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For a balanced two‐way mixed model, the maximum likelihood (ML) and restricted ML (REML) estimators of the variance components were obtained and compared under the non‐negativity requirements of the variance components by Lee and Kapadia (1984). In this note, for a mixed (random blocks) incomplete block model, explicit forms for the REML estimators of variance components are obtained. They are always non‐negative and have smaller mean squared error (MSE) than the analysis of variance (AOV) estimators. The asymptotic sampling variances of the maximum likelihood (ML) estimators and the REML estimators are compared and the balanced incomplete block design (BIBD) is considered as a special case. The ML estimators are shown to have smaller asymptotic variances than the REML estimators, but a numerical result in the randomized complete block design (RCBD) demonstrated that the performances of the REML and ML estimators are not much different in the MSE sense.

The advent of electronic computing permits the empirical analysis of economic models of far greater subtlety and rigour than before, when many interesting ideas were not followed up because the calculations involved made this impracticable. The estimation and testing of these more intricate models is usually based on the method of Maximum Likelihood, which is a well-established branch of mathematical statistics. Its use in econometrics has led to the development of a number of special techniques; the specific conditions of econometric research moreover demand certain changes in the interpretation of the basic argument. This book is a self-contained introduction to this field. It consists of three parts. The first deals with general features of Maximum Likelihood methods; the second with linear and nonlinear regression; and the third with discrete choice and related micro-economic models. Readers should already be familiar with elementary statistical theory, with applied econometric research papers, or with the literature on the mathematical basis of Maximum Likelihood theory. They can also try their hand at some advanced econometric research of their own

The similarities between the logistic regression model and the Rasch model (used in psychometric item response theory) are used to derive several methods based on logits that produce parameter estimates for the Rasch model. A result from LeCam and Dzhaparidze is used by which an initial consistent estimate is transformed by one scoring method iteration into an estimate that has the same asymptotic efficiency as the (in this case conditional) maximum likelihood estimate of the item parameters. Indirect evidence about the bias of this CML estimator is produced by studying the (more easily derived) bias of the estimator based on the unweighted logits. Finally, some simple weighted least squares logit‐based estimates are presented, and their performance is assessed. On the whole, the computationally simpler logit‐based estimates give a fairly good approximation to the CML estimates.

Statistical inference for fixed effects, random effects and components of variance in an unbalanced linear model with variance components will be discussed. Variance components will be estimated by Restricted Maximum Likelihood. Iterative procedures for computing the estimates, such as Fisher scoring and the EM‐algorithm, are described.

AbstractOne branch of the reliability literature is concerned with devising statistical procedures with various nonparametric "restricted family" model assumptions because of the potential improved operating characteristics of such procedures over totally nonparametric ones. In the single‐sample problem with unknown increasing failure rate (IFR) distribution F, (1) maximum‐likelihood estimators of F have been calculated, (2) upper or lower tolerance limits for F have been determined, and (3) tests of the null hypothesis that F is exponential have been constructed. Barlow and Campo proposed graphical methods for assessing goodness of fit to the IFR model when the validity of this assumption is unknown. This article proposes several analytic tests of the IFR null hypothesis based on the maximum distance and area between the cumulative hazard function and its greatest convex minorant (GCM), and the maximum distance and area between the total time on test statistic and its GCM. A table of critical points is provided to implement a specific test having good overall power properties.

A smooth and detailed distribution is fitted to coarsely grouped frequency data by a nonparametric approach, based on penalized maximum likelihood. The estimated distribution conserves mean and variance of the data. The numerical solution is described and a compact and simplified algorithm is given. The procedure is applied to two empirical datasets.

While demand estimates are used in policy making in a number
of areas, there has not been a substantial literature on demand patterns
and responses in Pakistan. We present estimates for thirteen classes of
goods, based on a complete demand system, a modification of the Unear
Expenditure System, using maximum likelihood techniques and observations
at the household level for Pakistan and urban and rurll areas for
1976.

THIS PAPER DEVELOPS A FINITE-HORIZON DYNAMIC STOCHASTIC MODEL OF DISCRETE CHOICE WITH RESPECT TO LIFE-CYCLE FERTILITY WITHIN AN ENVIRONMENT WHERE INFANT SURVIVAL IS UNCERTAIN. THE MODEL YIELDS IMPLICATIONS FOR THE NUMBER, TIMING, AND SPACING OF CHILDREN. A TRACTABLE ESTIMATION METHOD IS DEVELOPED FOR THE LINEAR CONSTRAINT-QUADRATIC UTILITY CASE THAT IS INTIMATELY TIED TO THE DYNAMIC OPTIMIZATION PROBLEM, AND THE METHOD IS APPLIED TO MALAYSIAN HOUSEHOLD DATA. ESTIMATION IS BASED ON INTEGRATING THE NUMERICAL SOLUTION OF THE DYNAMIC PROGRAMMING MODEL OF BEHAVIOR WITH A MAXIMUM LIKELIHOOD PROCEDURE.

The econometric analysis of demand in Pakistan has, until
recently, been a relatively neglected field of analysis. Much of the
earlier work, reviewed in Ali (1985), consists of linear Engel curves
based on grouped data published by the Bureau of Statistics. Ahmad,
Leung and Stern (1984), and Ahmad, Ludlow and Stern (1987) use household
observations from the 1976 Micro-Nutrient Survey (MNS), to estimate 17
(9 of which are food items) and 13 commodity parameters and elasticities
based on a modified linear Expenditure System (LES) using Maximum
likelihood methods. The modified LES is a method of obtaining LES
parameters without independent price information, analogous to the ELES.
This method differs from the ELES in that expenditure information is
used, rather than income, see Ahmad, Ludlow and Stern (1987) for
details.

ABSTRACTCertain motor vehicle safety standards stipulate a collision test speed and a set of performance criteria that vehicles must satisfy during or after the collision test. For example, Federal Motor Vehicle Safety Standard 301 requires a 30 mile per hour (mph) barrier collision and specifies a certain maximum allowable limit on the total spillage of fuel. Vehicle designs are required to meet this standard; however, when collision tests are conducted at speeds higher than the standard, vehicles do not always satisfy the performance criteria. This paper develops a mathematical model for estimating the probability of meeting the standard by using a Bayesian framework to incorporate engineering judgment with collision test results. The model is based on the idea that there are random features to a vehicle's ability to meet performance standards in a collision, especially at such elevated speeds. Example calculations are included to illustrate the estimation of the probability of meeting the standard and to compare it with a maximum likelihood approach.

This paper gives an overview of several (mostly recent) statistical contributions to the theory of Limiting and Serial Dilution Assays (LDA's, SDA's). A simple and useful method is presented for the setup of a design for an LDA or an SDA. This method is based on several user‐supplied design parameters, consisting in the researcher's advance information and other parameters inherent to the particular problem. The commonly used Maximum Likelihood (ML) and Minimum Chi‐square methods for the estimation of the unknown parameter in an LDA or an SDA are described and compared to several bias‐reducing estimation methods, e.g. jackknife and bootstrap versions of the ML method. One particular jackknife version is recommended.

A statistical model for the evaluation of the effectiveness of the Demerit Points System (DPS) in reducing traffic offenses is presented. The model for the waiting times between detected traffic offenses is based on an exponential distribution. Since traffic offenses are relatively rare events, the length of the study period was such that censoring was unavoidable. Under these circumstances Maximum Likelihood (ML) estimates of the waiting time between offenses are determined and the corresponding hypotheses are tested. The empirical results showed that the DPS was responsible for most of the deterrent effect reflected in the increased mean time until the third offense subsequent to the first and second offense detected less than three years apart.

An examination of the determinants of the award & receipt of child support payments for ever-married mothers (N = 2,416) based on the Mar/Apr 1979 Match File of the Current Population Survey. Previous studies are improved on by using a large nationally representative data set & nonlinear maximum likelihood estimation techniques. The results show that SE characteristics associated with the needs of the custodial mother tend to be more important as a determinant of the award of child support than its receipt, while characteristics associated with the ability or desire of the absent father to pay support are important in both its receipt & award. 4 Tables, 10 References. HA

R. G. Niemi ("Majority Decision Making with Partial Unidimensionality," American Political Science Review, 1969, 63, 488-497), in an important but neglected paper, found that when orderings were drawn from a simulation based on the impartial culture, the greater the proportion of voter orderings that were single-peaked (a condition he called partial single-peakedness), the more likely there was to be a transitive group ordering. In addition, the likelihood of transitivity increased with group size. However, Niemi's simulation was restricted to the case of three alternatives, & he provided no theoretical explanation for the results of his simulation. This is provided here in terms of a model based on the idea of net preferences, & Niemi's results are extended for the general case of any finite number of alternatives, for electorates that are large relative to the number of alternatives being considered. In addition to providing a rationale for Niemi's simulation results, the ideas of net preferences & opposite preferences have a wide range of potential applications. 23 References. HA

Part I of this research examined the transformation of British politics in the 1885-1910 period: the expansion of suffrage in 1885, the incorporation of the newly enfranchised into political life, and the resulting changes in party alignments. Latent variable partial least-squares (LVPLS) algorithms generated dynamic across-time models of political change. These models were then tested with maximum likelihood (ML) methods. The research concluded that the seeds of realignment emerged in the period as the Labour movement successfully mobilized class voting while the Liberal party became progressively isolated from middle-class Nonconformism. Part II of the research examines the 1918-1950 period for further evidence of partisan realignment following the expansion of the electorate in 1918 and 1928 as Britain approached the "one adult, one value, one vote" ideal. LVPLS and ML models support the previous conclusions by highlighting the stability of party alignments during the period, which are increasingly supported by class-based voting but not to the exclusion of religion for the Conservatives.