A comparison of three methods of estimating the logistic regression coefficients

A Sampling experiment performed using data collected for a large clinical trial shows that the discriminant function estimates of the logistic regression coefficients for discrete variables may be severely biased. The simulations show that the mixed variable location model coefficient estimates have bias which is of the same magnitude as the bias in the coefficient estimates obtained using conditional maximum likelihood estimates but require about one-tenth of the computer time.     

Correcting Estimation Bias in Dynamic Term Structure Models

The affine dynamic term structure model (DTSM) is the canonical empirical finance representation of the yield curve. However, the possibility that DTSM estimates may be distorted by small-sample bias has been largely ignored. We show that conventional estimates of DTSM coefficients are indeed severely biased, and this bias results in misleading estimates of expected future short-term interest rates and of long-maturity term premia. We provide a variety of bias-corrected estimates of affine DTSMs, for both maximally flexible and overidentified specifications. Our estimates imply interest rate expectations and term premia that are more plausible from a macrofinance perspective. This article has supplementary material online.     

Robust estimates for GARCH models

In this paper we present two robust estimates for GARCH models. The first is defined by the minimization of a conveniently modified likelihood and the second is similarly defined, but includes an additional mechanism for restricting the propagation of the effect of one outlier on the next estimated conditional variances. We study the asymptotic properties of our estimates proving consistency and asymptotic normality. A Monte Carlo study shows that the proposed estimates compare favorably with respect to other robust estimates. Moreover, we consider some real examples with financial data that illustrate the behavior of these estimates.     

Best linear corrector of classification estimates of proportions of objects in several unknown classes

It has been recognized that counting the objects allocated by a rule of classification to several unknown classes often does not provide good estimates of the true class proportions of the objects to be classified. We propose a linear transformation of these classification estimates, which minimizes the mean squared error of the transformed estimates over all possible sets of true proportions. This so-called best-linear-corrector (BLC) transformation is a function of the confusion (classification-error) matrix and of the first and second moments of the prior distribution of the vector of proportions. When the number of objects to be classified increases, the BLC tends to the inverse of the confusion matrix. The estimates that are obtained directly by this inverse-confusion corrector (ICC) are also the maximum-likelihood unbiased estimates of the probabilities that the objects originate from one or the other class, had the objects been preselected with those probabilities. But for estimating the actual proportions, the ICC estimates behave less well than the raw classification estimates for some collections. In that situation, the BLC is substantially superior to the ICC even for some large collections of objects and is always substantially superior to the raw estimates. The statistical model is applied concretely to the measure of forest covers in remote sensing.     

Statistical inference for heteroscedastic semi-varying coefficient EV models

This paper proposes an estimation procedure for a class of semi-varying coefficient regression models when the covariates of the linear part are subject to measurement errors. Initial estimates for the regression and varying coefficients are first constructed by the profile least-squares procedure without input from heteroscedasticity, a bias-corrected kernel estimate for the variance function then is proposed, which in turn is used to define re-weighted bias-corrected estimates of the regression and varying coefficients. Large sample properties of the proposed estimates are thoroughly investigated. The finite-sample performance of the proposed estimates is assessed by an extensive simulation study and an application to the Boston housing data set. The simulation results show that the re-weighted bias-corrected estimates outperform the initial estimates and the naive estimates.     

On the Computation and Finite Sample Behavior of the Constrained M-Estimates for Multivariate Location and Scatter

Abstract

Constrained M (CM) estimates of multivariate location and scatter [Kent, J. T., Tyler, D. E. (1996). Constrained M-estimation for multivariate location and scatter. Ann. Statist. 24:1346–1370] are defined as the global minimum of an objective function subject to a constraint. These estimates combine the good global robustness properties of the S estimates and the good local robustness properties of the redescending M estimates. The CM estimates are not explicitly defined. Numerical methods have to be used to compute the CM estimates. In this paper, we give an algorithm to compute the CM estimates. Using the algorithm, we give a small simulation study to demonstrate the capability of the algorithm finding the CM estimates, and also to explore the finite sample behavior of the CM estimates. We also use the CM estimators to estimate the location and scatter parameters of some multivariate data sets to see the performance of the CM estimates dealing with the real data sets that may contain outliers.     

An iterative procedure for the estimation of parameters in a dose-response model

The least squares estimates of the parameters in the multistage dose-response model are unduly affected by outliers in a data set whereas the minimum sum of absolute errors, MSAE estimates are more resistant to outliers. Algorithms to compute the MSAE estimates can be tedious and computationally burdensome. We propose a linear approximation for the dose-response model that can be used to find the MSAE estimates by a simple and computationally less intensive algorithm. A few illustrative ex-amples and a Monte Carlo study show that we get comparable values of the MSAE estimates of the parameters in a dose-response model using the exact model and the linear approximation.     

Logistic Regression and Discriminant Analysis by Ordinary Least Squares

If the observations for fitting a polytomous logistic regression model satisfy certain normality assumptions, the maximum likelihood estimates of the regression coefficients are the discriminant function estimates. This article shows that these estimates, their unbiased counterparts, and associated test statistics for variable selection can be calculated using ordinary least squares regression techniques, thereby providing a convenient method for fitting logistic regression models in the normal case. Evidence is given indicating that the discriminant function estimates and test statistics merit wider use in nonnormal cases, especially in exploratory work on large data sets.     

Polynomial estimation of eigenvalues

In estimating the eigenvalues of the covariance matrix of a multivariate normal population, the usual estimates are the eigenvalues of the sample covariance matrix. It is well known that these estimates are biased. This paper investigates obtaining improved eigenvalue estimates through improved estimates of the characteristic polynomial, which is a function of the sample eigenvalues. A numerical study investigates the improvements evaluated under both a square error and an entropy loss function.     

Repeated measurement analysis for nonnormal data in small samples

The small sample performance of Zeger and Liang's extended generalized linear models for the analysis of longitudinal data (Biometrics, 42,121-130,1986) is investigated for correlated gamma data. Results show that the confidence intervals do not provide desirable coverage of the true parameter due to considerably biased point estimates. Improved estimates are proposed using the jackknife procedure. Simulations performed to evaluate the proposed estimates indicate superior properties to the previous estimates.     

Assessing the bias of maximum likelihood estimates of contaminated garch models

It is well known that Gaussian maximum likelihood estimates of time series models are not robust. In this paper we prove this is also the case for the Generalized Autoregressive Conditional Heteroscedastic (GARCH) models. By expressing the Gaussian maximum likelihood estimates as Ψ estimates and by assuming the existence of a contaminated process, we prove they possess zero breakdown point and unbounded influence curves. By simulating GARCH processes under several proportions of contaminations we assess how much biased the maximum likelihood estimates may become and compare these results to a robust alternative. The t-student maximum likelihood estimates of GARCH models are also considered.     

Admissible minimax estimators for the shape parameter of Topp–Leone distribution

Abstract

The shape parameter of Topp–Leone distribution is estimated in this article from the Bayesian viewpoint under the assumption of known scale parameter. Bayes and empirical Bayes estimates of the unknown parameter are proposed under non informative and suitable conjugate priors. These estimates are derived under the assumption of squared and linear-exponential error loss functions. The risk functions of the proposed estimates are derived in analytical forms. It is shown that the proposed estimates are minimax and admissible. The consistency of the proposed estimates under the squared error loss function is also proved. Numerical examples are provided.     

A two-stage procedure to pool information across quantile levels in linear quantile regression

In linear quantile regression, the regression coefficients for different quantiles are typically estimated separately. Efforts to improve the efficiency of estimators are often based on assumptions of commonality among the slope coefficients. We propose instead a two-stage procedure whereby the regression coefficients are first estimated separately and then smoothed over quantile level. Due to the strong correlation between coefficient estimates at nearby quantile levels, existing bandwidth selectors will pick bandwidths that are too small. To remedy this, we use 10-fold cross-validation to determine a common bandwidth inflation factor for smoothing the intercept as well as slope estimates. Simulation results suggest that the proposed method is effective in pooling information across quantile levels, resulting in estimates that are typically more efficient than the separately obtained estimates and the interquantile shrinkage estimates derived using a fused penalty function. The usefulness of the proposed method is demonstrated in a real data example.     

Updating small area population estimates in England and Wales

"Population estimates have important implications for resource allocation within government and commerce, and are often assumed to be without error. Currently, central government provides annual population estimates for all the local and health authority districts in Britain, but estimates are needed for smaller areas, typically for electoral wards and postal sectors. Small area estimates are provided by some local authorities and commercial organizations, using different methods; the accuracy of these estimates is modelled here within a multilevel framework. Certain characteristics of the small area and of the method of estimation are included as explanatory variables. Results show that the method of estimation used is of great importance."     

Index to Articles,by Author,Volume 2 (1984)

This article investigates the statistical properties of the U.S. sacrifice ratio—the cumulative output loss arising from a permanent reduction in inflation. We derive estimates of the sacrifice ratio from three structural vector autoregression models and then conduct a series of simulation exercises to analyze their sampling distribution. We obtain point estimates of the sacrifice ratio that are consistent with results reported in earlier studies. However, the estimates are very imprecise, which we suggest reflects the poor quality of instruments used in estimation. We conclude that the estimates provide a very unreliable guide for assessing the output cost of disinflation policy.     

Multivariate Fay-Herriot models for small area estimation with application to household consumption per capita expenditure in Indonesia

ABSTRACT

Multivariate Fay-Herriot (MFH) models become popular methods to produce reliable parameter estimates of some related multiple characteristics of interest that are commonly produced from many surveys. This article studies the application of MFH models for estimating household consumption per capita expenditure (HCPE) on food and HCPE of non-food. Both of those associated direct estimates, which are obtained from the National Socioeconomic Surveys conducted regularly by Statistics Indonesia, have a strong correlation. The effects of correlation in MFH models are evaluated by employing a simulation study. The simulation showed that the strength of correlation between variables of interest, instead of the number of domains, plays a prominent role in MFH models. The application showed that MFH models have more efficient than univariate models in terms of standard errors of regression parameter estimates. The roots of mean squared errors (RMSEs) of the estimates obtained from the empirical best linear unbiased prediction (EBLUP) estimators of MFH models are smaller than RMSEs obtained from the direct estimators. Based on MFH model, the HCPE estimates of food by districts in Central Java, Indonesia, are higher than the HCPE estimates of non-food. The average of HCPE estimates of food and non-food in Central Java, Indonesia in 2015 are IDR 383,100.6 and IDR 280,653.6, respectively.     

Why does “last week” reporting give higher estimates than “last month”?

Abstract

Experiments in various countries with “last week” and “last month” reference periods for reporting of households’ food consumption have generally found that “week”-based estimates are higher. In India the National Sample Survey (NSS) has consistently found that “week”-based estimates are higher than month-based estimates for a majority of food item groups. But why are week-based estimates higher than month-based estimates? It has long been believed that the reason must be recall lapse, inherent in a long reporting period such as a month. But is household consumption of a habitually consumed item “recalled” in the same way as that of an item of infrequent consumption? And why doesn’t memory lapse cause over-reporting (over-assessment) as often as under-reporting? In this paper, we provide an alternative hypothesis, involving a “quantity floor effect” in reporting behavior, under which “week” may cause over-reporting for many items. We design a test to detect the effect postulated by this hypothesis and carry it out on NSS 68th round HCES data. The test results strongly suggest that our hypothesis provides a better explanation of the difference between week-based and month-based estimates than the recall lapse theory.     

The use of resighting data to estimate the rate of population growth of the snail kite in Florida

The rate of population growth ( u ) is an important demographic parameter used to assess the viability of a population and to develop management and conservation agendas. We examined the use of resighting data to estimate u for the snail kite population in Florida from 1997-2000. The analyses consisted of (1) a robust design approach that derives an estimate of u from estimates of population size and (2) the Pradel (1996) temporal symmetry (TSM) approach that directly estimates u using an open-population capture-recapture model. Besides resighting data, both approaches required information on the number of unmarked individuals that were sighted during the sampling periods. The point estimates of u differed between the robust design and TSM approaches, but the 95% confidence intervals overlapped substantially. We believe the differences may be the result of sparse data and do not indicate the inappropriateness of either modelling technique. We focused on the results of the robust design because this approach provided estimates for all study years. Variation among these estimates was smaller than levels of variation among ad hoc estimates based on previously reported index statistics. We recommend that u of snail kites be estimated using capture-resighting methods rather than ad hoc counts.     

Estimation of structural impulse responses: short-run versus long-run identifying restrictions

There is evidence that estimates of long-run impulse responses of structural vector autoregressive (VAR) models based on long-run identifying restrictions may not be very accurate. This finding suggests that using short-run identifying restrictions may be preferable. We compare structural VAR impulse response estimates based on long-run and short-run identifying restrictions and find that long-run identifying restrictions can result in much more precise estimates for the structural impulse responses than restrictions on the impact effects of the shocks.