Search

Comments on the paper 'The effect of increasing sample size on the precision of an estimator' published in the Journal of The American Statistician. Applicability of the sampling to an infinite theoretical population; Considerations in sampling from finite population; Dependence of the estimator on the design.

The article presents a commentary on the paper "A Statistical Model of Earnings Estimation," by M. N. Greenball. The author notes that the dividend model used in the dividend tests was not in the form suggested by the empirical evidence in the finance literature. He says there is very little value relating to the dividend test results. The author acknowledges that Greenball's research is useful to the extent that it suggests alternative methods of accounting in light of implications of positive models.

This paper considers a test score model in which the true score and the measurement error are autocorrelated. After some preliminary remarks on corrections for attenuation, the paper focuses on the three-wave ease (t = 1, 2, 3), demonstrating identifiability, showing an estimation algorithm, and providing a numerical illustration. [ABSTRACT FROM AUTHOR]

This paper presents methods for computing point and interval estimates of descriptors of simulated queuing systems. The methods, which rely on the renewal process representation of certain processes, extend the results of CRANE and IGLEHART, and the author. In particular, the paper shows that computation of three sample quantities suffices to generate point and interval estimates for twelve system descriptors. [ABSTRACT FROM AUTHOR]

Radical changes, up and down, have taken place in the estimates of growth in total factor productivity in the U.S. made by different economists, or by the same economists at different times. If such estimates provide ‘some sort of measure of our ignorance,’ as Abramovitz once put it, we seemed to be a lot less ignorant in 1927 (when Cobb and Douglas published their famous paper), or in 1967 (when Jorgenson and Griliches published theirs), than we were in the years between (when Schmookler, Abramovitz, Kendrick, and Denison completed their studies), or than we are today (when we have, or will soon have, revised estimates by Denison and by Kendrick, and new estimates by Christensen and Jorgenson). Viewed in this perspective, many questions may be raised about the significance of the current estimates that something like a third or more of the rate of increase in U.S. national output is ‘due’ to increase in productivity, as well as about the concepts, data, and methods that underlie the estimates. A list of particular subjects worth considering for research is given and each is briefly discussed. [ABSTRACT FROM AUTHOR]

A Note on the. Treatment of Serial Correlation. There are essentially two courses of action open to the researcher who finds that the Durbin-Watson statistic is significant: (a) to re-estimate the original equation using a technique designed to take account of autoregressive errors; (b) to re-specify the equation until the Durbin-Watson statistic becomes insignificant. The purpose of this paper is to suggest a large sample test procedure to test the hypothesis that the first course of action is valid. The test only uses results from simple least squares estimation and so no complicated computation is required. The test is illustrated using data previously published in a paper by Durbin and Watson. [ABSTRACT FROM AUTHOR]

Cohort analyses in which the joint effects of aging, historical change and birth cohort membership are estimated for some dependent variable are often desirable on substantive grounds Unless two of these three variables are viewed as indexing identical unmeasured causal factors, any analysis which makes estimates for only two of the three variables is subject to spurious results. But three-way cohort analysis is problematic because age, time period and birth cohort are linearly dependent on each other. Although this con founding makes estimation of some three-way cohort models impossible, this paper demonstrates that estimation is feasible in a number of such models. By exploring estimates derived for some of these models from hypothetical data for which the underlying effects are known, this paper also shows that meaningful three-way cohort analysis is difficult unless the researcher entertains relatively strong hypotheses about the nature of aging, period and cohort effects. [ABSTRACT FROM AUTHOR]

This paper presents a solution procedure for discrete stochastic programs with recourse (linear programs under uncertainty). It views the m stochastic elements of the requirements vector as an m-dimensional space in which each combination of the discrete values is a lattice point. For a given second-stage basis, certain of the lattice points are feasible. A procedure is presented to delete infeasible points from the space. Thus, the aggregate probability associated with points feasible for this basis can be enumerated, and used to weight the vector of dual variables defined by the basis. Finally, the paper presents a systematic procedure for changing optimal bases so that a feasible and optimal basis is found for every lattice point. [ABSTRACT FROM AUTHOR]

This paper considers the duel between two contestants with unlimited ammunition supplies, each one firing at the other. It assumes that the damage resulting from a round of fire is measurable and has a probability distribution. The cumulative damage function depends both on time and on number of rounds fired. For given rates of fire, damage functions, and other parameters, the paper calculates the probabilities that a given side will win. [ABSTRACT FROM AUTHOR]

This paper summarizes some suggested computational procedures for, and further progress on, estimating expected target damage for individual rounds, and for battery or battalion volley-type fire. In particular, it recommends the computational procedures that are best followed for suitably accurate estimation of target damage. Some other useful results relating to the target-damage analysis problem, and possibly to other applied studies, are also recorded. [ABSTRACT FROM AUTHOR]

This paper derives an expression for the expected completion time of a repair project, such as the servicing of end products, when the servicing is composed of a sequence of repair activities on parts of the end product. These parts are subject to repair with a specified probability and, at first, it is assumed that the completion time of each activity is constant. Subsequently, this assumption is relaxed so that an arbitrary probability distribution can be specified for the activity completion times. The concluding parts of the paper show how to compute the expected end-product service time for a particular class of activity-time probability distributions. [ABSTRACT FROM AUTHOR]

This paper finds sufficient conditions for the ergodicity and recurrence of irreducible and aperiodic Markov chains. They extend some of the ones commonly used. The paper also indicates their use in discussing a certain class of queuing problem with state dependent service times. [ABSTRACT FROM AUTHOR]

The article focuses on rules of thumb and optimally imperfect decisions. In this paper, authors argue that rules of thumb are among the more efficient pieces of equipment of optimal decision-making. Therefore authors investigate in fairly general terms how "good" rules of thumb can be designed and evaluated. The paper also reports on an illustrative application of the analysis. A simulation procedure is used to determine the relevant properties of a number of alternative pricing rules of thumb and to compare their performance as guides to decision-making in a single-product monopolistic firm. The more refined the decision-making process, the more expensive it is likely to be; and therefore, especially where a decision is not of crucial importance, no more than an approximate solution may be justified. Since all real decisions are made under conditions of imperfect information, calculation down to the last decimal place is pointless in any event. A crucial step in the determination of an optimal rule of thumb is the calculation of the expected consequences of the adoption of any particular rule of thumb.

This paper comprises an extension of Model I of a recent paper of GLUSS, Opns Res 7, 468ñ477 (1969), and its purpose is to dictate strategies that minimize the expected cost (in time) of locating a fault in a complex system of equipment. These strategies are specialized for use with automatic testing equipment. The model assumes that the complex system consists of N modules containing n(1), , n(N) elements respectively, that the cost of examining the modules are t1, tN respectively, and that the costs of examining the elements within the rth module are tr1 , , trn(r). It is further assumed that module tests are performed to find which module is faulty before element tests are performed, and that there exist probabilities at each stage that errors of two kinds can be made (1) that the test fails to detect an actual fault in the module or item tested, (2) that the test finds a fault that does not exist. The estimation of the probabilities of faults lying in respective modules or elements is performed in a different way from that in Gluss' paper they are computed from element reliability data by manipulation of their γ parameters, where γ is the element failure rate. Furthermore, consideration is given to fault symptoms that are supplied by weighting the probabilities according to the symptom information. Because of the anticipated difficulty in obtaining the necessary parameter estimates, the analysis may be most useful for its illumination of the influence the several required estimates have on the optimum search routine. [ABSTRACT FROM AUTHOR]

The article discusses the optimality of adaptive forecasting. The authors build on a previous paper by W. M. Gorman and H. Theil, which formulated a stochastic model underlying the procedure of adaptive forecasting of an economic time series. They believe that while the series created by Theil and Wage is nonstationary, it can be transformed into one that is stationary. They also present a simplification of the forecasting procedure proposed by Theil and Wage for forecasts one period level ahead, which are dependent on two previous predictions and realized values of the second difference of the series forecast.

While the activity of marketing research can be fruitfully viewed within a statistical decision theoretic model, relatively little is known concerning the descriptive aspects of how people-managers or consumers-revise probabilities in the light of new information. This paper reports the results of a behavioral study in probability revision and the implications of these findings for the operational use of decision theoretic concepts in prescriptive and descriptive choice-making models [ABSTRACT FROM AUTHOR]

The article seeks to elaborate upon an idea put forward by Richard P. Brief and Joel Owen on allocation in accounting by considering costs, revenues, and the collection of cash, which are all an aspect of an estimation problem. It is noted that estimation theory can be used when there are uncertain period costs but revenues are set. The article concludes that recognizing uncertainty helps to better show cost allocation. Using estimation theory is a way, the author states, of avoiding confusion about matching permits and realization.

This article discusses the concept of least squares allocation model. The authors explain that the model offers one approach to the unification of a broad class of allocation problems and provides a basis for summarizing, comparing, and evaluating diverse allocation schemes. They state that first, the model formally unifies a number of accounting problems so that methods that have been proposed to account for joint product costs, depreciation and installments sales, share a common allocation model. The article says that this unification of different accounting problems gives insight into their comparative nature.

The approach of selecting a portfolio of stocks on the basis of expected return and variance was introduced by Markowitz [18] in 1952 and subsequently was more fully developed by him [19] in 1959. Since this time, there has been considerable research either directly concerned with, or related to, the Markowitz model. The utility implications of his assumption that an investor chooses a portfolio solely on the basis of expected return and variance (where variance is identified with risk) have been studied, [1], [4], [22], and [31]. A simplified method of solving for the efficient set of portfolios under the assumption of a regression structure has been developed by Sharpe [26], and approximation methods have been suggested [25] and [29]. Empirical tests (with partially contradictory conclusions) of portfolio selection theory are described in [5], [7], [8], [20], and [27]. Studies of economic questions (such as liquidity preference, equilibrium stock prices, substitutability of risky assets, etc.), as formulated within the portfolio model, can be found in [10], [11], [13], [14], [16], [23], and [28]. A related portfolio selection approach, based on the assumption of a Pareto underlying distribution, has been suggested by Fama [6]. A modification by Baumol [2] introduced a confidence limit criterion. Also, some initial attempts have been made at deriving related adaptive models of portfolio selection, [2l], [30]. In ail of the theoretical work, the question of estimating the required parameters in the models has been largely side-stepped (with the exception of Mao and Sarndall [17]) by assuming that the parameter values are known exactly. In empirical work, statistical estimates have been used as if they were the true parameter values. This paper deals with the problem of assessing portfolio risk (or variance) in view of the fact that, in an operational situation, the true values of the parameters of the distribution of returns are not known with certainty but... [ABSTRACT FROM AUTHOR]

The article presents a critique of the study by Ronald L. Teigen called "A Structural Approach to the Impact of Monetary Policy" that appeared in this issue of the journal. The author points out that several of the equations that are discussed in Teigen's paper are not included therein and will focus on Teigen's estimates. Of particular interest to the author is Teigen's use of impact and transmission effects because the two are closely linked. These equations dealt specifically with money supply, interest rates, and the gross national product. The author provides his own opinion about the variables used in the equation and feels that potential money stock and the discount rate are not exogenous.

This article analyzes the statistical estimation of labor input and output in manufacturing in the U.S. using the short-run increasing returns to labor paradox. The relation between output and labor input in manufacturing is important in quantitative analysis of economic fluctuations. Empirical work on this topic generally supports the conclusion that labor inputs respond with a delay, and not in full proportion, to changes in output. Thus, variations in output are accompanied by corresponding variations in average labor productivity. This phenomenon is something of a paradox, for shortrun increasing returns to labor, or SRIRL, are difficult to rationalize if the sector being explained is assumed to operate on a static production function in which labor is the most variable factor. One need not make this assumption, and a variety of plausible deviations from it, which can explain the qualitative empirical results, have been advanced. It also seems possible that some of the apparent SRIRL reported in previous studies reflects statistical bias in estimating the labor-output relation. Most previous studies have estimated single-equation distributed lag regressions, treating labor input as the dependent variable. The justification for doing so appears to be that output changes are thought to be causally prior to employment changes in the firm-level behavioral mechanisms most often invoked to explain SRIRL. Since these mechanisms do not generate a theory of the error term in the aggregate labor-output relation, they do not justify making labor the dependent variable in a regression. Indeed, if some of the error in the relation resides in output, inappropriate regressions of labor on output might imply spuriously large estimates of SRIRL.

A description is given of a quick and simple technique for checking, by means of the usual χ² and Kolmogorov-Smirnov tests, the goodness of fit of Weibull's distribution to data relating to the fatigue of textile materials tested for abrasion, repeated extension, repeated bending, etc., or subjected to any type of action susceptible of being treated by means of such a distribution. [ABSTRACT FROM AUTHOR]

The article presents information about distribution and extent of unemployment among farm laborers in the U.S. The present paper is an analysis of unemployment among farm wageworkers based on data from the 1937 Census of Unemployment, Bureau of Agricultural Economics employment estimates and other Census data. The Census of Unemployment taken in November of 1937 gives data on total and partial unemployment by occupational classes. These data provide a base for the determination of the total number of unemployed farm laborers in the U.S. at that time. The data, however, require definite appraisal before they can be used intelligently in any analysis. In making its estimates the Bureau of Agricultural Economics, like the Census, classified croppers as farm operators rather than wageworkers and they are therefore not included in their figures. On the other hand, it is quite possible that many croppers, tenants, and even owners designated themselves as unemployed laborers when reporting for the Census of Unemployment. It should be noted, however, that in classifying the returns, an attempt was made to separate the unemployed farm "owners" and "tenants" from laborers as such insofar as possible. Also, a category for "new workers" was set up to include those who had not yet chosen an occupation.

This paper uses a first-order autoregressive scheme to investigate the effects of initial conditions in a simulation on the estimation of the population mean of a process of interest. The effects are measured by bias and variance. The results show that the elimination of observations near the beginning of the simulation reduces bias, as intended, but increases the variance, sometimes significantly. [ABSTRACT FROM AUTHOR]

Various statistical techniques have been employed in 'activation analysis' in order to provide a better means of estimating the amounts of various pure chemical elements contained in an unknown mixture. In particular, the method of least squares has been employed extensively. However, for the most part, the usual least squares applications in activation analysis have utilized the ordinary matrix model Y=XΒ+e, under the 'error' assumptions (a) zero means, (b) variances proportional to Y, and (c) zero covariances. In addition to the fact that assumptions (b) and (c) may lead to erroneous results, the usual applications allow only point estimation, with no provision for confidence intervals and tests for model goodness of fit. Further, the usual applications fail to eliminate the drawback that negative coefficients are sometimes obtained. The present paper sets forth an iterative quadratic programming estimation procedure that not only eliminates the necessity for assumptions (b) and (c), but also alleviates the other above mentioned difficulties. [ABSTRACT FROM AUTHOR]

This paper takes the notion of Markovian dependence, so well-known in the study of stochastic processes, and uses it in a study of utility theory for sequential processes. Markovian dependence in the utility sense is defined on the basis of indifference between special types of gambles for several sequential processes. Theorems that state how the basic utility function may be broken up into an additive form under Markovian dependence are presented. In addition, the notion of stationary transition value mechanisms is explored in the context of completely homogeneous sequential decision processes. [ABSTRACT FROM AUTHOR]

Sampling errors are generally a function of two factors the time spent making an observation, and the total number of observations In addition, if sampling error costs are not symmetrically distributed about the true value, there is a problem as to whether the sampling mean should be used as a basis for making a decision, or if a biased estimate should be used A general model is developed in this paper for the total expected cost of a sampling procedure as a function of the sample size, observation time per sample unit, and the use of a biased estimate The general model is then applied to a specific situation to illustrate the application of the model A method is also given for evaluating the observational variance as a function of observation time [ABSTRACT FROM AUTHOR]

Copyright of Demography (Springer Nature) is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This article focuses on estimation of the vintage Cobb-Douglas production function for the United States for the period 1900-1960. It is shown in this paper that for the Cobb-Douglas vintage production function an identification problem arises that may cause serious biases in the estimated parameters if conditional estimation techniques are used with the wrong values of the parameters that are given. A further disquieting aspect of this evidence is that sometimes the parameter that is given is the rate of embodied technical progress which is usually the parameter through which the embodied hypothesis is expressed. In these cases no standard error may be attached to the rate of embodied technical progress and so no direct test of the embodiment hypothesis may be made. In this paper an attempt is made to obtain parameters of the vintage production functions and their standard errors using nonlinear estimation methods. Although the estimates derived are not completely free from conditioning assumptions they do indicate that once cyclical movements in output are adequately treated their evidence alone is not sufficient to support the embodiment hypothesis.

The paper deals with two parametric control policies for a single service facility when the arrivals are distributed as Poisson and the service durations have a general distribution. The N-policy is to turn on the server (i. e., open the service channel for service) when the queue size reaches the number N and turn him off when the system is empty. The D-policy is to turn on the server when the total work to be done reaches the value D instead. The optimum policies are compared for both the policies when the costs assumed are linear. It is shown that for constant service the optimal policies are equivalent and for exponential service the D-policy is not superior to the N-policy. [ABSTRACT FROM AUTHOR]

In this paper, the sampling experiment approach is used to evaluate the performance of alternative estimators that may be employed to estimate the transition matrix for a Markov probability model when only the aggregated data, reflecting the proportion of the sample in each state over a sequence of trials, are known. In addition, the experiments provide some initial information relative to the sampling properties of restricted estimators when time series data are used. [ABSTRACT FROM AUTHOR]

Exponential forecasting or smoothing models are presented which take into account all combinations of trend and cyclical effects in additive and multiplicative form. Although other authors have hinted that the proposed models existed, no one has ever presented them in comprehensive form. This paper presents the nine possible models in graphical form and summarizes them by one summary formula. [ABSTRACT FROM AUTHOR]

This paper reports the findings of the study of maintenance policies for the IBM 1620 system installed at the university's computing center. Three Maintenance policies were investigated by studying the operating characteristics of the system's two functional units, IBM 1620 Processor and IBM 1622 Card-Punch, covering the period of twenty-nine months. Cost minimization approach is used to determine the optimum policy among three alternatives. These three alternatives are: 1) repairs only; 2) scheduled maintenance at a time interval of t hours of operation without failure; 3) performing maintenance procedures at t, 2t, 3t, … regardless of intervening repairs. The problems of gathering information and the condition of optimum for the alternatives 2 and 3 are discussed. The empirical result of this study is in favor of alternative 1 for servicing both functional units, 1622 and 1620. This paper reports the findings of the study of maintenance policies for the IBM 1620 system installed at the university's computing center. Three Maintenance policies were investigated by studying the operating characteristics of the system's two functional units, IBM 1620 Processor and IBM 1622 Card-Punch, covering the period of twenty-nine months. Cost minimization approach is used to determine the optimum policy among three alternatives. These three alternatives are: 1) repairs only; 2) scheduled maintenance at a time interval of t hours of operation without failure; 3) performing maintenance procedures at t, 2t, 3t, … regardless of intervening repairs. The problems of gathering information and the condition of optimum for the alternatives 2 and 3 are discussed. The empirical result of this study is in favor of alternative 1 for servicing both functional units, 1622 and 1620. [ABSTRACT FROM AUTHOR]

This paper presents a case study in the application of some statistical theory, and a mathematical model, to an actual business problem. The problem was to determine the pattern of mortality of subscriptions to a daily newspaper, and thereby to ascertain the average life of such subscriptions. The method of solution, herewith indicated, involved the collection of data from a probability sample of subscribers to the newspaper, and use of these data to construct a Markov chain. [ABSTRACT FROM AUTHOR]

This paper presents some results of an analysis of time estimating behavior on critical path networks used in large scale development projects. The general results appear to confirm the validity of the tentative conclusions previously reported by King and Wilson. The objective of the historical analysis is to test the potential of adjustment models based on historical estimating behavior. If such models can be developed, the utility of critical path techniques should be greatly enhanced. [ABSTRACT FROM AUTHOR]

This paper presents a forecasting technique which attempts to combine the advantages of both time series analysis and multiple regression. In this two-stage technique, an exponentially smoothed moving average model is used to forecast values of the dependent variable and/or selected independent variables as desired. These forecasts, along with data for other (lagged) independent variables, are then used as inputs to a multiple regression program. The observations are selected sequentially by the regression model so that each equation is based only upon data which would have been available at the time of the forecast, and the coefficients of the equation are updated as new information becomes available. The final section of the paper describes a successful application of the two-stage model to a demand deposit forecasting problem. [ABSTRACT FROM AUTHOR]

In PERT-type networks, where activity times are random variables, the expected duration of the total project can be approximated by first substituting the expected values of the individual activities, and then evaluating the length of the critical path. This paper develops two improved estimates. Both estimates approach the true expected duration from below, i.e., they are both optimistic estimates. [ABSTRACT FROM AUTHOR]

The article seeks to examine the results of the empirical research reported in the two frequency-domain studies and to keep the discussion open by explaining further about some of the econometric aspects of estimation from the data that has been aggregated over time, since aggregation may bring about a certain amount of bias on its own. In order to determine the effect of time aggregation, the current research paper will examine the distributed lag relationship between long-term and short-term interest rates for various digitizing intervals over the same amount of time.

The article offers a reply from the authors of the paper "The Markets for Housing and Housing Services" to Craig Swan, who wrote a review of their work. The authors review Swan's comments, including his criticism of their treatment of productivity change and his belief that their model is inappropriate and their estimation procedure is incorrect, resulting in no value to their evidence. In order to address the issues raised about the model, the authors retested the propositions in a way that stays away from Swan's criticisms. The tests and the evidence are provided.

This paper presents the derivation of formulae for estimating fraction defective for a process from either continuous production or discrete lots. The estimators derived are the best linear unbiased estimators (BLUE). Also presented are the variances of the estimators. [ABSTRACT FROM AUTHOR]

Investigates the accuracy of comparative estimating. Examination of two different methods of time interval selection; Emphasis on planner estimation error; Implications for managerial decision making.

The article examines the effects of applying price-level adjustments where uncertainty exists by using estimation theory to examine the implementation of price-level adjustments. Estimation theory explains how accountants relate the financial events of a firm in a single and multiasset case, and the results imply that an adjustment is needed for book values for changes in price level estimates of the expected overall and period rates of return. The magnitude of these biases depends on the precise changes in the index of price indexes used. As long as period rates are used as estimators of overall rates, the adjustments of book values for price-level changes cause biased predictors. The author considers a case when "double counting" is shown and stochastic analysis is used with the estimation theory.

Two equations have been obtained using regression analysis techniques which can be applied to determine storage space requirements with acceptable accuracy and minimum effort. By defining all items by means of a common parameter--packing factor--it was possible to ignore the individual weights of each item, yet still load the transport and storage unit to some practical load limits. The method used in this paper is general and can be applied to similar problems with different boundary conditions. [ABSTRACT FROM AUTHOR]

This article discusses the estimation theory in financial accounting, considering the single-asset situation which is the norm of most modern accounting theory. The authors argue that estimation theory is a practical model for handling multi-asset estimation problems, and they discuss the estimating horizon and allocation schemes in a decision-theory framework. The author discuss the problem with the estimating theory--predicting the future cash flows and internal rate of return, and consider the estimation procedure by assuming certainty about the future.

The article focuses on the application of statistical sampling to auditing with auxiliary information estimators, and explores the role of the auditor in creating sample surveys when the auditor possesses more information about his sample than the social scientist does about his. The article examines the statistical estimators which use all available auxiliary information, and demonstrates how the standard distribution theory is often not applicable to statistical inference. The article further demonstrates how new sampling methods may be necessary for statistical sampling in auditing.

The article discusses the estimation problem in financial accounting. In a previously published article R. Brief and J. Owen restructured the allocation problem in financial accounting as part of a more general estimation problem. The result was a solution to the traditional dilemma with respect to the jointness of revenues and costs over a fixed time horizon. Accountants can use a statistical estimation theory to estimate values for the parameters of financial accounting in allocation situations. The purpose of the Brief-Owen allocation model is to create a new emphasis and direction in the various accounting procedures involving the jointness of costs and revenues over time.

This article focuses on the development of a theory of estimation in financial accounting. The author explains the challenge that comes along with allocating costs with varying periods of time. Without a consensus on this matter, there is no established way to measure performance. The author explains that various accounting methods are measured through the use of certainty models. The author is concerned because these certainty models are used in scenarios in which future outcomes and financial situations that cannot be assumed without a level of inaccuracy.

The article presents commentary and extensions to the dangers of multicollinearity in multiple regression equations by t tests initially asserted within the research of Bruce Cohen and Damodar Gujarati in their report "The Student's t Test in Multiple Regression Under Simple Collinearity," from the September 1970 issue. The particular faults within the mechanical t test specifications are emphasized and criticisms are given regarding a lack of diagnostic methods to detect the error.

The article focuses on the familiar problem of the identifiability of parameters of linear simultaneous equation systems subject to linear constraints on the parameters of the equations. The approach taken on this paper is based on what statisticians refer to as the "theory of estimable functions." The discussion in the paper is carried out at the level of the whole system of equations and all the results are stated in a form applicable to linear restrictions; that is to say they are not confined to restrictions on the parameters of a particular equation.