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Alternative Estimator (alternative + estimator)
Selected AbstractsOn Estimating Conditional Mean-Squared Prediction Error in Autoregressive ModelsJOURNAL OF TIME SERIES ANALYSIS, Issue 4 2003CHING-KANG ING Abstract. Zhang and Shaman considered the problem of estimating the conditional mean-squared prediciton error (CMSPE) for a Gaussian autoregressive (AR) process. They used the final prediction error (FPE) of Akaike to estimate CMSPE and proposed that FPE's effectiveness be judged by its asymptotic correlation with CMSPE. However, as pointed out by Kabaila and He, the derivation of this correlation by Zhang and Shaman is incomplete, and the performance of FPE in estimating CMSPE is also poor in Kabaila and He's simulation study. Kabaila and He further proposed an alternative estimator of CMSPE, V, in the stationary AR(1) model. They reported that V has a larger normalized correlation with CMSPE through Monte Carlo simulation results. In this paper, we propose a generalization of V, V,, in the higher-order AR model, and obtain the asymptotic correlation of FPE and V, with CMSPE. We show that the limit of the normalized correlation of V, with CMSPE is larger than that of FPE with CMSPE, and hence Kabaila and He's finding is justified theoretically. In addition, the performances of the above estimators of CMSPE are re-examined in terms of mean-squared errors (MSE). Our main conclusion is that from the MSE point of view, V, is the best choice among a family of asymptotically unbiased estimators of CMSPE including FPE and V, as its special cases. [source] Maximum likelihood estimators of clock offset and skew under exponential delaysAPPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 4 2009Jun Li Abstract Accurate clock synchronization is essential for many data network applications. Various algorithms for synchronizing clocks rely on estimators of the offset and skew parameters that describe the relation between times measured by two different clocks. Maximum likelihood estimation (MLE) of these parameters has previously been considered under the assumption of exponentially distributed network delays with known means. We derive the MLEs under the more common case of exponentially distributed network delays with unknown means and compare their mean-squared error properties to a recently proposed alternative estimator. We investigate the robustness of the derived MLE to the assumption of non-exponential network delays, and demonstrate the effectiveness of a bootstrap bias-correction technique. Copyright © 2009 John Wiley & Sons, Ltd. [source] Highest Density Difference Region Estimation with Application to Flow Cytometric DataBIOMETRICAL JOURNAL, Issue 3 2009Tarn Duong Abstract Motivated by the needs of scientists using flow cytometry, we study the problem of estimating the region where two multivariate samples differ in density. We call this problem highest density difference region estimation and recognise it as a two-sample analogue of highest density region or excess set estimation. Flow cytometry samples are typically in the order of 10,000 and 100,000 and with dimension ranging from about 3 to 20. The industry standard for the problem being studied is called Frequency Difference Gating, due to Roederer and Hardy (2001). After couching the problem in a formal statistical framework we devise an alternative estimator that draws upon recent statistical developments such as patient rule induction methods. Improved performance is illustrated in simulations. While motivated by flow cytometry, the methodology is suitable for general multivariate random samples where density difference regions are of interest. [source] Estimating Disease Prevalence Using Relatives of Case and Control ProbandsBIOMETRICS, Issue 1 2010Kristin N. Javaras Summary We introduce a method of estimating disease prevalence from case,control family study data. Case,control family studies are performed to investigate the familial aggregation of disease; families are sampled via either a case or a control proband, and the resulting data contain information on disease status and covariates for the probands and their relatives. Here, we introduce estimators for overall prevalence and for covariate-stratum-specific (e.g., sex-specific) prevalence. These estimators combine the proportion of affected relatives of control probands with the proportion of affected relatives of case probands and are designed to yield approximately unbiased estimates of their population counterparts under certain commonly made assumptions. We also introduce corresponding confidence intervals designed to have good coverage properties even for small prevalences. Next, we describe simulation experiments where our estimators and intervals were applied to case,control family data sampled from fictional populations with various levels of familial aggregation. At all aggregation levels, the resulting estimates varied closely and symmetrically around their population counterparts, and the resulting intervals had good coverage properties, even for small sample sizes. Finally, we discuss the assumptions required for our estimators to be approximately unbiased, highlighting situations where an alternative estimator based only on relatives of control probands may perform better. [source] Time-Dependent ROC Curves for Censored Survival Data and a Diagnostic MarkerBIOMETRICS, Issue 2 2000Patrick J. Heagerty Summary. ROC curves are a popular method for displaying sensitivity and specificity of a continuous marker, X, for a binary disease variable, D. However, many disease outcomes are time dependent, D(t, and ROC curves that vary as a function of time may be mire appropriate. A common examples of a time-dependent variable is vital status, where D(t) = 1 if a patient has died prior to time t and zero otherwise. We propose summarizing the discrimination potential of a marker X, measured at baseline (t= 0), by calculating ROC Curves for cumulative disease or death incidence by time t, which we denote as ROC(t). A typical complexity with survival data is that observations may be censored. Two ROC curve estimators are proposed that can accommodate censored data. A simple estimator is based on using the Kaplan-Meier estimated for each possible subset X > c. However, this estimator does not guarantee the necessary condition that sensitivity and specificity are monotone in X. An alternative estimator that does guarantee monotonicity is based on a nearest neighbor estimator for the bivariate distribution function of (X, T), where T represents survival time (Akritas, M. J., 1994, Annals of Statistics22, 1299,1327). We present an example where ROC(t) is used to compare a standard and a modified flow cytometry measurement for predicting survival after detection of breast cancer and an example where the ROC(t) curve displays the impact of modifying eligibility criteria for sample size and power in HIV prevention trials. [source] Structural Equations, Treatment Effects, and Econometric Policy Evaluation1ECONOMETRICA, Issue 3 2005James J. Heckman This paper uses the marginal treatment effect (MTE) to unify the nonparametric literature on treatment effects with the econometric literature on structural estimation using a nonparametric analog of a policy invariant parameter; to generate a variety of treatment effects from a common semiparametric functional form; to organize the literature on alternative estimators; and to explore what policy questions commonly used estimators in the treatment effect literature answer. A fundamental asymmetry intrinsic to the method of instrumental variables (IV) is noted. Recent advances in IV estimation allow for heterogeneity in responses but not in choices, and the method breaks down when both choice and response equations are heterogeneous in a general way. [source] Comparing alternative models: log vs Cox proportional hazard?HEALTH ECONOMICS, Issue 8 2004Anirban Basu Abstract Health economists often use log models (based on OLS or generalized linear models) to deal with skewed outcomes such as those found in health expenditures and inpatient length of stay. Some recent studies have employed Cox proportional hazard regression as a less parametric alternative to OLS and GLM models, even when there was no need to correct for censoring. This study examines how well the alternative estimators behave econometrically in terms of bias when the data are skewed to the right. Specifically we provide evidence on the performance of the Cox model under a variety of data generating mechanisms and compare it to the estimators studied recently in Manning and Mullahy (2001). No single alternative is best under all of the conditions examined here. However, the gamma regression model with a log link seems to be more robust to alternative data generating mechanisms than either OLS on ln(y) or Cox proportional hazards regression. We find that the proportional hazard assumption is an essential requirement to obtain consistent estimate of the E(y,x) using the Cox model. Copyright © 2004 John Wiley & Sons, Ltd. [source] Estimation in integer-valued moving average modelsAPPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 3 2001Kurt Brännäs Abstract The paper presents new characterizations of the integer-valued moving average model. For four model variants, we give moments and probability generating functions. Yule,Walker and conditional least-squares estimators are obtained and studied by Monte Carlo simulation. A new generalized method of moment estimator based on probability generating functions is presented and shown to be consistent and asymptotically normal. The small sample performance is in some instances better than those of alternative estimators. Copyright © 2001 John Wiley & Sons, Ltd. [source] Efficiency of Functional Regression Estimators for Combining Multiple Laser Scans of cDNA MicroarraysBIOMETRICAL JOURNAL, Issue 1 2009C. A. Glasbey Abstract The first stage in the analysis of cDNA microarray data is estimation of the level of expression of each gene, from laser scans of hybridised microarrays. Typically, data are used from a single scan, although, if multiple scans are available, there is the opportunity to reduce sampling error by using all of them. Combining multiple laser scans can be formulated as multivariate functional regression through the origin. Maximum likelihood estimation fails, but many alternative estimators exist, one of which is to maximise the likelihood of a Gaussian structural regression model. We show by simulation that, surprisingly, this estimator is efficient for our problem, even though the distribution of gene expression values is far from Gaussian. Further, it performs well if errors have a heavier tailed distribution or the model includes intercept terms, but not necessarily in other regions of parameter space. Finally, we show that by combining multiple laser scans we increase the power to detect differential expression of genes. (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Ratio Estimation with Measurement Error in the Auxiliary VariateBIOMETRICS, Issue 2 2009Timothy G. Gregoire Summary With auxiliary information that is well correlated with the primary variable of interest, ratio estimation of the finite population total may be much more efficient than alternative estimators that do not make use of the auxiliary variate. The well-known properties of ratio estimators are perturbed when the auxiliary variate is measured with error. In this contribution we examine the effect of measurement error in the auxiliary variate on the design-based statistical properties of three common ratio estimators. We examine the case of systematic measurement error as well as measurement error that varies according to a fixed distribution. Aside from presenting expressions for the bias and variance of these estimators when they are contaminated with measurement error we provide numerical results based on a specific population. Under systematic measurement error, the biasing effect is asymmetric around zero, and precision may be improved or degraded depending on the magnitude of the error. Under variable measurement error, bias of the conventional ratio-of-means estimator increased slightly with increasing error dispersion, but far less than the increased bias of the conventional mean-of-ratios estimator. In similar fashion, the variance of the mean-of-ratios estimator incurs a greater loss of precision with increasing error dispersion compared with the other estimators we examine. Overall, the ratio-of-means estimator appears to be remarkably resistant to the effects of measurement error in the auxiliary variate. [source] | ||||||||||