共查询到20条相似文献,搜索用时 15 毫秒
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Neil A. Butler & Michael C. Denham 《Journal of the Royal Statistical Society. Series B, Statistical methodology》2000,62(3):585-593
Partial least squares regression has been widely adopted within some areas as a useful alternative to ordinary least squares regression in the manner of other shrinkage methods such as principal components regression and ridge regression. In this paper we examine the nature of this shrinkage and demonstrate that partial least squares regression exhibits some undesirable properties. 相似文献
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We consider the pooled cross-sectional and time series regression model when the disturbances follow a serially correlated
one-way error components. In this context we discovered that the first difference estimator for the regression coefficients
is equivalent to the generalized least squares estimator irrespective of the particular form of the regressor matrix when
the disturbances are generated by a first order autoregressive process where the autocorrelation is close to unity. 相似文献
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《Journal of Statistical Computation and Simulation》2012,82(1-4):341-356
This paper investigates two “non-exact” t-type tests, t( k2) and t(k2), of the individual coefficients of a linear regression model, based on two ordinary ridge estimators. The reported results are built on a simulation study covering 84 different models. For models with large standard errors, the ridge-based t-tests have correct levels with considerable gain in powers over those of the least squares t-test, t(0). For models with small standard errors, t(k1) is found to be liberal and is not safe to use while, t(k2) is found to slightly exceed the nominal level in few cases. When tie two ridge tests art: not winners, the results indicate that they don't loose much against t(0). 相似文献
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Oguz Akbilgic 《Journal of applied statistics》2015,42(8):1773-1781
This paper introduces a novel hybrid regression method (MixReg) combining two linear regression methods, ordinary least square (OLS) and least squares ratio (LSR) regression. LSR regression is a method to find the regression coefficients minimizing the sum of squared error rate while OLS minimizes the sum of squared error itself. The goal of this study is to combine two methods in a way that the proposed method superior both OLS and LSR regression methods in terms of R2 statistics and relative error rate. Applications of MixReg, on both simulated and real data, show that MixReg method outperforms both OLS and LSR regression. 相似文献
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《Journal of Statistical Computation and Simulation》2012,82(11):1557-1569
We present an estimating framework for quantile regression where the usual L 1-norm objective function is replaced by its smooth parametric approximation. An exact path-following algorithm is derived, leading to the well-known ‘basic’ solutions interpolating exactly a number of observations equal to the number of parameters being estimated. We discuss briefly possible practical implications of the proposed approach, such as early stopping for large data sets, confidence intervals, and additional topics for future research. 相似文献
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This article considers both Partial Least Squares (PLS) and Ridge Regression (RR) methods to combat multicollinearity problem. A simulation study has been conducted to compare their performances with respect to Ordinary Least Squares (OLS). With varying degrees of multicollinearity, it is found that both, PLS and RR, estimators produce significant reductions in the Mean Square Error (MSE) and Prediction Mean Square Error (PMSE) over OLS. However, from the simulation study it is evident that the RR performs better when the error variance is large and the PLS estimator achieves its best results when the model includes more variables. However, the advantage of the ridge regression method over PLS is that it can provide the 95% confidence interval for the regression coefficients while PLS cannot. 相似文献
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It is well known that it is difficult to construct minimax optimal designs. Furthermore, since in practice we never know the true error variance, it is important to allow small deviations and construct robust optimal designs. We investigate a class of minimax optimal regression designs for models with heteroscedastic errors that are robust against possible misspecification of the error variance. Commonly used A-, c-, and I-optimality criteria are included in this class of minimax optimal designs. Several theoretical results are obtained, including a necessary condition and a reflection symmetry for these minimax optimal designs. In this article, we focus mainly on linear models and assume that an approximate error variance function is available. However, we also briefly discuss how the methodology works for nonlinear models. We then propose an effective algorithm to solve challenging nonconvex optimization problems to find minimax designs on discrete design spaces. Examples are given to illustrate minimax optimal designs and their properties. 相似文献
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Nonparametric regression techniques such as spline smoothing and local fitting depend implicitly on a parametric model. For instance, the cubic smoothing spline estimate of a regression function ∫ μ based on observations ti, Yi is the minimizer of Σ{Yi ‐ μ(ti)}2 + λ∫(μ′′)2. Since ∫(μ″)2 is zero when μ is a line, the cubic smoothing spline estimate favors the parametric model μ(t) = αo + α1t. Here the authors consider replacing ∫(μ″)2 with the more general expression ∫(Lμ)2 where L is a linear differential operator with possibly nonconstant coefficients. The resulting estimate of μ performs well, particularly if Lμ is small. They present an O(n) algorithm for the computation of μ. This algorithm is applicable to a wide class of L's. They also suggest a method for the estimation of L. They study their estimates via simulation and apply them to several data sets. 相似文献
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This study compares the SPSS ordinary least squares (OLS) regression and ridge regression procedures in dealing with multicollinearity data. The LS regression method is one of the most frequently applied statistical procedures in application. It is well documented that the LS method is extremely unreliable in parameter estimation while the independent variables are dependent (multicollinearity problem). The Ridge Regression procedure deals with the multicollinearity problem by introducing a small bias in the parameter estimation. The application of Ridge Regression involves the selection of a bias parameter and it is not clear if it works better in applications. This study uses a Monte Carlo method to compare the results of OLS procedure with the Ridge Regression procedure in SPSS. 相似文献
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Consider the linear regression model Y = Xθ+ ε where Y denotes a vector of n observations on the dependent variable, X is a known matrix, θ is a vector of parameters to be estimated and e is a random vector of uncorrelated errors. If X'X is nearly singular, that is if the smallest characteristic root of X'X s small then a small perurbation in the elements of X, such as due to measurement errors, induces considerable variation in the least squares estimate of θ. In this paper we examine for the asymptotic case when n is large the effect of perturbation with regard to the bias and mean squared error of the estimate. 相似文献
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《Journal of Statistical Computation and Simulation》2012,82(9):625-649
In this article we investigate the asymptotic and finite-sample properties of predictors of regression models with autocorrelated errors. We prove new theorems associated with the predictive efficiency of generalized least squares (GLS) and incorrectly structured GLS predictors. We also establish the form associated with their predictive mean squared errors as well as the magnitude of these errors relative to each other and to those generated from the ordinary least squares (OLS) predictor. A large simulation study is used to evaluate the finite-sample performance of forecasts generated from models using different corrections for the serial correlation. 相似文献
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J. Michael Price 《统计学通讯:理论与方法》2013,42(17):1965-1984
It is not always prossible to establish a preference ordering among regression estimators in terms of the generalized mean square error criterion. In the paper, we determine when it is feasible to use this criteion to couduct comparisons among ordinary least squares, principal components, ridge regression, and shrunken least squares estimators. 相似文献
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H. D. Brunk 《统计学通讯:理论与方法》2013,42(11):1101-1136
The regression function R(?) to be estimated is assumed to have an expansion in terms of specified functions, orthogonalized vich respect to values of the explanatory variable. Relative precisions of OBSERVATION are assumed known. The estimate is the posterior linear mean of R(?) given the data. The investigator plots graphs of appropriate functions as an aid in eliciting his prior means and precisions for the coefficients in the expansion. The method is illustrated by an example using simulated data, an example in which effects of various dosages of Vitamin D are estimated, and an example in which a utility function is estimated. 相似文献
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Theobald (1974) compares Ordinary Least Squares and Ridge Regression estimators of regression parameters using a generalized mean squared error criterion. This paper presents the generalized mean squared error of a Principal Components Regression estimator and comparisons are made with each of the above estimators. In general the choice of which estimator to use depends on the magnitude and the orientation of the unknown parameter vector. 相似文献
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《Journal of Statistical Computation and Simulation》2012,82(3-4):131-146
In at least one important application of stochastic linear programming (Lavaca-Tres Palacios Estuary:A Study of the Influence of Freshwater Inflows, 1980)constraint parameters are simultaneously estimated using multiple regression with historic data for the values of the decision variables and the right hand side of the constraint function. In this circumstance, the question immediately arises "How stable is the linear programming (LP) solution with regard to regression issues such as sample size, magnitude of the error variance, centroids of the decision variables, apd collinearity?" This paper reports a simulation designed to assess the stability of the LP solution and to compare the effectiveness of ridge as an alternative to ordinary least squares (OLS) regression. For the given scenario, the LP solution is consistently "biased." The amount of bias is exacerbated by small samples, large error variances, and collinearity among observations of the decision variables. The best regression criterion is a function not only of collinearity, but also of the magnitude of the error variance and the sum of the means of the decision variables relative to the right hand side of the stochastic constraint In the application that motivated this research, the LP solutions were recommended fresh water inflows from Lake Texana into the estuaries of the Gulf of Mexico. The stochastic constraint estimates commercial fish harvest as a function of seasonal fresh water inflow. The historic data set used to estimate parameters of the constraint comprised rainfall data and fish harvest data prior to the construction of the Lake Texana dam, of necessity a small sample with collinear seasonal rainfall. It is not the authors' intent to solve this application, but rather to investigate through a simpler simulated systemwhether or not regression estimates in similar circumstances might introduce a systematic and predictable bias. The answer to this latter question is a qualified Yes!. 相似文献
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Pierre Pinson Henrik Aa. Nielsen Henrik Madsen Torben S. Nielsen 《Statistics and Computing》2008,18(1):59-71
Short-term forecasting of wind generation requires a model of the function for the conversion of meteorological variables
(mainly wind speed) to power production. Such a power curve is nonlinear and bounded, in addition to being nonstationary.
Local linear regression is an appealing nonparametric approach for power curve estimation, for which the model coefficients
can be tracked with recursive Least Squares (LS) methods. This may lead to an inaccurate estimate of the true power curve,
owing to the assumption that a noise component is present on the response variable axis only. Therefore, this assumption is
relaxed here, by describing a local linear regression with orthogonal fit. Local linear coefficients are defined as those
which minimize a weighted Total Least Squares (TLS) criterion. An adaptive estimation method is introduced in order to accommodate
nonstationarity. This has the additional benefit of lowering the computational costs of updating local coefficients every
time new observations become available. The estimation method is based on tracking the left-most eigenvector of the augmented
covariance matrix. A robustification of the estimation method is also proposed. Simulations on semi-artificial datasets (for
which the true power curve is available) underline the properties of the proposed regression and related estimation methods.
An important result is the significantly higher ability of local polynomial regression with orthogonal fit to accurately approximate
the target regression, even though it may hardly be visible when calculating error criteria against corrupted data. 相似文献
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Young-Ju Kim Chong Gu 《Journal of the Royal Statistical Society. Series B, Statistical methodology》2004,66(2):337-356
Summary. Smoothing splines via the penalized least squares method provide versatile and effective nonparametric models for regression with Gaussian responses. The computation of smoothing splines is generally of the order O ( n 3 ), n being the sample size, which severely limits its practical applicability. We study more scalable computation of smoothing spline regression via certain low dimensional approximations that are asymptotically as efficient. A simple algorithm is presented and the Bayes model that is associated with the approximations is derived, with the latter guiding the porting of Bayesian confidence intervals. The practical choice of the dimension of the approximating space is determined through simulation studies, and empirical comparisons of the approximations with the exact solution are presented. Also evaluated is a simple modification of the generalized cross-validation method for smoothing parameter selection, which to a large extent fixes the occasional undersmoothing problem that is suffered by generalized cross-validation. 相似文献
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Chi-Lun Cheng Hans Schneeweiss & Markus Thamerus 《Journal of the Royal Statistical Society. Series B, Statistical methodology》2000,62(4):699-709
An adjusted least squares estimator, introduced by Cheng and Schneeweiss for consistently estimating a polynomial regression of any degree with errors in the variables, is modified such that it shows good results in small samples without losing its asymptotic properties for large samples. Simulation studies corroborate the theoretical findings. 相似文献