摘要:

We present a new class of regression estimates called generalized τ estimates. These estimates are defined by minimizing the τ scale of the weighted residuals, with weights that penalize high-leverage observations. Like the τ estimates, the generalized τ estimates utilize for their definition two loss functions, ρ1and ρ2, which together with the weights can be chosen to achieve simultaneously high breakdown point, finite gross error sensitivity, and high efficiency. We recommend, however, choosing these functions so as to control the bias behavior of the estimate for a large range of possible contaminations and then boosting the efficiency by a simple least squares reweighting step. The generalized τ estimate with loss functions ρ1and ρ2is related to the Hill–RyanGMestimate with a loss function ρ, which is a linear combination of ρ1and ρr. In fact, both estimates have the same influence function and asymptotic distribution under the central model. We show that a certain generalized τ estimate has good maximum bias behavior and performs well in an extensive Monte Carlo simulation study and three numerical examples.

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10473834

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

The main paradigm of the modern wavelet theory of spatial adaptation formulated by Donoho and Johnstone is that there is a divergence between the linear minimax adaptation theory and the heuristic guiding algorithm development that leads to the necessity of using strongly nonlinear adaptive thresholded methods. On the other hand, it is well known that linear adaptive estimates are the best whenever an estimated function is smooth. Is it possible to suggest a quasi-linear wavelet estimate, by adding to a linear adaptive estimate a minimal number of nonlinear terms on finest scales, that offers advantages of linear adaptive estimates and at the same time matches asymptotic properties of strongly nonlinear procedures like the benchmark SureShrink? The answer is “yes,” and we discuss quasi-linear estimation both theoretically and via a Monte Carlo study. In particular, I show that, asymptotically, a quasi-linear procedure not only matches properties of SureShrink over the Besov scale, but also allows us to relax familiar assumptions and solve a long-standing problem of rate and sharp optimal estimation of monotone functions. For the case of small sample sizes and functions that contain spiky/jumps parts and smooth parts, a quasi-linear estimate performs exceptionally well in terms of visual aesthetic appeal, approximation, and data compression.

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10473835

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

A weighted rank estimate is proposed that has 50% breakdown and is asymptotically normal at rate √n. Based on this theory, inferential procedures, including asymptotic confidence and tests, and diagnostic procedures, such as studentized residuals, are developed. The influence function of the estimate is derived and shown to be continuous and bounded everywhere in (x,Y) space. Examples show that robustness against outlying high-leverage clusters may approach that of the least median of squares, while retaining more stability against inliers. The estimator uses weights that correct for both factor and response spaces. A Monte Carlo study shows that the estimate is more efficient than the generalized rank estimates, which are generalizedRestimates with weights that only correct for factor space. When weights are constant, the estimate reduces to the regular Wilcoxon rank estimate.

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10473836

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

When analyzing the productivity of firms, one may want to compare how the firms transform a set of inputsx(typically labor, energy or capital) into an outputy(typically a quantity of goods produced). The economic efficiency of a firm is then defined in terms of its ability to operate close to or on the production frontier, the boundary of the production set. The frontier function gives the maximal level of output attainable by a firm for a given combination of its inputs. The efficiency of a firm may then be estimated via the distance between the attained production level and the optimal level given by the frontier function. From a statistical viewpoint, the frontier function may be viewed as the upper boundary of the support of the population of firms density in the input and output space. It is often reasonable to assume that the production frontier is a concave monotone function. Then a famous estimator in the univariate input and output case is the data envelopment analysis (DEA) estimator, the lowest concave monotone increasing function covering all sample points. This estimator is biased downward, because it never exceeds the true production frontier. In this article we derive the asymptotic distribution of the DEA estimator, which enables us to assess the asymptotic bias and hence to propose an improved bias-corrected estimator. This bias-corrected estimator involves consistent estimation of the density function as well as of the second derivative of the production frontier. We also briefly discuss the construction of asymptotic confidence intervals. The finite-sample performance of the bias-corrected estimator is investigated via a simulation study, and the procedure is illustrated for a real data example.

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10473837

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

Graphical models offer simple and intuitive interpretations in terms of conditional independence relationships, and these are especially valuable when large numbers of variables are involved. In some settings, restrictions on experiments and other forms of data collection may result in our being able to estimate only parts of a large graphical model; for example, when the data in a large contingency table are extremely sparse. In other settings, we might use a model building strategy that constructs component pieces first, and then tries to combine those pieces into a larger model. In this article we address this problem of combining component models in the context of cross-classified categorical data, and we show how to derive partial information about an underlying log-linear structure from its conditional log-linear structures and then how to use this information to choose a log-linear structure under the assumption that it is graphical. We illustrate the results using a simulated dataset based on a problem arising in cognitive psychology applied to learning.

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10473838

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

We consider a logistic model for binary response data that allows the possibility of power transformation ofx; that is, log[p/(1 -p)] = α + βx(λ)+ γI, wherexis a continuous variable,x(λ)is the Box–Cox transformation, andIis a binary variable indicating treatment or group. This model is applicable to observational studies or randomized trials when a treatment effect is investigated after controlling for a confounding variablex. Our focus is on inference concerning γ, the treatment effect. In the analysis, a common approach might be to treat the estimated value of λ as fixed and ignore uncertainty associated with its estimation in inference about γ. Alternatively, we might perform an unconditional analysis in which λ is regarded as a parameter. We show that under the null hypothesis, γ = 0, these two approaches are asymptotically equivalent if the two groups have the same distribution ofxand the same sample size. This result also holds for the situation of multiple covariates each with their own transformation. Furthermore, we find that when γ ≠ 0 and when there is reasonable overlap between the two distributions ofxgivenI, the two procedures differ asymptotically; however, the difference between them is extremely small. The asymptotic findings are supported by a simulation study.

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10473839

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

Markov chain Monte Carlo algorithms are widely used in the fitting of generalized linear models (GLMs). Such model fitting is somewhat of an art form, requiring suitable trickery and tuning to obtain results in which one can have confidence. A wide range of practical issues arise. The focus here is on parameter identifiability and posterior propriety. In particular, we clarify that nonidentifiability arises for usual GLMs and discuss its implications for simulation-based model fitting. Because often some part of the prior specification is vague, we consider whether the resulting posterior is proper, providing rather general and easily checked results for GLMs. We also show that if a Gibbs sampler is run with an improper posterior, then it may be possible to use the output to obtain meaningful inference for certain model unknowns.

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10473840

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

This article considers variance estimation for Horvitz–Thompson–type estimated totals based on survey data with imputed non-respondents and with nonnegligible sampling fractions. A method based on a variance decomposition is proposed. Our method can be applied to complicated situations where a composite of some deterministic and/or random imputation methods is used, including using imputed data in subsequent imputations. Although here linearization or Taylor expansion–type techniques are adopted, replication methods such as the jackknife, balanced repeated replication, and random groups can also be used in applying our method to derive variance estimators. Using our method, variance estimators can be derived under either the customary design-based approach or the model-assisted approach, and are asymptotically unbiased and consistent. The Transportation Annual Survey conducted at the U.S. Census Bureau, in which nonrespondents are imputed using a composite of cold deck and ratio type imputation methods, is used as an example as well as the motivation for our study.

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10473841

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

We present properties of statistics arising from the Block, Borges, and Savits age-dependent minimal repair model. These properties are analogous to the order statistic properties in homogeneous Poisson processes. These properties are exploited to obtain an algorithm for generating a realization from the minimal repair model, and for testing hypothesis concerning the initial distribution function or hazard function of the repair model.

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10473842

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

A set of permutation tests that are both exact and distribution-free are proposed to simultaneously detect differences in marginal locations and/or scales in bivariate data. The tests take advantage of the fact that when the marginal means and variances are equal, the pairwise differences are symmetrically distributed about 0 and are uncorrelated with the pairwise sums. Two statistics for detecting the marginal location and scale differences are combined in a quadratic form. A permutation distribution for this quadratic form follows from considering all 2nconditionally equally likely sign changes on the differences. Several methods of estimating the covariance matrix of the quadratic form are examined, including conditional and unconditional (plug-in) approaches. These new tests are compared with the standard tests in the literature and, through simulation for several families of bivariate distributions, are found to compare quite favorably. This article also brings to light the largely overlooked likelihood ratio test for equal means and variances in the bivariate normal and shows its relationship to more recent approaches, including those presented here.

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10473843

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor