摘要:

A correction method is proposed for models including the generalized linear model when the covariate is measured with error. The method requires a separate validation data set that consists of the surrogateWand the true covariateXor an unbiased estimateX⊃ofX.We do not require the classical additive measurement error model in which the surrogate is unbiased for the true covariates. We first obtain an estimate ofE(X|W) by using nonparametric kernel regression ofXorX⊃onWbased on the validation data. Then we perform a standard analysis with the unknownXreplaced by the estimate ofE(X|W). The asymptotic distribution of the resulting regression parameter estimator is obtained. Generalizations to include components ofXmeasured without error are also discussed.

ISSN:0162-1459    

DOI:10.1080/01621459.1994.10476875

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

This article generalizes continuum regression (CR) in the hope that regressors “jointly constructed” for several predictands might improve on the separate prediction of individual predictands. The generalization developed is a mixture of principal components regression and de Jong's modification of partial least squares for multiple predictands. The balance of ingredients can be chosen by cross-validation, as can the number of regressors constructed. The new method has been tested on real and simulated data. The indications are that conditions for the superiority of the joint approach may be rare in practice.

ISSN:0162-1459    

DOI:10.1080/01621459.1994.10476876

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

This article explores best estimation (in some sense) of the variance matrix V of the vector of disturbances in a normal linear regression model. More precisely, we consider the regression model y = Xβ+ U, where U is distributed asN(0, V) and where the spectral form of V isV= Σnj1 λjRj. The Rjare known and the λjare the (possibly) distinct positive eigenvalues we wish to estimate. More generally, we wish to estimate a linear combination of the eigenvalues. This model involves, among others, the class of error components models. The estimates are required to be quadratic in y, nonnegative, and invariant with respect toβ.Thus they are of the form y'Ay, where A is nonnegative definite and such that AX = 0. Given these restrictions and possibly others, we seek the minimum mean squared error estimate or the minimum variance unbiased estimate, a problem that has received much attention in the literature. Working on estimation of demands for transportation using an error components model, we noticed that prior knowledge on parameters of V was ignored; we believe that it would be a waste (translated in terms of nonoptimality) not to use it. The main goal of this article is to attempt to combine prior knowledge, or even reasonable guess, into the classical context of estimation just described. The solution of the problem is not trivial and requires somewhat complex techniques (presented in an Appendix). Fortunately, the obtained estimators are explicit and straightforward to implement: the MATLAB software is particularly well adapted for the computations. The applicability of the estimators and the statistical model go well beyond econometrics, including geology, hydrogeology, mining exploration, and cartography. An application on real data is given, to illustrate how they work.

ISSN:0162-1459    

DOI:10.1080/01621459.1994.10476877

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

This article develops a semiparametric, minimum chi-squared estimation method of the proportional hazard model for the case when durations are grouped and covariates are categorical. The proposed estimator is easy to compute, yet asymptotically as efficient as the maximum likelihood estimator. This article also suggests simple specification tests for the proportional hazard model. If proportionality holds, then two sets of minimum chi-squared estimators, one from a further grouped data and the other from the original grouped data, will converge to the same quantity; otherwise, they will not. Therefore, a test of the equality of these two sets of estimators will offer a test for proportionality. Monte Carlo simulations demonstrate the performance of these estimators and specification tests. In addition, two real data applications illustrate the implementation of the suggested methods and the contexts in which these methods are useful.

ISSN:0162-1459    

DOI:10.1080/01621459.1994.10476878

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

We study the possibility of identifying general linear and nonlinear time series models using nonparametric methods. The kernel estimators of the conditional mean and variance are used as a basis, and the properties of these quantities as model indicators are briefly discussed. Some drawbacks are pointed out, and motivated by these we introduce projections as tools of identification. The projections are especially useful for additive modeling. Expressions for the asymptotic bias and variance are obtained. The projection of the conditional variance is suggested as a tool for identifying heteroscedastic time series. The results are illustrated by simulations for both the estimators of the projections and the estimators of the conditional mean and variance.

ISSN:0162-1459    

DOI:10.1080/01621459.1994.10476879

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

In this article we suggest a nonparametric procedure for selecting significant lags in the model description of a general nonlinear stationary time series. The procedure can be applied to both the conditional mean and the conditional variance and is valid for heteroscedastic series. The procedure is illustrated by simulations and sunspot data, lynx data, and blowfly data are analyzed. It is indicated that projectors can be used in conjunction with the procedure for selecting significant lags to check the adequacy of an additive time series model.

ISSN:0162-1459    

DOI:10.1080/01621459.1994.10476880

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

This article proposes tests for unit root and other forms of nonstationarity that are asymptotically locally most powerful against a certain class of alternatives and have asymptotic critical values given by the chi-squared distribution. Many existing unit root tests do not share these properties. The alternatives include fractionally and seasonally fractionally differenced processes. There is considerable flexibility in our choice of null hypothesis, which can entail one or more integer or fractional roots of arbitrary order anywhere on the unit circle in the complex plane. For example, we can test for a fractional degree of integration of order 1/2; this can be interpreted as a test for nonstationarity against stationarity. “Overdifferencing” stationary null hypotheses can also be tested. The test statistic is derived via the score principle and is conveniently expressed in the frequency domain. The series tested are regression errors, which, when the hypothesized differencing is correct, are white noise or more generally have weak parametric autocorrelation. We establish the null and local limit distributions of the statistic under mild regularity conditions. We find that Bloomfield's exponential spectral model can provide an especially neat form for the test statistic. We apply the tests to a number of empirical time series originally analyzed by Box and Jenkins, and in several cases find that our tests reject the order of differencing that Box and Jenkins proposed. We also report Monte Carlo studies of finite-sample behavior of versions of our tests and comparisons with other tests.

ISSN:0162-1459    

DOI:10.1080/01621459.1994.10476881

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

When paired comparisons are made sequentially over time as for example in chess competitions, it is natural to assume that the underlying abilities do change with time. Previous approaches are based on fixed updating schemes where the increments and decrements are fixed functions of the underlying abilities. The parameters that determine the functions have to be specified a priori and are based on rational reasoning. We suggest an alternative scheme for keeping track with the underlying abilities. Our approach is based on two components: a response model that specifies the connection between the observations and the underlying abilities and a transition model that specifies the variation of abilities over time. The response model is a very general paired comparison model allowing for ties and ordered responses. The transition model incorporates random walk models and local linear trend models. Taken together, these two components form a non-Gaussian state-space model. Based on recent results, recursive posterior mode estimation algorithms are given and the relation to previous approaches is worked out. The performance of the method is illustrated by simulation results and an application to soccer data of the German Bundesliga.

ISSN:0162-1459    

DOI:10.1080/01621459.1994.10476882

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

Methodology is developed for analysis of observations that are random linear combinations of point “source components.” Dual goals are to estimate unknown source identities and to characterize the mixing process by which sources contribute to the observations. Observations are modeled as arising from a mixture distribution, whereby the mixing component characterizes the process of interest and the kernel component captures measurement error. A parametric model is proposed, and maximum likelihood estimates of source and mixing parameters are obtained. Estimate performance is investigated by Monte Carlo simulation. Major results are devoted to studying a constraint framework within which model identifiability is guaranteed. For maximal generality, a compositional framework is applied throughout. The resolution problem discussed in this article is common in the physical sciences. For illustration, an application to air pollution data is presented.

ISSN:0162-1459    

DOI:10.1080/01621459.1994.10476883

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

A coherent reliability system is a machine composed of a number of components that fails as soon as the set of failed components reaches certain fatal set-thresholds. On failure of the machine, an autopsy report reveals its time of failure and the set of failed components. I use incomplete data methods to obtain maximum likelihood estimates of parameters characterizing the lifetime distributions of the components, based on a sample of autopsy reports.

ISSN:0162-1459    

DOI:10.1080/01621459.1994.10476884

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor