Concepts of Nonparametric Theory

Pratt, John W.; Gibbons, Jean Dickinson

doi:10.1007/978-1-4612-5931-2

Cited by 228 publications

(85 citation statements)

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“…Second, in the presence of general heteroskedasticity, Lehmann and Stein (1949) and Pratt and Gibbons (1981) show that sign methods are the only possible way of producing valid inference in finite samples; see also Dufour and Hallin (1991) and Dufour (2003). If a test has level α for testing the null hypothesis that observations are independent each with a distribution symmetric about zero, then its level must be equal to α conditional on the absolute values of the observations: in other words, it must be a sign test.…”

Section: Introductionmentioning

confidence: 99%

Exact optimal inference in regression models under heteroskedasticity and non-normality of unknown form

Dufour

Taamouti

2010

Computational Statistics & Data Analysis

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Simple point-optimal sign-based tests are developed for inference on linear and nonlinear regression models with non-Gaussian heteroskedastic errors. The tests are exact, distribution-free, robust to heteroskedasticity of unknown form, and may be inverted to build confidence regions for the parameters of the regression function. Since point-optimal sign tests depend on the alternative hypothesis considered, an adaptive approach based on a split-sample technique is proposed in order to choose an alternative that brings power close to the power envelope. The performance of the proposed quasi-point-optimal sign tests with respect to size and power is assessed in a Monte Carlo study. The power of quasi-point-optimal sign tests is typically close to the power envelope, when approximately 10% of the sample is used to estimate the alternative and the remaining sample to compute the test statistic. Further, the proposed procedures perform much better than common least-squares-based tests which are supposed to be robust against heteroskedasticity.

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Section: Introductionmentioning

confidence: 99%

Exact optimal inference in regression models under heteroskedasticity and non-normality of unknown form

Dufour

Taamouti

2010

Computational Statistics & Data Analysis

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“…), of the Pitman asymptotic relative efficiency (ARE) of Wilcoxon (i.e., linear scores) rank tests with respect to their normal-theory competitors (namely, standard two-sample t-tests) is .864. In other words, Wilcoxon tests, asymptotically never-that is, whatever the distribution of the underlying noise-need more than 14.6% observations more than t-tests to achieve the same power (see, e.g., Pratt and Gibbons [4] for a more formal definition of ARE).…”

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confidence: 99%

“…The reason for this is not that the uniform dominance of normal-score rank procedures over parametric Gaussian ones is some kind of miracle that is specific to univariate location models, but rather that rank-based methods for a long time have been essentially limited to statistical models involving univariate independent observations. Except for a few exceptions (such as testing against bivariate dependence, tests based on runs, tests for scale, or goodness-of-fit methods that do not address any specific alternative), classical monographs (Hájek andŠidák [5] and Hájek,Šidák, and Sen [6]; Lehmann [7]; Randles and Wolfe [8]; Pratt and Gibbons [4]; Hettmansperger [9]; Puri and Sen [10]-to quote only a few) mainly deal with single-response linear models with independent errors: one-and two-sample location, analysis of variance, regression, etc.…”

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confidence: 99%

A unified and elementary proof of serial and nonserial, univariate and multivariate, Chernoff–Savage results

Paindaveine

2004

Statistical Methodology

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We provide a simple proof that the Chernoff-Savage [1] result, establishing the uniform dominance of normal-score rank procedures over their Gaussian competitors, also holds in a broad class of problems involving serial and/or multivariate observations. The non-admissibility of the corresponding everyday practice Gaussian procedures (multivariate least-squares estimators, multivariate t-tests and F -tests, correlogram-based methods, multivariate portmanteau and Durbin-Watson tests, etc.) follows. The proof, which generalizes to the multivariate-possibly serial-setup the idea developed in Gastwirth and Wolff [2] in the context of univariate location problems, allows for avoiding technical convexity and variational arguments.

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“…Sensitivities of single or multiple cytologic examinations, CUC, and BWFCM were compared using the standard binomial test for two-way tables (11). This statistical test accounts for overlap in detection by various techniques and is more sensitive than direct comparison of overall detection sensitivities.…”

Section: Estimates and Comparison Of Sensitivitiesmentioning

confidence: 99%

Detection of bladder carcinoma in females by flow cytometry and cytology

et al. 1989

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The sensitivity of bladder wash flow cytometry (BWFCM), voided urinary cytology (VUC), and cytology of catheterized urine obtained at the time of cystoscopy (CUC) were reviewed on all women evaluated for bladder cancer at Memorial Sloan-Kettering Cancer Center between June 1985 and December 1986. This comprised sixty-four episodes of pathologically proven bladder cancer in 48 women. Considering positive and suspicious results jointly the sensitivities of BWFCM, CUC and 3 VUC were 75%, 64% and 56%, respectively. If only positive results were considered (i.e., suspicious results considered as negative), the sensitivities of BWFCM, CUC and 3 VUC were 64%, 31% and 32%, respectively. The sensitivities of these tests are less than for a predominantly male population, presumably related to the presence of squamous epithelium and greater frequency of pyuria. However, bladder wash flow cytometry and conventional cytology are still a very valuable addition to cystoscopic examination, and the combination of BWFCM with conventional cytology is more sensitive than either procedure alone.Key terms: Bladder wash flow cytometry, voided urinary cytology, cystoscopyThe diagnosis and surveillance of patients with suspected bladder cancer are a multimodality process that may include cystoscopy, biopsy, cytology, and, in recent years, flow cytometry of bladder irrigation specimens. Data on the sensitivity of this latter examination have been based on patients unselected for sex, in a primarily male population (1). The urinary bladder in women is known to undergo squamous metaplasia, particularly about the trigone (6), and a difference in the cytology of urine specimens from men and women is well recognized (7). Both voided urine and bladder irrigation specimens of women contain more squamous epithelium and frequently more inflammatory cells than is the case in men. We have been concerned that these squamous and inflammatory cells in specimens from women might mask the presence of small populations of DNA aneuploid cells and lower the sensitivity of flow cytometry. Hence, this study was designed to evaluate the sensitivity of flow cytometry in the diagnosis of carcinoma of the bladder specifically in the female urologic patient. MATERIALS AND METHODS Selection of Patients and Tumor CategoryForty-eight female patients evaluated a t Memorial Sloan-Kettering Cancer Center (MSKCC), over a n 18 month period in 1985 and 1986, had 64 separate episodes of histologically proved bladder cancer and simultaneous bladder wash flow cytometry (BWFCM). All patients were also evaluated by urinary cytology within 24 h r prior to the endoscopic biopsy. Based on the biopsy results, the neoplasms were divided into three groups: 26 low-grade, superficial papillary carcinomas (Ta and Tl); 13 grade 11-111, muscle-infiltrating carcinomas (T2); and 25 in situ carcinomas (TIS).Patient Population All 48 patients were white women ranging in age from 33 to 87 years, with a mean age of 63.9 years.~~~~~ ~

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Concepts of Nonparametric Theory

Cited by 228 publications

References 0 publications

Exact optimal inference in regression models under heteroskedasticity and non-normality of unknown form

Exact optimal inference in regression models under heteroskedasticity and non-normality of unknown form

A unified and elementary proof of serial and nonserial, univariate and multivariate, Chernoff–Savage results

Detection of bladder carcinoma in females by flow cytometry and cytology

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