摘要:

We explore the aims of, and relationships between, various kernel-type regression estimators. To do so, we identify two general types of (direct) kernel estimators differing in their treatment of the nuisance density function associated with regressor variable design. We look at the well-known Gasser-Müller, Nadaraya-Watson, and Priestley-Chao methods in this light. In the random design case, none of these methods is totally adequate, and we mention a novel (direct) kernel method with appropriate properties. Disadvantages of even the latter idea are remedied by kernel-weighted local linear fitting, a well-known technique that is currently enjoying renewed popularity. We see how to fit this approach into our general framework, and hence form a unified understanding of how these kernel-type smoothers interrelate. Though the mission of this article is unificatory (and even pedagogical), the desire for better understanding of superficially different approaches is motivated by the need to improve practical estimators. In the end, we concur with other authors that kernel-weighted local linear fitting deserves much further attention for applications.

ISSN:0162-1459    

DOI:10.1080/01621459.1994.10476816

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

A common complication in analyzing binomial data is overdispersion, where the observed variation exceeds that predicted from the binomial distribution with parametersNandP.We consider the situation whereNis not observed and variable. To estimate the regression parameters associated with covariates, we apply the transform-both-sides method. Based on the first-order asymptotic variance stabilizing transformation, we develop the arcsine transformation family indexed by a single parameter. This family includes the square root and the arcsine transformations as special cases. Asymptotic properties of the transformation methods are obtained. Simulation study indicates that the arcsine transformation family is more efficient than the square root and arcsine transformations when there is moderate overdispersion. These approaches are applied to a data set from radiobiology.

ISSN:0162-1459    

DOI:10.1080/01621459.1994.10476817

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

In applied problems it is common to specify a model for the conditional mean of a response given a set of regressors. A subset of the regressors may be missing for some study subjects either by design or happenstance. In this article we propose a new class of semiparametric estimators, based on inverse probability weighted estimating equations, that are consistent for parameter vector α0of the conditional mean model when the data are missing at random in the sense of Rubin and the missingness probabilities are either known or can be parametrically modeled. We show that the asymptotic variance of the optimal estimator in our class attains the semiparametric variance bound for the model by first showing that our estimation problem is a special case of the general problem of parameter estimation in an arbitrary semiparametric model in which the data are missing at random and the probability of observing complete data is bounded away from 0, and then deriving a representation for the efficient score, the semiparametric variance bound, and the influence function of any regular, asymptotically linear estimator in this more general estimation problem. Because the optimal estimator depends on the unknown probability law generating the data, we propose locally and globally adaptive semiparametric efficient estimators. We compare estimators in our class with previously proposed estimators. We show that each previous estimator is asymptotically equivalent to some, usually inefficient, estimator in our class. This equivalence is a consequence of a proposition stating that every regular asymptotic linear estimator of α0is asymptotically equivalent to some estimator in our class. We compare various estimators in a small simulation study and offer some practical recommendations.

ISSN:0162-1459    

DOI:10.1080/01621459.1994.10476818

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

We discuss estimation and prediction in a Markov renewal model where intensities of the one-step transitions follow a Cox regression model with baseline hazards and covariates depending on the backward recurrence time. A modification of the Andersen and Gill results is given to extend the asymptotic properties of the partial likelihood estimates to this setting. We further consider prediction of the realization of the process in a single individual based on the follow-up information. Data of the International Bone Marrow Transplant Registry are used for illustration purposes.

ISSN:0162-1459    

DOI:10.1080/01621459.1994.10476819

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

Self-validating computation based on interval arithmetic can produce computed values with a guaranteed error bound. Such methods are especially useful whenever the computed results must satisfy given accuracy requirements. This article reports methods for obtaining self-validating results when computing probabilities and percentiles of univariate continuous distributions. Probability functions dealt with explicitly in the article are normal, incomplete gamma, incomplete beta, and noncentral chi-squared.

ISSN:0162-1459    

DOI:10.1080/01621459.1994.10476820

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

Estimation of multivariate shape and location in a fashion that is robust with respect to outliers and is affine equivariant represents a significant challenge. The use of compound estimators that use a combinatorial estimator such as Rousseeuw's minimum volume ellipsoid (MVE) or minimum covariance determinant (MCD) to find good starting points for high-efficiency robust estimators such as S estimators has been proposed. In this article we indicate why this scheme will fail in high dimension due to combinatorial explosion in the space that must be searched for the MVE or MCD. We propose a meta-algorithm based on partitioning the data that enables compound estimators to work in high dimension. We show that even when the computational effort is restricted to a linear function of the number of data points, the algorithm results in an estimator with good asymptotic properties. Extensive computational experiments are used to confirm that significant benefits accrue in finite samples as well. We also give empirical results indicating that the MCD is preferred over the MVE for this application.

ISSN:0162-1459    

DOI:10.1080/01621459.1994.10476821

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

We introduce robust tests for testing hypotheses in a general parametric model. These are robust versions of the Wald, scores, and likelihood ratio tests and are based on general M estimators. Their asymptotic properties and influence functions are derived. It is shown that the stability of the level is obtained by bounding the self-standardized sensitivity of the corresponding M estimator. Furthermore, optimally bounded-influence tests are derived for the Wald- and scores-type tests. Applications to real and simulated data sets are given to illustrate the tests' performance.

ISSN:0162-1459    

DOI:10.1080/01621459.1994.10476822

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

A Monte Carlo algorithm is described that can be used in place of the nested bootstrap. It is particularly advantageous when there is a premium on the number of bootstrap samples, either because samples are hard to generate or because expensive computations are applied to each sample. Thisrecycling algorithmis useful because it enables inference procedures like prepivoting and bootstrap iteration in models where nested bootstrapping is computationally impractical. Implementation of the recycling algorithm is quite straightforward. As a replacement of the double bootstrap, for example, bootstrap recycling involves two stages of sampling, as does the double bootstrap. The first stage of both algorithms is the same: simulate from the fitted model. In the second stage of recycling, one batch of samples is simulated from one measure; a measure dominating all the first-stage fits. These samples are recycled with each first-stage sample to yield estimated adjustments to the original inference procedure. Choice of this second-stage measure affects the efficiency of the recycling algorithm. Gains in efficiency are slight for the nonparametric bootstrap but can be substantial in parametric problems. Applications are given to testing with sparse contingency tables and to construction of likelihood-based confidence sets in a hidden Markov model from hematology.

ISSN:0162-1459    

DOI:10.1080/01621459.1994.10476823

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

This article studies the problem of multiple change points in the variance of a sequence of independent observations. We propose a procedure to detect variance changes based on an iterated cumulative sums of squares (ICSS) algorithm. We study the properties of the centered cumulative sum of squares function and give an intuitive basis for the ICSS algorithm. For series of moderate size (i.e., 200 observations and beyond), the ICSS algorithm offers results comparable to those obtained by a Bayesian approach or by likelihood ratio tests, without the heavy computational burden required by these approaches. Simulation results comparing the ICSS algorithm to other approaches are presented.

ISSN:0162-1459    

DOI:10.1080/01621459.1994.10476824

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

In this article, the saddlepoint approximations to the density and tail probability of a ratio of quadratic forms in normal variables are derived. A numerical exposition via the Durbin-Watson test statistic reveals several desirable features. The approximations, which involve only a limited number of computable functions, provide the practitioner with an accessible and a very powerful tool.

ISSN:0162-1459    

DOI:10.1080/01621459.1994.10476825

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor