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A NEW nonparametric estimator FOR THE MEAN OF THE SELECTED POPULATION

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 1992年第11期21卷 3229-3246页

作者： SWANEPOEL, JWH DEBEER, CF POTCHEFSTROOM UNIV CHRISTIAN HIGHER EDUC DEPT STAT & OPERAT RESPOTCHEFSTROOM 2520SOUTH AFRICA

A modified bootstrap estimator of the mean of the population selected from two populations is proposed which is a convex combination of the two sample means, where the weights are random quantities. The estimator is shown to be strongly consistent. The small sample behavior of the estimator is investigated and compared with some competitors by means of Monte Carlo studies. It is found that the newly proposed estimator has smaller mean squared error for a wide range of parameter values.

关键词： SELECTED MEAN nonparametric estimator MODIFIED BOOTSTRAP MEAN SQUARED ERROR

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A fully nonparametric estimator of the marginal survival function based on case-control clustered age-at-onset data

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BIOSTATISTICS 2017年第1期18卷 76-90页

作者： Gorfine, Malka Bordo, Nadia Hsu, Li Tel Aviv Univ Sch Math Sci Dept Stat & Operat Res IL-69978 Tel Aviv Israel Technion Israel Inst Technol Fac Ind Engn & Management Techn City IL-3200003 Haifa Israel Fred Hutchinson Canc Res Ctr Div Publ Hlth Sci 1100 Fairview Ave NPOB 19024 Seattle WA 98109 USA

Consider a popular case-control family study where individuals with a disease under study (case probands) and individuals who do not have the disease (control probands) are randomly sampled from a well-defined population. Possibly right-censored age at onset and disease status are observed for both probands and their relatives. For example, case probands are men diagnosed with prostate cancer, control probands are men free of prostate cancer, and the prostate cancer history of the fathers of the probands is also collected. Inherited genetic susceptibility, shared environment, and common behavior lead to correlation among the outcomes within a family. In this article, a novel nonparametric estimator of the marginal survival function is provided. The estimator is defined in the presence of intra-cluster dependence, and is based on consistent smoothed kernel estimators of conditional survival functions. By simulation, it is shown that the proposed estimator performs very well in terms of bias. The utility of the estimator is illustrated by the analysis of case-control family data of early onset prostate cancer. To our knowledge, this is the first article that provides a fully nonparametric marginal survival estimator based on case-control clustered age-at-onset data.

关键词： Case-control Family study Multivariate survival nonparametric estimator Smoothed kernel estimator

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A consistent nonparametric spectral estimator for randomly sampled signals

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2004年第9期52卷 2383-2395页

作者： Rivoira, A Fleury, GA SUPELEC Serv Mesures Gif Sur Yvette France

In this paper, the nonparametric spectral analysis of a randomly sampled signal is discussed. For this purpose, the general form of Masry's recursive spectral estimators is considered and improved. The corresponding algorithms require the knowledge of the sampling times, the samples, and the sampling law and that the high-frequency decay of the spectrum be at least roughly known. The minimization of the asymptotic equivalent of the mean square estimation error leads to an estimator that is not only consistent but also asymptotically optimal. Theoretical and simulation results regarding this new estimator are given and compared with the standard methods. Besides, the developed theoretical framework strictly includes the case where the sampling time process is Poisson and the signal is Gaussian.

关键词： irregular sampling nonparametric estimator slotting technique spectral analysis

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nonparametric estimators of probability characteristics using unbiased prior conditions

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STATISTICAL PAPERS 2018年第4期59卷 1559-1575页

作者： Dmitriev, Yury G. Koshkin, Gennady M. Natl Res Tomsk State Univ Tomsk Russia

A class of nonparametric estimators of the main functional of distribution constructed by making use auxiliary information is proposed. It is shown that the knowledge usage of other distribution functionals in estimation of the main functional can often provide the mean squared error (MSE) smaller than that of estimators constructed without such auxiliary information. In the paper, the adaptive estimators are proposed. The asymptotic normality of all the proposed estimators is proved. The simulation results show that the usage of auxiliary information in estimation procedure improves the MSE of estimators.

关键词： nonparametric estimator Auxiliary information U-statistics Mises functional Asymptotic normality

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An estimator of number of species from quadrat sampling

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BIOMETRICS 2006年第1期62卷 135-141页

作者： Haas, PJ Liu, YS Stokes, L IBM Corp Almaden Res Ctr San Jose CA 95120 USA PPDI Wilmington NC 28412 USA So Methodist Univ Dept Stat Sci Dallas TX 75275 USA

We consider the problem of estimating the number of distinct species Sin a study area from the recorded presence or absence of species in each of a sample of quadrats. A generalized jackknife estimator of S is derived, along with an estimate of its variance. It is compared with the jackknife estimator for S proposed by Heltshe and Forrester (1983, Biometrics 39,1-12) and the empirical Bayes estimator of Mingoti and Meeden (1992, Biometrics 48, 863-875). We show that the empirical Bayes estimator has the form of a generalized jackknife estimator under a specific model for species distribution. We compare the new estimators of S to the empirical Bayes estimator via simulation. We characterize circumstances under which each is superior.

关键词： block sampling cluster sampling distinct values jackknife estimator nonparametric estimator number of classes

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MINIMAX INVARIANT estimator OF A CONTINUOUS DISTRIBUTION FUNCTION

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ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS 1992年第4期44卷 729-735页

作者： YU, QQ SUNY STONY BROOK DEPT APPL MATHSTONY BROOKNY 11794

Consider the problems of the continuous invariant estimation of a distribution function with a wide class of loss functions. It has been conjectured for long that the best invariant estimator is minimax for all sample... 详细信息

关键词： MINIMAXITY INVARIANT estimator nonparametric estimator PRODUCT MEASURE LEBESGUE MEASURE UNIFORM DISTRIBUTION ON A SET

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Semiparametric estimator of Time Series Conditional Variance

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JOURNAL OF BUSINESS & ECONOMIC STATISTICS 2010年第2期28卷 256-274页

作者： Mishra, Santosh Su, Liangjun Ullah, Aman Oregon State Univ Dept Econ Corvallis OR 97330 USA Singapore Management Univ Sch Econ Singapore 178903 Singapore Univ Calif Riverside Dept Econ Riverside CA 92521 USA

We propose a new combined semiparametric estimator, which incorporates the parametric and nonparametric estimators of the conditional variance in a multiplicative way. We derive the asymptotic bias, variance, and normality of the combined estimator under general conditions. We show that under correct parametric specification, our estimator can do as well as the parametric estimator in terms of convergence rates;whereas under parametric misspecification our estimator can still be consistent. It also improves over the nonparametric estimator of Ziegelmann (2002) in terms of bias reduction. The superiority of our estimator is verfied by Monte Carlo simulations and empirical data analysis.

关键词： Conditional variance nonparametric estimator Semiparametric models

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Reconstructing the Kaplan-Meier estimator as an M-estimator

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AMERICAN STATISTICIAN 2022年第1期76卷 37-43页

作者： Gu, Jiaqi Fan, Yiwei Yin, Guosheng Univ Hong Kong Dept Stat & Actuarial Sci Run Run Shaw BldgPokfulam Rd Hong Kong Peoples R China

The Kaplan-Meier (KM) estimator, which provides a nonparametric estimate of a survival function for time-to-event data, has broad applications in clinical studies, engineering, economics and many other fields. The theoretical properties of the KM estimator including its consistency and asymptotic distribution have been well established. From a new perspective, we reconstruct the KM estimator as an M-estimator by maximizing a quadratic M-function based on concordance, which can be computed using the expectation-maximization (EM) algorithm. It is shown that the convergent point of the EM algorithm coincides with the traditional KM estimator, which offers a new interpretation of the KM estimator as an M-estimator. As a result, the limiting distribution of the KM estimator can be established using M-estimation theory. Application on two real datasets demonstrates that the proposed M-estimator is equivalent to the KM estimator, and the confidence intervals and confidence bands can be derived as well.

关键词： Censored data Confidence interval Loss function nonparametric estimator Survival curve

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Generalized kernel regularized least squares estimator with parametric error covariance

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EMPIRICAL ECONOMICS 2023年第6期64卷 3059-3088页

作者： Dang, Justin Ullah, Aman Univ San Diego Dept Econ San Diego CA 92110 USA Univ Calif Riverside Dept Econ Riverside CA USA

A two-step estimator of a nonparametric regression function via Kernel regularized least squares (KRLS) with parametric error covariance is proposed. The KRLS, not considering any information in the error covariance, is improved by incorporating a parametric error covariance, allowing for both heteroskedasticity and autocorrelation, in estimating the regression function. A two step procedure is used, where in the first step, a parametric error covariance is estimated by using KRLS residuals and in the second step, a transformed model using the error covariance is estimated by KRLS. Theoretical results including bias, variance, and asymptotics are derived. Simulation results show that the proposed estimator outperforms the KRLS in both heteroskedastic errors and autocorrelated errors cases. An empirical example is illustrated with estimating an airline cost function under a random effects model with heteroskedastic and correlated errors. The derivatives are evaluated, and the average partial effects of the inputs are determined in the application.

关键词： nonparametric estimator Semiparametric models Machine learning Kernel regularized least squares Covariance Heteroskedasticity Serial correlation C C01 C1 C13 C14 C5 C51 C52

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An Improved Nearest Neighbor Based Entropy estimator with Local Ellipsoid Correction and its Application to Evaluation of MCMC Posterior Samples

An Improved Nearest Neighbor Based Entropy Estimator with Lo...

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作者： Chien Lu University of Tampere

学位级别：硕士

Entropy estimation is an important technique to summarize the uncertainty of a distribution underlying a set of samples. It ties to important research problems in fields such as statistics, machine learning and so on. The k-nearest neighbor (kNN) estimator is one widely used classical nonparametric method although it suffers bias issue especially when the dimensionality of the data is high. In this thesis, an improved kNN entropy estimator is developed. The proposed method has the advantage of a learning a local ellipsoid to be used in the estimation, in order to mitigate the bias issue which results from the local uniformity. Several numerical experiments have been conducted and the results have shown that the proposed approach can efficiently reduce the bias especially in when the dimension is high. Another studied topic in this thesis is the evaluation of the correctness of the posterior samples when conducting Bayesian inferences. This thesis demonstrates that the proposed estimator can be applied to such a task. We show that the simulation-based approach is more efficient and discriminative than a lower bound based method by one simple experiment, and the proposed kNN estimation can improve the accuracy of the state-of-the-art simulation-based approach.

关键词： entropy estimation nonparametric estimator Bayesian inference

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