AN ALTERNATIVE PARAMETRIC APPROACH FOR DISCRETE MISSING DATA PROBLEMSLyles, Robert
H.; Taylor, Douglas
J.; Hanfelt, John
J.; Kupper, Lawrence
L.
doi: 10.1081/STA-100106057pmid: N/A
We propose an iterative method of estimation for discrete missing data problems that is conceptually different from the Expectation–Maximization (EM) algorithm and that does not in general yield the observed data maximum likelihood estimate (MLE). The proposed approach is based conceptually upon weighting the set of possible complete-data MLEs. Its implementation avoids the expectation step of EM, which can sometimes be problematic. In the simple case of Bernoulli trials missing completely at random, the iterations of the proposed algorithm are equivalent to the EM iterations. For a familiar genetics-oriented multinomial problem with missing count data and for the motivating example with epidemiologic applications that involves a mixture of a left censored normal distribution with a point mass at zero, we investigate the finite sample performance of the proposed estimator and find it to be competitive with that of the MLE. We give some intuitive justification for the method, and we explore an interesting connection between our algorithm and multiple imputation in order to suggest an approach for estimating standard errors.
AN EXAMINATION OF ESTIMATED RESIDUALS IN A REGRESSION WITH AN INFINITE ORDER PARAMETRIC MODELUsami, Yoshihiro; Toyooka†, Yasuyuki
doi: 10.1081/STA-100106058pmid: N/A
We consider a linear regression with the error term that obeys an autoregressive model of infinite order and estimate parameters of the models. The parameters of the autoregressive model should be estimated based on estimated residuals obtained by means of the method of ordinary least squares, because the errors are unobservable. The consistency of the coefficients, variance and spectral density of the model obeyed by the error term is shown. Further, we estimate the coefficients of the linear regression by means of the method of estimated generalized least squares. We also show the consistency of the estimator. †Professor Toyooka sadly died at 8 April 1998. I, Usami, pray his soul may rest in peace. Most of the results in Section 3 had already been obtained before April 1998. Usami derived the results in Section 4.
EVALUATION OF POWER OF TESTS INVOLVING COVARIATES UNDER NONCONSTANT VARIANCEJackson, J.
Michael; Hewett, John
E.
doi: 10.1081/STA-100106059pmid: N/A
In many experiments where pre-treatment and post-treatment measurements are taken, investigators wish to determine if there is a difference between two treatment groups. For this type of data, the post-treatment variable is used as the primary comparison variable and the pre-treatment variable is used as a covariate. Although most of the discussion in this paper is written with the pre-treatment variable as the covariate the results are applicable to other choices of a covariate. Tests based on residuals have been proposed as alternatives to the usual covariance methods. Our objective is to investigate how the powers of these tests are affected when the conditional variance of the post-treatment variable depends on the magnitude of the pre-treatment variable. In particular, we investigate two cases. [1] The conditional variance of the post-treatment variable gradually increases as the magnitude of the pre-treatment variable increases. (In many biological models this is the case.) [2] The conditional variance of the post-treatment variable is dependent upon natural or imposed subgroups contained within the pre-treatment variable. Power comparisons are made using Monte Carlo techniques.
ASYMPTOTIC STABILITY OF THE OSCV SMOOTHING PARAMETER SELECTIONYi, Seongbaek
doi: 10.1081/STA-100106061pmid: N/A
The smoothing parameter selection by the one-sided cross-validation (OSCV) method is completely automatic in that it does not require extra parameters estimation. Also it reduces the variability comparable to that of plug-in rules. In this paper we derive analytically the asymptotic variance of the smoothing parameter selected by OSCV. It shows the dependency of the stability on the one-sided kerenl and tells the possibility of the optimal one-sided kernel which minimizes the asymptotic variability.
SEGMENTED DOSE-RESPONSE MODELS FOR REPEATED MEASURES DATAPark, Taesung
doi: 10.1081/STA-100106062pmid: N/A
In a dose-response analysis, logit-transformed responses are modelled as a function of log-transformed doses. The linear trend is commonly observed. The comparison among treatment groups can be made based on the linear trend. An example in this paper came from a study to estimate the effect of aminophylline on dose-response curve of atracurium. Unlike the usual dose-response curve, this example has repeated measures and seems to have two slopes to which the usual dose-response model is not adequate to fit. We propose segmented regression models that allow two different slopes. The proposed model is an extension of the segmented regression model with a univariate response per subject. We illustrate the proposed model fits data better than the usual dose-response model.
COMPARATIVE CALIBRATION WITH SUBGROUPSGarcia-Alfaro, K.
H.; Bolfarine, H.
doi: 10.1081/STA-100106063pmid: N/A
The main object of this paper is to consider structural comparative calibration models under the assumption that the unknown quantity being measured is not identically distributed for all units. We consider the situation where the mean of the unknown quantity being measured is different within subgroups of the population. Method of moments and maximum likelihood estimators are considered for estimating the parameters in the model. Large sample inference is facilitated by the derivation of the asymptotic variances. An application to a data set which indeed motivated the consideration of such general model and was obtained by measuring the heights of a group of trees with five different instruments is considered.
EFFICIENCY OF LINEAR REGRESSION ESTIMATORS BASED ON PRESMOOTHINGJanssen, Paul; Swanepoel, Jan; Veraverbeke, Noël
doi: 10.1081/STA-100106064pmid: N/A
Consider the estimation of the regression parameters in the usual linear model. For design densities with infinite support, it has been shown by Faraldo Roca and González Manteiga [1] that it is possible to modify the classical least squares procedure and to obtain estimators for the regression parameters whose MSE's (mean squared errors) are smaller than those of the usual least squares estimators. The modification consists of presmoothing the response variables by a kernel estimator of the regression function. These authors also show that the gain in efficiency is not possible for a design density with compact support. We show that in this case local linear presmoothing does not fix this inefficiency problem, in spite of the well known fact that local linear fitting automatically corrects the bias in the endpoints of the (design density) support. We demonstrate on a theoretical basis how this inefficiency problem can be rectified in the compact design case: we prove that presmoothing with boundary kernels studied in Müller [2] and Müller and Wang [3] leads to regression estimators which are superior over the least squares estimators. A very careful analytic treatment is needed to arrive at these asymptotic results.
ON UMP INVARIANT F-TEST PROCEDURES IN A GENERAL LINEAR MODELNoda, Kazuo; Ono, Hideo
doi: 10.1081/STA-100106065pmid: N/A
A simple method of setting linear hypotheses for a split mean vector testable by F-tests in a general linear model, when the covariance matrix has a general form and is completely unknown, is provided by extending the method discussed in Ukita et al. The critical functions in these F-tests are constructed as UMP invariants, when the covariance matrix has a known structure. Further critical functions in F-tests of linear hypotheses for the other split mean vector in the model are shown to be UMP invariant if the same known structure of the covariance matrix is assumed.
A NONPARAMETRIC TEST OF SYMMETRY VERSUS ASYMMETRY FOR RANKED-SET SAMPLESÖztürk, Ömer
doi: 10.1081/STA-100106066pmid: N/A
This paper introduces a nonparametric test of symmetry for ranked-set samples to test the asymmetry of the underlying distribution. The test statistic is constructed from the Cramér-von Mises distance function which measures the distance between two probability models. The null distribution of the test statistic is established by constructing symmetric bootstrap samples from a given ranked-set sample. It is shown that the type I error probabilities are stable across all practical symmetric distributions and the test has high power for asymmetric distributions.