Search

In this paper age replacement (AR) and opportunity-based age replacement (OAR) for a unit are considered, based on a one-cycle criterion, both for a known and unknown lifetime distribution. In the literature, AR and OAR strategies are mostly based on a renewal criterion, but in particular when the lifetime distribution is not known and data of the process are used to update the lifetime distribution, the renewal criterion is less appropriate and the one-cycle criterion becomes an attractive alternative. Conditions are determined for the existence of an optimal replacement age T in an AR model and optimal threshold age [T.sup.*.sub.opp] in an OAR model, using a one-cycle criterion and a known lifetime distribution. In the optimal threshold age [T.sup.*.sub.opp], the corresponding minimal expected costs per unit time are equal to the expected costs per unit time in an AR model. It is also shown that for a lifetime distribution with increasing hazard rate, the optimal threshold age is smaller than the optimal replacement age. For unknown lifetime distribution, AR and OAR strategies are considered within a nonparametric predictive inferential (NPI) framework. The relationship between the NPI-based expected costs per unit time in an OAR model and those in an AR model is investigated. A small simulation study is presented to illustrate this NPI approach. Keywords: age replacement; opportunity-based age replacement; one-cycle criterion; nonparametric predictive inference

Functional mapping based on parametric and nonparametric modeling of functional data can estimate the developmental pattern of genetic effects on a complex dynamic or longitudinal process triggered by quantitative trait loci (QTLs). But existing functional mapping models have a limitation for mapping dynamic QTLs with irregular functional data characterized by many local features, such as peaks. We derive a statistical model for QTL mapping of longitudinal curves of any form based on wavelet shrinkage techniques. The fundamental idea of this model is a repeated splitting of an intial sequence into detail coefficents that quantify local fluctuations at a particular scale and smooth coefficients that quantify remaining low-frequency variation in the signal after the high-frequency detail is removed and,. subsequently, QTL mapping with the smooth coefficients extracted from noisy longitudinal data. Compared with conventional full-dimensional functional mapping, wavelet-based nonparametric functional mapping provides consistent results, and better results in some circumstances. and is much more computationally efficient. This wavelet-based model is validated by the analysis of a real example for stem diameter growth trajectories in a forest tree, and its statistical properties are examined through extensive simulation studies. Wavelet-based functional mapping broadens the use of functional mapping to studying an arbitrary form of longitudina curves and will have many implications for investigating the interplay between gene actions/interactions and developmental pathways in various complex biological processes and networks. KEY WORDS: Denoising: Dimensionaliyt reduction; Functional mapping; Haar function; Mixture model; Quantitative trait loei: Thresholding rule; Wavelet.

Usage of nonparametric model to study over rejection observed in Granger non-causality is presented.

This paper discusses estimation of nonparametric models whose regressor vectors consist of a vector of exogenous variables and a univariate discrete endogenous regressor with finite support. Both identification and estimators are derived from a transform of the model that evaluates the nonparametric structural function via indicator functions in the support of the discrete regressor. A two-step estimator is proposed where the first step constitutes nonparametric estimation of the instrument and the second step is a nonparametric version of two-stage least squares. Linear functionals of the model are shown to be asymptotically normal, and a consistent estimator of the asymptotic covariance matrix is described. For the binary endogenous regressor case, it is shown that one functional of the model is a conditional (on covariates) local average treatment effect, that permits both unobservable and observable heterogeneity in treatments. Finite sample properties of the estimators from a Monte Carlo simulation study illustrate the practicability of the proposed estimators. JEL classification: C13; C14; C23; C31 Keywords: Nonparametric estimation; Instrumental variables; Series estimation; Conditional local average treatment effects; Binary endogenous; Discrete endogenous regressors

A partially linear model of cointegration is developed where stationary covariates enter non-parametrically. We propose tests for cointegration using singular values of the estimated autoregressive matrix. The tests are based on eigenvalues of standardized matrices and are relatively simple to compute. Asymptotic theory of the proposed test is developed. It is shown that the limiting distribution of the proposed test is similar to that of several tests in the recent literature. A Gamma approximation of the distribution is discussed to facilitate inference. Finite sample properties of the proposed procedure are illustrated in some limited Monte Carlo experiments. An empirical application to US macroeconomic time series is conducted to highlight the approach. JEL classification. C12; C14; C22 Keywords: Cointegration; Nonparametric; Partially linear models; Semiparametric

This paper considers a multiperiod random effects panel model with attrition of observations over the panel, allowing for flexible regressions, unknown distributions and attrition in one period to be followed by reappearance in a future period. In each time period, the regression in the retained data is additive in the function of interest and a time-varying correction term that depends on the contemporaneous probability of retention in the sample. These retention probabilities themselves depend on a regressor vector that grows with time. In particular, for the tth and (t + s)th periods, these vectors differ by exactly's terms. The paper gives two-step estimators that correct for attrition bias by including estimates of these retention probabilities, one for each period that experiences attrition. Asymptotic normality for a class of functionals of the model is derived, also including as special cases the linear and partially linear versions of the model. JEL classification: C13; C14; C23 Keywords: Attrition; Selection on unobservables; Nonparametric estimation; Panel data; Random effects; Two-step estimation

This article considers the problem of assessing the performance of MCMC model selection algorithms using a variety of nonparametric techniques. We consider a wide range of model selection problems to [...]

A rich nonparametric analysis of the finite normal mixture model is obtained by working with a precise truncation approximation of the Dirichlet process. Model fitting is carried out by a [...]

Peter Muller is Associate Professor, Institute of Statistics and Decision Sciences, Duke University, Durham, NC 27708. (E-mail: pin@stat.duke.edu). Gary L. Rosner is Professor, and Lurdes Y. T. Inoue is Research Associate, Department of Biostatistics, The University of Texas M. D. Anderson Cancer Center, Houston, TX 77030. Mark W. Dewhirst is Professor, Department of Radiation Oncology, Duke University Medical Center, Durham, NC 27710. Research supported by NIH/NCI under grants RO1 CA75981 and R01 CA40355 and by NSF under grant NSF/DMS-9704934., ********** We propose a model for longitudinal data with random effects that includes model-based smoothing of measurements over time. This research is motivated by experiments evaluating the hemodynamic effects of [...]

We introduce a new nonparametric regression estimator that uses prior information on regression shape in the form of a parametric model. In effect, we nonparametrically encompass the parametric model. We obtain estimates of the regression function and its derivatives along with local parameter estimates that can be interpreted from within the parametric model. We establish the uniform consistency and derive the asymptotic distribution of the local parameter estimates and of the corresponding regression and derivative estimates. For estimating the regression function our method has superior performance compared to the usual kernel estimators at or near the parametric model. It is particularly well motivated for binary data using the probit or logit parametric model as a base. We include an application to the Horowitz (1993, Journal of Econometrics 58, 49-70) transport choice dataset.

Nonparametric programming models have been developed to measure technical efficiency and scale economies. The programming models used for public sector applications, however, are based on standard private sector production theory. In the public sector environmental variables have a significant impact on the provision of public services. Without controlling for these environmental factors point estimates of efficiency and returns to scale will be biased. This paper extends nonparametric methods to allow measurement of returns to scale in the provision of public services. The method is applied to the provision of educational services in New York State school districts for illustrative purposes.

This paper proposes estimators of location and size of structural breaks in a, possibly dynamic, nonparametric regression model. The structural breaks can be located at given periods of time and/or they can be explained by the values taken by some regressor, as in threshold models. No previous knowledge of the underlying regression function is required. The paper also studies the case in which several regressors explain the breaks. We derive the rate of convergence and provide Central Limit Theorems for the estimators of the location(s) and size(s). A Monte Carlo experiment illustrates the performance of our estimators in small samples.

A nonparametric Bayesian modeling is described and is compared to the one used by Shively, Kohn and Wood in their study. The former is concerned with broad features of the data, such as the general form in which a covariate enters the model or if interaction terms are required. A parametric element is needed when there is a substantive differential effect across a range of values for a covariate. For instance, a piecewise linear term, can account for most of the overall trend of the data., This is a landmark article in applied statistics. It takes a subject of interest to many, who is the best - in hockey, golf and baseball - and applies a [...]

The use of function estimation in the study done by Shively, Kohn and Wood, on selecting the correct model in a multiple predictor semiparametric regression is discussed. Function estimation is made up of a model expressed as a line plus an integrated Wiener process, wherein fitting is attained by using a state-space formulation and Kalman filtering. However, the Wiener process is a difficult procedure and the researchers should have used simpler method instead., My comments concern the questions of scientific interest in longitudinal studies and the usefulness (appropriateness) of causal inference about the effects of time-varying exposures on the prevalence of an outcome [...]

We consider a binary response model yi = 1{xibetai plus epsiloni is greater than or equal to 0} with xi independent of the unobservables (betai, espiloni). A nonparametric maximum likelihood estimator for F0 is shown to be consistent. We analyze some conditions under which F0 is or is not identified. In particular, we show that if the support of F0 is a subset of any half of the unit hypersphere, then F0 is identified relative to all distributions on the unit hypersphere. We also provide some Monte Carlo evidence on the small sample performance of our estimator.

A concept of generalized degrees of freedom (GDF) in the theory of linear models that can be applied to complex modeling procedures is described. Based on the sum of the sensitivity of fitted values to perturbation in corresponding observed values, the DGF concept is non-asymptotic in nature and does not require analytic knowledge of modeling procedures. Results indicated philosophic implications and suggested that the stability of identified structures is correlated with perturbed responses., 1. INTRODUCTION In the theory of linear models, the concept of degrees of freedom plays an important role. This concept has several different interpretations. The degrees of freedom in regression [...]

A nonparametric estimation method called locally weighted (LW) regression was created to assess employment density in the city of Chicago, IL. Unlike an OLS regression, LW regression is more precise in modeling polycentric cities, such as Chicago. LW regression helped reveal the highly centralize setting of Chicago city, with the Chicago central business district and O'Hare Airport as focal points of employment.

A semiparametric version of the generalized linear model for regression response was developed by replacing the linear combination with nonparametric components. The generalized partially linear single-index models were formed by combining simpler, conventional models such as single-index and partially linear models. Furthermore, the asymptotic distributions of the linear combination involving unknown parameters and unknown function was obtained by using local linear methods.

A semi-nonparametric binary response model is estimated to obtain the willingness to pay for the environmental quality improvement when the willingness to pay is restricted to be nonnegative. The model estimation is straightforward by using conventional maximum likelihood software. Because the semi-nonparametric model is the generalization of the parametric model, the generality can be assessed by a likelihood ratio test. By using an existing referendum survey data set, it is shown that the semi-nonparametric estimation provides a significant improvement over the parametric estimation. The willingness to pay is sensitive to the distribution assumption. Key words: Semi-nonparametric estimation; Binary response model; Contingent valuation; Willingness to pay

Linear quantile regression and quantile regression techniques have been developed as models for conditional functionals. However, these techniques have limited applications because they assume parametric linear properties with single or multiple linear predictor effects and discount nonparametric possibilities. Thus, a general regression model has been developed with semiparametric linear and nonparametric linear applications. The model must be given sample sizes of 50 and above for conditional functionals., 1. INTRODUCTION Regression methods are used to study the relationship of the response Y with p predictor variables ([X.sub.1], . . ., [X.sub.p]) based on data consisting of p + [...]

A nonparametric formulation based on mathematical programming (MP) can be used to solve the classification problem in discriminant analysis. This second order MP formulation has a linear objective function and is also linear in terms of parameter estimation. However, it has a classification function which is nonlinear when it comes to the attributes or predictor variables. Compared with previous MP methods, it leads to better accuracy in the nonparametric MP-based analysis of a broader category of classification problems.

For the density estimation problem the global window width kernel density estimator does not perform well when the underlying density has features that require different amounts of smoothing at different locations. In this article we propose to transform the data with the intention that a global window width is more appropriate for the density of the transformed data. The density estimate of the original data is the 'back-transform' by change of variables of the global window width estimate of the transformed data's density. We explore choosing the transformation from suitable parametric families. Data-based selection rules for the choice of transformations and the window width are discussed. Application to real and simulated data demonstrates the usefulness of our proposals. KEY WORDS: Box-Cox transformations; Kernel estimators; Nonparametric density estimation; Shifted power transformations; Window width selection., 1. INTRODUCTION Nonparametric density estimation provides a means of exploring the probability structure of a population corresponding to a given data set, especially when parametric models are inappropriate. Silverman (1986) [...]

Comments made by Brumback et al., E.I. George et al., Steven N. MacEachern and Peter Muller on Shively, Kohn and Wood's study on additive nonparametric regression models are discussed. For instance, Brumback et al. recommends the use of regression splines as a prior for one-dimensional curve instead of a Wiener process before simplifying the computations and making nonparametric smoothing easier. On the other hand, George et al. argue that a conditional mean instead of the marginal mean should be used as the prior., We thank the discussants for their kind words and insightful criticisms. We first address some general concepts touched on by each of the discussants, then address each discussant's specific comments [...]

We propose a procedure for testing the equality of several nonparametric multivariate regressions. We allow the regressors' designs and the number of observations to differ across subsamples. The division into subsamples is defined through a variable C which can be either fixed or random. For a random C, our procedure is a general test of significance for qualitative variables in a nonparametric regression. For a fixed C, our procedure provides a `nonparametric analysis of covariance', which is valid for cross-section or panel data. In both cases, the test is a one-sided normal test and is consistent against all alternatives. JEL classification: Primary C52; Secondary C14 Keywords: Hypothesis testing; Nonparametric methods; Qualitative variables; Covariance analysis, Please see the abstract in the 'Author Abstract' area.

Nonparametric multivariate analysis of ecological data using permutation tests has two main challenges: (1) to partition the variability in the data according to a complex design or model, as is often required in ecological experiments, and (2) to base the analysis on a multivariate distance measure (such as the semimetric Bray-Curtis measure) that is reasonable for ecological data sets. Previous nonparametric methods have succeeded in one or other of these areas, but not in both. A recent contribution to Ecological Monographs by Legendre and Anderson, called distance-based redundancy analysis (dbRDA), does achieve both. It does this by calculating principal coordinates and subsequently correcting for negative eigenvalues, if they are present, by adding a constant to squared distances. We show here that such a correction is not necessary. Partitioning can be achieved directly from the distance matrix itself, with no corrections and no eigenanalysis, even if the distance measure used is semimetric. An ecological example is given to show the differences in these statistical methods. Empirical simulations, based on parameters estimated from real ecological species abundance data, showed that db-RDA done on multifactorial designs (using the correction) does not have type 1 error consistent with the significance level chosen for the analysis (i.e., does not provide an exact test), whereas the direct method described and advocated here does. Key words: distance measures; distance-based redundancy analysis (db-RDA); hypothesis testing; linear models; MANOVA; multivariate analysis; nonparametric; partitioning; principal coordinate analysis; redundancy analysis; semimetric measures; statistical method.

1. INTRODUCTION Modern computing facilities allow statisticians to explore fine data structures that were unimaginable two decades ago. Driven by many sophisticated applications, demanded by the need of nonlinear modeling [...]

A hierarchical Bayesian approach is proposed for variable selection and function estimation in additive nonparametric Gaussian regression models and additive nonparametric binary regression models. The prior for each component function is an integrated Wiener process resulting in a posterior mean estimate that is a cubic smoothing spline. Each of the explanatory variables is allowed to be in or out of the model, and the regression functions are estimated by model averaging. To allow variable selection and model averaging, data-based priors are used for the smoothing parameter and the slope at 0 of each component function. A two-step Markov chain Monte Carlo method is used to efficiently obtain the data-based prior and to carry out variable selection and function estimation. It is shown by simulation that significant improvements in the function estimators can be obtained over an approach that estimates all the unknown functions simultaneously. The methodology is illustrated for a binary regression using heart attack data. KEY WORDS: Bayesian information criterion; Binary regression; Gaussian errors; Model averaging; Posterior probabilities; Time series models., 1. INTRODUCTION This article addresses the problem of variable selection and function estimation in additive nonparametric Gaussian regression models and additive nonparametric binary regression models. For the binary model, the [...]

A 'data-based prior' is used in estimating the hyperparameter values in additive nonparametric Gaussian regression models and additive nonparametric binary regression models. An advantage of using the data-based prior is that its influence dies out asymptotically such that the problem becomes insignificant with a large sample size. Its use results in a posterior that accumulates near submodel regions. Substantial gains are also realized when one or more of the variables are not related to the dependent variable., Berry, Reese and Larkey (BRL) have developed interesting models that shed light on the structure and evolution of player performance in three distinct sports: baseball, golf and hockey. Their article [...]

This paper considers the estimation of the random coefficient dummy endogenous variable model under a symmetry and index condition for the error distribution. We follow a two-step approach. The selection equation is estimated first; in the second step an instrumental variables estimator is proposed for the ourcome equation through a pairwise comparison method. Our approach can be readily extended to the general switching regression model. In constrast to the existing literature on sample selection models, the exclusion restriction is not needed here for model identification; furthermore, the intercept term for the outcome equation can be estimated at the usual parametric rate. Keywords: Distribution-free estimation; Random-coefficient model; Sample selection; Exclusion restriction

The selection of the probability model, the data-based prior and the marginal prior in Shively, Kohn and Wood's study in selecting variables and estimating functions in nonparametric Gaussian models and binary regression models is discussed. They should be commended for synthesizing state-of-the-art theories and numerical methods for resolving problems related with additive nonparametric regression., 1. INTRODUCTION This article addresses a fascinating question: How can one compare the accomplishments of players in a given sport from different eras? In the sport of baseball, is it [...]

A statistical alternative approach to the problem of detecting influential observations in nonparametric deterministic Data Envelopment Analysis models is proposed. It is designed to classify those sample observations which appear as influential. The analyst will then have to check whether these observations are contaminated by data errors or not. Further, this method determines when efficiency changes owing to the presence of a given unit in the sample are statistically important.

Nonparametric statistics independence is tested using data-driven rank tests. The proposed tests are sensitive for both grade linear correlation and grade correlations of higher-order polynomials. Monte Carlo simulation results show that the rank tests possess greater power stability than other well-known tests such as Spearman's test or Hoeffding's test. The consistency of the tests is proven to obtain theoretical support., 1. INTRODUCTION In many statistical studies we are interested in the relationship between several quantities - in particular, the independence of random measurements. Under bivariate normality, dependence is completely described [...]

Differences in marginal locations and/or scales in bivariate data can be simultaneously detected using a set of exact and distribution-free permutation tests. The proposed tests make use of the fact that pairwise differences are symmetrically distributed about zero and are not associated with the pairwise sums when the marginal means and variances are equal. Simulation results show that the permutation tests are quite favorably comparable with the standard tests in literature., 1. INTRODUCTION When the same experimental units are used in both the treatment and control groups, the result is often highly correlated paired observations. Situations like this naturally involve the [...]

Quasi-linear estimation of the modern wavelet theory of spatial adaptation proposed by Donoho and Johnstone is made possible by introducing a minimal number of nonlinear terms on finest scales to a linear adaptive estimate. The proposed quasi-linear wavelet estimation technique provides the advantages of linear adaptive estimates while matching the asymptotic behavior of highly nonlinear procedures. These properties enable the relaxation of familiar assumptions and the solution of a long-standing problem of rate and sharp optimal estimation of monotone functions., 1. INTRODUCTION 1.1 Motivation Consider a classical nonparametric regression setting [Y.sub.l] = f(l/n) + [[Epsilon].sub.l], l = 1, 2, ..., n with zero-mean normal errors [[Epsilon].sub.l], where the problem is [...]

Nonparametric regression problems are examined using linear estimators of multivariate means. To this end, generalizations of some popular theorems about admissibility of linear estimators are considered, and results are analyzed to show that kernel-type estimators normally used in nonparametric regression problems can be constructively improved in a simple manner. Examples of smaller sample size exhibit relative risk gains of up to 18% in realistic settings., 1. INTRODUCTION Consider the ordinary multivariate means problems. Observe [y.sub.1], ..., [y.sub.n], and assume that Y has mean [Theta] and variance [[Sigma].sup.2][Sigma], where Y = ([y.sub.1], ..., [y.sub.n])[prime], [Theta] = [...]