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nonparametric inference based on conditional moment inequalities

JOURNAL OF ECONOMETRICS 2014年第1期179卷 31-45页

作者： Andrews, Donald W. K. Shi, Xiaoxia Yale Univ Cowles Fdn Res Econ New Haven CT 06520 USA Univ Wisconsin Dept Econ Madison WI 53706 USA

This paper develops methods of inference for nonparametric and semiparametric parameters defined by conditional moment inequalities and/or equalities. The parameters need not be identified. Confidence sets and tests are introduced. The correct uniform asymptotic size of these procedures is established. The false coverage probabilities and power of the CS's and tests are established for fixed alternatives and some local alternatives. Finite-sample simulation results are given for a nonparametric conditional quantile model with censoring and a nonparametric conditional treatment effect model. The recommended CS/test uses a Cramer-von-Mises-type test statistic and employs a generalized moment selection critical value. (C) 2013 Elsevier B.V. All rights reserved.

关键词： Asymptotic size Kernel Local power Moment inequalities nonparametric inference Partial identification

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nonparametric inference for the spectral measure of a bivariate pure-jump semimartingale

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STOCHASTIC PROCESSES AND THEIR APPLICATIONS 2019年第2期129卷 419-451页

作者： Todorov, Viktor Northwestern Univ Dept Finance Evanston IL 60208 USA

We develop a nonparametric estimator for the spectral density of a bivariate pure-jump Ito semimartingale from high-frequency observations of the process on a fixed time interval with asymptotically shrinking mesh of the observation grid. The process of interest is locally stable, i.e., its Levy measure around zero is like that of a time-changed stable process. The spectral density function captures the dependence between the small jumps of the process and is time invariant. The estimation is based on the fact that the characteristic exponent of the high-frequency increments, up to a time-varying scale, is approximately a convolution of the spectral density and a known function depending on the jump activity. We solve the deconvolution problem in Fourier transform using the empirical characteristic function of locally studentized high-frequency increments and a jump activity estimator. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Deconvolution Fourier transform High-frequency data Ito semimartingale nonparametric inference Spectral density

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nonparametric inference in small data sets of spatially indexed curves with application to ionospheric trend determination

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2013年第1期59卷 82-94页

作者： Gromenko, Oleksandr Kokoszka, Piotr Utah State Univ Dept Math & Stat Logan UT 84322 USA Colorado State Univ Dept Stat Ft Collins CO 80523 USA

This paper is concerned with estimation and testing in data sets consisting of a small number (about 20-30) of curves observed at unevenly distributed spatial locations. Such data structures may be referred to as spatially indexed functional data. Motivated by an important space physics problem, we model such data as a mean function plus spatially dependent error functions. Given a small number of spatial locations, the parametric methods for the estimation of the spatial covariance structure of the error functions are not satisfactory. We propose a fully nonparametric estimator for the mean function. We also derive a test to determine the significance of the regression coefficients if the mean function is a linear combination of known covariate functions. In particular, we develop methodology for the estimation a trend in spatially indexed functional data, and for assessing its statistical significance. We apply the new tools to global ionosonde records to test the hypothesis of ionospheric cooling. nonparametric modeling of the space-time covariances is surprisingly simple, much faster than those previously proposed, and less sensitive to computational errors. In simulated data, the new estimator and test uniformly dominate those based on parametric modeling. (C) 2012 Elsevier B.V. All rights reserved.

关键词： Functional data Ionosphere Long-term trend nonparametric inference Spatial statistics

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nonparametric inference on the E/O ratio in model validation

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STATISTICS IN MEDICINE 2008年第17期27卷 3340-3349页

作者： Qu, Yongming Wang, Yanping Eli Lilly & Co Dept Commercial Informat Sci Indianapolis IN 46285 USA

In preventing diseases such as cancers and osteoporosis, statistical models are often used to identify subjects with high risks. The ratio of the expected (or predicted) number of cases in the target population and the observed numbers of cases (the E/O ratio) is a useful quantity to evaluate the goodness of fit of the model. The model is usually evaluated on a sample taken from the target population and, in the literature, statistical inferences on the E/O ratio often assume that the expected number is a constant and the observed number follows a Poisson distribution. In this paper, we introduce a nonparametric method that takes into account the variability of the predicted number due to sampling and its correlation with the observed number. By estimating the variance of the estimated E/O ratio more accurately, this nonparametric approach offers better inferences. In addition, we propose to use an F-statistic to test the goodness of a model across subgroups defined by certain risk factors. Copyright (c) 2007 John Wiley & Sons, Ltd.

关键词： model validation E/O ratio nonparametric inference

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nonparametric inference IN N REPLICATED 2M FACTORIAL EXPERIMENTS

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ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS 1970年第2期22卷 281-&页

作者： SEN, PK University of North Carolina Chapel Hill

For experiments involvingm factors (A 1,…,A m), each at 2 levels (1, 2), and replicated inn(≧2) blocks, a class of nonparametric procedures for estimating and testing the various main effects and interactions are considered. The procedures are based on a simple alignment process and involve the use of some well known rank statistics. Their performance characteristics are compared with those of the standard (normal-theory) parametric procedures. Extensions to confounded or partially confounded designs are also considered.

关键词： Rank Statistic Asymptotic Relative Efficiency nonparametric inference Variance Ratio Test Rank Order Test

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nonparametric inference IN GENERALIZED FUNCTIONAL LINEAR MODELS

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ANNALS OF STATISTICS 2015年第4期43卷 1742-1773页

作者： Shang, Zuofeng Cheng, Guang Purdue Univ Dept Stat W Lafayette IN 47906 USA

We propose a roughness regularization approach in making nonparametric inference for generalized functional linear models. In a reproducing kernel Hilbert space framework, we construct asymptotically valid confidence intervals for regression mean, prediction intervals for future response and various statistical procedures for hypothesis testing. In particular, one procedure for testing global behaviors of the slope function is adaptive to the smoothness of the slope function and to the structure of the predictors. As a by-product, a new type of Wilks phenomenon [Ann. Math. Stat. 9 (1938) 60-62;Ann. Statist. 29 (2001) 153-193] is discovered when testing the functional linear models. Despite the generality, our inference procedures are easy to implement. Numerical examples are provided to demonstrate the empirical advantages over the competing methods. A collection of technical tools such as integro-differential equation techniques [Trans. Amer Math. Soc. (1927) 29 755-800;Trans. Amer. Math. Soc. (1928) 30 453-471;Trans. Amer Math. Soc. (1930) 32 860-868], Stein's method [Ann. Statist. 41 (2013) 2786- 2819] [Stein, Approximate Computation of Expectations (1986) IMS] and functional Bahadur representation [Ann. Statist. 41 (2013) 2608-2638] are employed in this paper.

关键词： Generalized functional linear models minimax adaptive test nonparametric inference reproducing kernel Hilbert space roughness regularization

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nonparametric inference under a monotone hazard ratio order

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ELECTRONIC JOURNAL OF STATISTICS 2023年第2期17卷 3181-3225页

作者： Wu, Yujian Westling, Ted Univ Massachusetts Dept Math & Stat Amherst MA 01003 USA

The ratio of the hazard functions of two populations or two strata of a single population plays an important role in time-to-event analy-sis. Cox regression is commonly used to estimate the hazard ratio under the assumption that it is constant in time, which is known as the proportional hazards assumption. However, this assumption is often violated in practice, and when it is violated, the parameter estimated by Cox regression is dif-ficult to interpret. The hazard ratio can be estimated in a nonparametric manner using smoothing, but smoothing-based estimators are sensitive to the selection of tuning parameters, and it is often difficult to perform valid inference with such estimators. In some cases, it is known that the hazard ratio function is monotone. In this article, we demonstrate that monotonic-ity of the hazard ratio function defines an invariant stochastic order, and we study the properties of this order. Furthermore, we introduce an esti-mator of the hazard ratio function under a monotonicity constraint. We demonstrate that our estimator converges in distribution to a mean-zero limit, and we use this result to construct asymptotically valid confidence intervals. Finally, we conduct numerical studies to assess the finite-sample behavior of our estimator, and we use our methods to estimate the hazard ratio of progression-free survival in pulmonary adenocarcinoma patients treated with gefitinib or carboplatin-paclitaxel.

关键词： and phrases Shape constrained estimation nonparametric inference stochastic orders survival analysis time-varying treatment haz-ard ratio

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nonparametric inference on Levy measures of compound Poisson-driven Ornstein-Uhlenbeck processes under macroscopic discrete observations

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ELECTRONIC JOURNAL OF STATISTICS 2019年第2期13卷 2521-2565页

作者： Kurisu, Daisuke Tokyo Inst Technol Sch Engn Dept Ind Engn & Econ Meguro Ku 2-12-1 Ookayama Tokyo 1528552 Japan

This study examines a nonparametric inference on a stationary Levy-driven Ornstein-Uhlenbeck (OU) process X = (X-t)(t >= 0) with a compound Poisson subordinator. We propose a new spectral estimator for the Levy measure of the Levy-driven OU process X under macroscopic observations. We also derive, for the estimator, multivariate central limit theorems over a finite number of design points, and high-dimensional central limit theorems in the case wherein the number of design points increases with an increase in the sample size. Built on these asymptotic results, we develop methods to construct confidence bands for the Levy measure and propose a practical method for bandwidth selection.

关键词： nonparametric inference compound Poisson-driven Ornstein-Uhlenbeck process spectral estimation high-dimensional central limit theorem macroscopic observations

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nonparametric inference under competing risks and selection-biased sampling

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JOURNAL OF MULTIVARIATE ANALYSIS 2008年第4期99卷 589-605页

作者： Dauxois, Jean-Yves Guilloux, Agathe Univ Franche Comte CNRS UMR 6623 Dept Math F-25030 Besancon France Univ Paris 06 LSTA F-75013 Paris France

The aim of this paper is to carry out statistical inference in a competing risks setup when only selection-biased observation of the data of interest is available. We introduce estimators of the cumulative incidence f... 详细信息

关键词： competing risks selection bias right-censored data cumulative incidence function nonparametric inference weak convergence of processes Skorohod space Martingale counting process

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nonparametric-inference FOR A CLASS OF SEMI-MARKOV PROCESSES WITH CENSORED OBSERVATIONS

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ANNALS OF STATISTICS 1984年第1期12卷 142-160页

作者： VOELKEL, JG CROWLEY, J UNIV WISCONSIN MADISON WI 53706 USA FRED HUTCHINSON CANC RES CTR EPIDEMIOL & BIOSTAT ZD08 SEATTLE WA 98104 USA

A class of semi-Markov models, those which have proportional hazards and which are forward-going (if state j can be reached from i, then i cannot be reached from j), are shown to fit into the multiplicative intensity model of counting processes after suitable random time changes. Standard large-sample results for counting processes following this multiplicative model can therefore be used to make inferences on the above class of semi-Markov models, including the case where observations may be censored. Large-sample results for a four-state model used in clinical trials are presented.

关键词： 62G05 60K15 censored observations Clinical trials nonparametric inference semi-Markov models

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