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Kernel Estimator (kernel + estimator)
Selected AbstractsIdentification and Estimation of Regression Models with MisclassificationECONOMETRICA, Issue 3 2006Aprajit Mahajan This paper studies the problem of identification and estimation in nonparametric regression models with a misclassified binary regressor where the measurement error may be correlated with the regressors. We show that the regression function is nonparametrically identified in the presence of an additional random variable that is correlated with the unobserved true underlying variable but unrelated to the measurement error. Identification for semiparametric and parametric regression functions follows straightforwardly from the basic identification result. We propose a kernel estimator based on the identification strategy, derive its large sample properties, and discuss alternative estimation procedures. We also propose a test for misclassification in the model based on an exclusion restriction that is straightforward to implement. [source] Non-parametric confidence bands in deconvolution density estimationJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 3 2007Nicolai Bissantz Summary., Uniform confidence bands for densities f via non-parametric kernel estimates were first constructed by Bickel and Rosenblatt. In this paper this is extended to confidence bands in the deconvolution problem g=f*, for an ordinary smooth error density ,. Under certain regularity conditions, we obtain asymptotic uniform confidence bands based on the asymptotic distribution of the maximal deviation (L, -distance) between a deconvolution kernel estimator and f. Further consistency of the simple non-parametric bootstrap is proved. For our theoretical developments the bias is simply corrected by choosing an undersmoothing bandwidth. For practical purposes we propose a new data-driven bandwidth selector that is based on heuristic arguments, which aims at minimizing the L, -distance between and f. Although not constructed explicitly to undersmooth the estimator, a simulation study reveals that the bandwidth selector suggested performs well in finite samples, in terms of both area and coverage probability of the resulting confidence bands. Finally the methodology is applied to measurements of the metallicity of local F and G dwarf stars. Our results confirm the ,G dwarf problem', i.e. the lack of metal poor G dwarfs relative to predictions from ,closed box models' of stellar formation. [source] Estimation of integrated squared density derivatives from a contaminated sampleJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 4 2002A. Delaigle Summary. We propose a kernel estimator of integrated squared density derivatives, from a sample that has been contaminated by random noise. We derive asymptotic expressions for the bias and the variance of the estimator and show that the squared bias term dominates the variance term. This coincides with results that are available for non-contaminated observations. We then discuss the selection of the bandwidth parameter when estimating integrated squared density derivatives based on contaminated data. We propose a data-driven bandwidth selection procedure of the plug-in type and investigate its finite sample performance via a simulation study. [source] Failure time regression with continuous covariates measured with errorJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 4 2000Halbo Zhou We consider failure time regression analysis with an auxiliary variable in the presence of a validation sample. We extend the nonparametric inference procedure of Zhou and Pepe to handle a continuous auxiliary or proxy covariate. We estimate the induced relative risk function with a kernel smoother and allow the selection probability of the validation set to depend on the observed covariates. We present some asymptotic properties for the kernel estimator and provide some simulation results. The method proposed is illustrated with a data set from an on-going epidemiologic study. [source] Kernel estimation of quantile sensitivitiesNAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 6 2009Guangwu Liu Abstract Quantiles, also known as value-at-risks in the financial industry, are important measures of random performances. Quantile sensitivities provide information on how changes in input parameters affect output quantiles. They are very useful in risk management. In this article, we study the estimation of quantile sensitivities using stochastic simulation. We propose a kernel estimator and prove that it is consistent and asymptotically normally distributed for outputs from both terminating and steady-state simulations. The theoretical analysis and numerical experiments both show that the kernel estimator is more efficient than the batching estimator of Hong 9. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009 [source] Testing the martingale hypothesis for futures prices: Implications for hedgersTHE JOURNAL OF FUTURES MARKETS, Issue 11 2008Cédric de Ville de Goyet The martingale hypothesis for futures prices is investigated using a nonparametric approach where it is assumed that the expected futures returns depend (nonparametrically) on a linear combination of predictors. We first collapse the predictors into a single-index variable where the weights are identified up to scale, using the average derivative estimator proposed by T. Stoker (1986). We then use the Nadaraya,Watson kernel estimator to calculate (and visually depict) the relationship between the estimated index and the expected futures returns. We discuss implications of this finding for a noninfinitely risk-averse hedger. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:1040,1065, 2008 [source] Variable kernel density estimationAUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 3 2003Martin L. Hazelton Summary This paper considers the problem of selecting optimal bandwidths for variable (sample-point adaptive) kernel density estimation. A data-driven variable bandwidth selector is proposed, based on the idea of approximating the log-bandwidth function by a cubic spline. This cubic spline is optimized with respect to a cross-validation criterion. The proposed method can be interpreted as a selector for either integrated squared error (ISE) or mean integrated squared error (MISE) optimal bandwidths. This leads to reflection upon some of the differences between ISE and MISE as error criteria for variable kernel estimation. Results from simulation studies indicate that the proposed method outperforms a fixed kernel estimator (in terms of ISE) when the target density has a combination of sharp modes and regions of smooth undulation. Moreover, some detailed data analyses suggest that the gains in ISE may understate the improvements in visual appeal obtained using the proposed variable kernel estimator. These numerical studies also show that the proposed estimator outperforms existing variable kernel density estimators implemented using piecewise constant bandwidth functions. [source] Legendre polynomial kernel estimation of a density function with censored observations and an application to clinical trialsCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 8 2007Simeon M. Berman Let f(x), x , ,M, M , 1, be a density function on ,M, and X1, ,., Xn a sample of independent random vectors with this common density. For a rectangle B in ,M, suppose that the X's are censored outside B, that is, the value Xk is observed only if Xk , B. The restriction of f(x) to x , B is clearly estimable by established methods on the basis of the censored observations. The purpose of this paper is to show how to extrapolate a particular estimator, based on the censored sample, from the rectangle B to a specified rectangle C containing B. The results are stated explicitly for M = 1, 2, and are directly extendible to M , 3. For M = 2, the extrapolation from the rectangle B to the rectangle C is extended to the case where B and C are triangles. This is done by means of an elementary mapping of the positive quarter-plane onto the strip {(u, v): 0 , u , 1, v > 0}. This particular extrapolation is applied to the estimation of the survival distribution based on censored observations in clinical trials. It represents a generalization of a method proposed in 2001 by the author [2]. The extrapolator has the following form: For m , 1 and n , 1, let Km, n(x) be the classical kernel estimator of f(x), x , B, based on the orthonormal Legendre polynomial kernel of degree m and a sample of n observed vectors censored outside B. The main result, stated in the cases M = 1, 2, is an explicit bound for E|Km, n(x) , f(x)| for x , C, which represents the expected absolute error of extrapolation to C. It is shown that the extrapolator is a consistent estimator of f(x), x , C, if f is sufficiently smooth and if m and n both tend to , in a way that n increases sufficiently rapidly relative to m. © 2006 Wiley Periodicals, Inc. [source] Detecting spatial hot spots in landscape ecologyECOGRAPHY, Issue 5 2008Trisalyn A. Nelson Hot spots are typically locations of abundant phenomena. In ecology, hot spots are often detected with a spatially global threshold, where a value for a given observation is compared with all values in a data set. When spatial relationships are important, spatially local definitions , those that compare the value for a given observation with locations in the vicinity, or the neighbourhood of the observation , provide a more explicit consideration of space. Here we outline spatial methods for hot spot detection: kernel estimation and local measures of spatial autocorrelation. To demonstrate these approaches, hot spots are detected in landscape level data on the magnitude of mountain pine beetle infestations. Using kernel estimators, we explore how selection of the neighbourhood size (,) and hot spot threshold impact hot spot detection. We found that as , increases, hot spots are larger and fewer; as the hot spot threshold increases, hot spots become larger and more plentiful and hot spots will reflect coarser scale spatial processes. The impact of spatial neighbourhood definitions on the delineation of hot spots identified with local measures of spatial autocorrelation was also investigated. In general, the larger the spatial neighbourhood used for analysis, the larger the area, or greater the number of areas, identified as hot spots. [source] | |||||||||||||