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作者：SCOTT, DW; WAND, MP
作者单位：Texas A&M University System; Texas A&M University College Station
摘要：The 'curse of dimensionality' has been interpreted as suggesting that kernel methods have limited applicability in more than several dimensions. In this note, qualitative and quantitative performance measures for multivariate density estimates are examined. Optimal pointwise and global window widths for mean absolute and mean squared errors are compared for multivariate data. One result is that the optimal pointwise absolute and squared error window widths are nearly equal for all dimensions. ...
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作者：MARZEC, L; MARZEC, P
摘要：Based on independent random samples from two distributions we consider the problem of testing that the distributions are identical except for an unknown location parameter against the alternative that one is less dispersed than the other. The proposed tests are shown to be asymptotically distribution-free and consistent. The asymptotic relative efficiencies with respect to several other tests for some specific alternatives are given.
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作者：LI, WK
摘要：Determining whether a time series has a unit root is an important problem in many time series analyses. For seasonal time series the problem is more complicated as one has to decide whether both regular and seasonal differencing or just one of them would suffice to transform a series into stationarity. This important problem is addressed via the Lagrange multiplier test approach. The large sample representations of the test statistics in terms of integrals of Wiener processes are obtained. The...
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作者：JONES, MC
摘要：A new kernel density estimator for length biased data which derives from smoothing the nonparametric maximum likelihood estimator is proposed and investigated. It has various advantages over an alternative method suggested by Bhattacharyya, Franklin & Richardson (1988): it is necessarily a probability density, it is particularly better behaved near zero, it has better asymptotic mean integrated squared error properties and it is more readily extendable to related problems such as density deriv...
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作者：SLUD, E
摘要：For large-sample clinical trials with independent individuals randomly allocated to two treatment groups, in which survival times follow a log linear multiplicative intensity model with treatment group as one covariate, this paper calculates the asymptotic relative efficiency of the log rank test for treatment effect as compared with the optimal score test. The method is to exhibit the failure hazard intensity, not of proportional hazards form, obtained by ignoring all covariates other than tr...
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作者：HALL, P; SHEATHER, SJ; JONES, MC; MARRON, JS
作者单位：University of New South Wales Sydney; Open University - UK; University of North Carolina; University of North Carolina Chapel Hill
摘要：A bandwidth selection method is proposed for kernel density estimation. This is based on the straightforward idea of plugging estimates into the usual asymptotic representation for the optimal bandwidth, but with two important modifications. The result is a bandwidth selector with the, by nonparametric standards, extremely fast asymptotic rate of convergence of n-1/2, where n --> infinity denotes sample size. Comparison is given to other bandwidth selection methods, and small sample impact is ...
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作者：RUIZVELASCO, S
摘要：We calculate the asymptotic efficiency of logistic regression relative to linear discriminant analysis for testing hypotheses about the parameters when the explanatory variables are normally distributed. The Pitman asymptotic efficiency for hypothesis tests in this context is the same as the asymptotic relative efficiency calculated using misclassification rates and is independent of the number of explanatory variables and the number of parameters to be tested.
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作者：CHAN, LY
摘要：In nonparametric regression, the variance of the response can be estimated by the sum of squares of differences of the observed response. In this paper we obtain the most efficient design for a general variance estimator defined by first order differences. It is found that for this estimator, in the majority of cases, a good approximation to the most efficient design is the uniform design. The least efficient designs are also discussed.
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作者：DIETRICH, CR
摘要：Numerical simulations recently reported in the literature have shown that the profile likelihood associated with the estimation of covariance range parameters for a Gaussian field can be multimodal. Here we complement these recent results by considering covariances with unknown nugget, scale and range parameters. Estimation is performed in a restricted maximum likelihood framework. For unbounded sampling domains and known range parameter, conditions ensuring asymptotic unimodality of the restr...
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作者：CHIU, ST
摘要：It is well known that the cross-validation score function of discretized data often tends to - infinity as the bandwidth tends to zero. This disturbing property causes some difficulty in applying cross-validation to discretized data. Since all data are rounded to some degree, the phenomenon limits the application of cross-validation in practice. Based on characteristic functions, the cause of the difficulty is explained, and a simple modification is suggested. Under some conditions, it is show...
