, to obtain a proper posterior prior distribution has become a popular method to resolve this issue and seems to result in reasonable outcomes of default Bayes factors, such as the intrinsic Bayes factor or a Bayes factor based on the empirical expected-posterior prior. 相似文献
18.
Robert J. Beaver 《Journal of statistical planning and inference》1983,7(3):209-218
A log linear multivariate paired comparison model for ties is proposed in which the cell probabilities under independence are those given by Davidson (1970). Altham's (1970) generalized measure of association (iv) is used to compare the association structure between two models, one having full, the other having reduced association structure. Based on the model with reduced association structure, the analysis of data from a consumer preference experiment is presented. 相似文献
19.
In this note, a hypothesis test based on relevant statistical differences is proposed for multivariate linear regression models whose design matrix rank does not equal the number of regression variables. A statistical example is also provided to illustrate the proposed hypothesis test. 相似文献