共查询到20条相似文献,搜索用时 9 毫秒
1.
We develop a novel computational methodology for Bayesian optimal sequential design for nonparametric regression. This computational methodology, that we call inhomogeneous evolutionary Markov chain Monte Carlo, combines ideas of simulated annealing, genetic or evolutionary algorithms, and Markov chain Monte Carlo. Our framework allows optimality criteria with general utility functions and general classes of priors for the underlying regression function. We illustrate the usefulness of our novel methodology with applications to experimental design for nonparametric function estimation using Gaussian process priors and free-knot cubic splines priors. 相似文献
2.
The authors introduce the formal notion of an approximately specified nonlinear regression model and investigate sequential design methodologies when the fitted model is possibly of an incorrect parametric form. They present small‐sample simulation studies which indicate that their new designs can be very successful, relative to some common competitors, in reducing mean squared error due to model misspecifi‐cation and to heteroscedastic variation. Their simulations also suggest that standard normal‐theory inference procedures remain approximately valid under the sequential sampling schemes. The methods are illustrated both by simulation and in an example using data from an experiment described in the chemical engineering literature. 相似文献
3.
Many wavelet shrinkage methods assume that the data are observed on an equally spaced grid of length of the form 2J for some J. These methods require serious modification or preprocessed data to cope with irregularly spaced data. The lifting scheme
is a recent mathematical innovation that obtains a multiscale analysis for irregularly spaced data.
A key lifting component is the “predict” step where a prediction of a data point is made. The residual from the prediction
is stored and can be thought of as a wavelet coefficient. This article exploits the flexibility of lifting by adaptively choosing
the kind of prediction according to a criterion. In this way the smoothness of the underlying ‘wavelet’ can be adapted to
the local properties of the function. Multiple observations at a point can readily be handled by lifting through a suitable
choice of prediction. We adapt existing shrinkage rules to work with our adaptive lifting methods.
We use simulation to demonstrate the improved sparsity of our techniques and improved regression performance when compared
to both wavelet and non-wavelet methods suitable for irregular data. We also exhibit the benefits of our adaptive lifting
on the real inductance plethysmography and motorcycle data. 相似文献
4.
In this note, we consider the problem of the existence of adaptive confidence bands in the fixed design regression model, adapting ideas in Hoffmann and Nickl [(2011), ‘On Adaptive Inference and Confidence Bands’, Annals of Statistics, 39, 2383–2409] to the present case. In the course of the proof, we show that sup-norm adaptive estimators exist as well in the regression setting. 相似文献
5.
In the past decade a number of fixed sampling methods have been developed for selecting the "best" or at least a "good" subset of vaiable in regression analysis. We are interested in deriving a sequential selection procedure to select a subset of a random size including equations. Tables for an example are given at the end of this paper 相似文献
6.
Designs for quadratic regression are considered when the possible choices of the controllable variable are points x=(x1,x2,…,xq) in the q-dimensional cube of side 2. The designs that are optimum with respect to such criteria as those of D-, A-, and E-optimality are compared in their performance relative to these and other criteria. Some of the results are developed algebraically; others, numerically. The possible supports of E-optimum designs are much more numerous than the D-optimum supports characterized earlier. The A-optimum design appears to be fairly robust in its efficiency, under variation of criterion. 相似文献
7.
We propose a new adaptive L1 penalized quantile regression estimator for high-dimensional sparse regression models with heterogeneous error sequences. We show that under weaker conditions compared with alternative procedures, the adaptive L1 quantile regression selects the true underlying model with probability converging to one, and the unique estimates of nonzero coefficients it provides have the same asymptotic normal distribution as the quantile estimator which uses only the covariates with non-zero impact on the response. Thus, the adaptive L1 quantile regression enjoys oracle properties. We propose a completely data driven choice of the penalty level λn, which ensures good performance of the adaptive L1 quantile regression. Extensive Monte Carlo simulation studies have been conducted to demonstrate the finite sample performance of the proposed method. 相似文献
8.
Linda M. Haines 《统计学通讯:理论与方法》2013,42(6):1613-1627
Two results for D θ-optimal designs for nonlinear regression models are shown to follow directly from approximate design theory. The first result considered is one concerning the replication of exact designs with minimum support, first established by Atkinson and Hunter and by M.J. Box in 1968, while the second pertains to a heteroscedastic model introduced by Velilla and Llosa in 1992. An illustrative example is provided. 相似文献
9.
Stefan Fremdt 《Statistics》2015,49(1):128-155
In a variety of different settings cumulative sum (CUSUM) procedures have been applied for the sequential detection of structural breaks in the parameters of stochastic models. Yet their performance depends strongly on the time of change and is best under early change scenarios. For later changes their finite sample behavior is rather questionable. We therefore propose modified CUSUM procedures for the detection of abrupt changes in the regression parameter of multiple time series regression models, that show a higher stability with respect to the time of change than ordinary CUSUM procedures. The asymptotic distributions of the test statistics and the consistency of the procedures are provided. In a simulation study it is shown that the proposed procedures behave well in finite samples. Finally the procedures are applied to a set of capital asset pricing data related to the Fama–French extension of the CAPM. 相似文献
10.
Ailing Yan 《统计学通讯:理论与方法》2013,42(20):5106-5120
AbstractThere has been much attention on the high-dimensional linear regression models, which means the number of observations is much less than that of covariates. Considering the fact that the high dimensionality often induces the collinearity problem, in this article, we study the penalized quantile regression with the elastic net (EnetQR) that combines the strengths of the quadratic regularization and the lasso shrinkage. We investigate the weak oracle property of the EnetQR under mild conditions in the high dimensional setting. Moreover, we propose a two-step procedure, called adaptive elastic net quantile regression (AEnetQR), in which the weight vector in the second step is constructed from the EnetQR estimate in the first step. This two-step procedure is justified theoretically to possess the weak oracle property. The finite sample properties are performed through the Monte Carlo simulation and a real-data analysis. 相似文献
11.
Mohamed Tahir 《统计学通讯:理论与方法》2013,42(12):4501-4509
Non-linear renewal theory is used to derive second order asymptotic expansions for the coverage probability of a fixed-width sequential confidence interval for an unknown parameter xin the inverse linear regression model. These expansions are obtained for a two-stage sequential procedure, proposed by Perng and Tong (1974) for the construction of a confidence interval for x. 相似文献
12.
Earl Nordbrock 《统计学通讯:理论与方法》2013,42(15):1469-1478
We investigate a sequential procedure for comparing two treatments in a binomial clinical trial. The procedure uses play-the-winner sampling with termination as soon as the absolute difference in the number of successes of the two treatments reaches a critical value. The important aspect of our procedure is that the critical value is modified as the experiment progresses. Numerical results are given which show that this procedure is preferred to all other existing procedures on the basis of the sample size on the poorer treatment and also on the basis of total sample size. 相似文献
13.
Peter Müller Don A. Berry Andy P. Grieve Michael Smith Michael Krams 《Journal of statistical planning and inference》2007
We consider simulation-based methods for exploration and maximization of expected utility in sequential decision problems. We consider problems which require backward induction with analytically intractable expected utility integrals at each stage. We propose to use forward simulation to approximate the integral expressions, and a reduction of the allowable action space to avoid problems related to an increasing number of possible trajectories in the backward induction. The artificially reduced action space allows strategies to depend on the full history of earlier observations and decisions only indirectly through a low dimensional summary statistic. The proposed rule provides a finite-dimensional approximation to the unrestricted infinite-dimensional optimal decision rule. We illustrate the proposed approach with an application to an optimal stopping problem in a clinical trial. 相似文献
14.
The linear regression models with the autoregressive moving average (ARMA) errors (REGARMA models) are often considered, in order to reflect a serial correlation among observations. In this article, we focus on an adaptive least absolute shrinkage and selection operator (LASSO) (ALASSO) method for the variable selection of the REGARMA models and extend it to the linear regression models with the ARMA-generalized autoregressive conditional heteroskedasticity (ARMA-GARCH) errors (REGARMA-GARCH models). This attempt is an extension of the existing ALASSO method for the linear regression models with the AR errors (REGAR models) proposed by Wang et al. in 2007. New ALASSO algorithms are proposed to determine important predictors for the REGARMA and REGARMA-GARCH models. Finally, we provide the simulation results and real data analysis to illustrate our findings. 相似文献
15.
Joaquín Diaz Federico J. OReilly Santiago Rincon-Gallardo 《Journal of statistical planning and inference》1983,8(1):21-25
In this paper a set of residuals for the multivariate linear regression model is introduced. These residuals are shown to be independent with known distributions which do not depend on the parameters of the model. Transformations of the mentioned residuals may be used to construct exact α goodness-of-fit tests for the multivariate regression model. 相似文献
16.
In this paper we propose and study two sequential elimination procedures for selecting all new treatments better than a standard or control treatment. These procedures differ from those previously proposed in that we assume variances are unequal and unknown. Expressions for asymptotic expected sample sizes are given. Confidence intervals associated with the procedures are also discussed. 相似文献
17.
Adaptive estimation of non-linear regression models 总被引:1,自引:0,他引:1
Charles F. Manski 《Econometric Reviews》1984,3(2):145-194
This paper summarizes from an econometric perspective recent work by statisticians on adaptive estimation. It also presents new findings concerning the adaptive estimability of non-linear regression models. 相似文献
18.
Motivated by the need to sequentially design experiments for the collection of data in batches or blocks, a new pseudo-marginal sequential Monte Carlo algorithm is proposed for random effects models where the likelihood is not analytic, and has to be approximated. This new algorithm is an extension of the idealised sequential Monte Carlo algorithm where we propose to unbiasedly approximate the likelihood to yield an efficient exact-approximate algorithm to perform inference and make decisions within Bayesian sequential design. We propose four approaches to unbiasedly approximate the likelihood: standard Monte Carlo integration; randomised quasi-Monte Carlo integration, Laplace importance sampling and a combination of Laplace importance sampling and randomised quasi-Monte Carlo. These four methods are compared in terms of the estimates of likelihood weights and in the selection of the optimal sequential designs in an important pharmacological study related to the treatment of critically ill patients. As the approaches considered to approximate the likelihood can be computationally expensive, we exploit parallel computational architectures to ensure designs are derived in a timely manner. 相似文献
19.
In this paper a new multivariate regression estimate is introduced. It is based on ideas derived in the context of wavelet estimates and is constructed by hard thresholding of estimates of coefficients of a series expansion of the regression function. Multivariate functions constructed analogously to the classical Haar wavelets are used for the series expansion. These functions are orthogonal in L2(μn), where μn denotes the empirical design measure. The construction can be considered as designing adapted Haar wavelets. 相似文献
20.
The paper considers regression problems with univariate design points. The design points are irregular and no assumptions
on their distribution are imposed. The regression function is retrieved by a wavelet based reproducing kernel Hilbert space
(RKHS) technique with the penalty equal to the sum of blockwise RKHS norms. In order to simplify numerical optimization, the
problem is replaced by an equivalent quadratic minimization problem with an additional penalty term. The computational algorithm
is described in detail and is implemented with both the sets of simulated and real data. Comparison with existing methods
showed that the technique suggested in the paper does not oversmooth the function and is superior in terms of the mean squared
error. It is also demonstrated that under additional assumptions on design points the method achieves asymptotic optimality
in a wide range of Besov spaces. 相似文献