摘要:

Past work on prediction formulas for time series, e.g., that of Wiener and Yaglom, has used powerful and general spectral techniques that result in integral formulas difficult to evaluate in practical cases. In this paper the more direct, less powerful approach developed by Muth produces useful and specific results for a broad class of cases that includes virtually every case of a higher order Markov process observed with error. The results provide plausible theoretical support for the expectations model widely and successfully applied by economists, although the distributions of the estimators of the prediction parameters (when the latter are unknown) are still unknown. The two-hundred-year series of sunspot data provides an illustrative application of the theoretical results, which bears comparison with the previous analyses of these data by Yule and others.

ISSN:0162-1459    

DOI:10.1080/01621459.1965.10480781

出版商:Taylor & Francis Group    

年代:1965

数据来源: Taylor

摘要:

This paper presents theorems which can be used to obtain sufficient and minimal sufficient statistics for the two-way classification mixed model design. Using the general linear hypothesis modelY=Xτ+Zβ+e the authors prove that the dimension of a minimal sufficient statistic is a function of the ranks of certain submatrices ofZ×X. Minimal sufficient statistics are presented in tabular form for some two-way classification designs and some of the distributional properties are given.

ISSN:0162-1459    

DOI:10.1080/01621459.1965.10480782

出版商:Taylor & Francis Group    

年代:1965

数据来源: Taylor

摘要:

The principal part of this paper is devoted to the study of the distribution and density functions of the ratio of two normal random variables. It gives several representations of the distribution function in terms of the vivariate normal distribution and Nicholson'sVfunction, both of which have been extensively studied, and for which tables and computational procedures are readily available. One of these representations leads to an easy derivation of the density function in terms of the Cauchy density and the normal density and integral. A number of graphs of the possible shapes of the density are given, together with an indication of when the density is unimodal or bimodal.

ISSN:0162-1459    

DOI:10.1080/01621459.1965.10480783

出版商:Taylor & Francis Group    

年代:1965

数据来源: Taylor

摘要:

Allocation of experimental data points is considered in order to provide efficient prediction of the dependent variable in simple linear regression. The region of experimental points is taken such that it need not coincide with the region for prediction where the regression is linear. The allocation which minimizes the maximum variance for a predicted value of the dependent variable is obtained. The allocation of experimental data points which minimizes the average variance of predicted values, occurring according to a density function in the region of prediction, is derived. The relative efficiency of balanced allocation (one-half of the data points at each end of the experimental region) to minimax or minimum average variance allocation is about 90 percent for prediction near the ends of the experimental region with small samples.

ISSN:0162-1459    

DOI:10.1080/01621459.1965.10480784

出版商:Taylor & Francis Group    

年代:1965

数据来源: Taylor

摘要:

In the classification of the elements in a binomial population, there is in many cases a chance of misclassifying an item. When an item in a sample from a binomial population is misclassified, it causes a bias, independent of the standard error, in the estimate of the population parameterP. This paper analyzes this bias when each of two interviewers independently classify the items in a single sample. Upper and lower bounds for the bias are derived.

ISSN:0162-1459    

DOI:10.1080/01621459.1965.10480785

出版商:Taylor & Francis Group    

年代:1965

数据来源: Taylor

摘要:

A common problem in many areas is to achieve a combination of control variables which will simultaneously maximize all of the responses which are functions of the control variables. The fact that in general we can not simultaneously maximize all of the responses has led to the formulation of compromise solutions to this vector maximum problem. A point in the control variable space is better than a second point if each response at the first point is greater than or equal to the corresponding response at the second point. If a point is such that there is no better point, it is said to be admissible, or efficient. A set of points is complete if given any point not in the set there is a point in the set which is better. In this paper this formulation is used to consider the allocation of sample size to several strata when there are several characteristics of interest.

ISSN:0162-1459    

DOI:10.1080/01621459.1965.10480786

出版商:Taylor & Francis Group    

年代:1965

数据来源: Taylor

摘要:

Regression upon principal components of the percentage points of the income and education distributions for 1950 census tracts in the city of Chicago led to the estimation of “beta coefficient profiles” for television receiver and refrigerator ownership, for central heating system usage, and for a measure of dwelling unit overcrowding. The betas are standardized coefficients of regression of a dependent variable upon the proportions of families in the classes of the marginal income and education distributions. They measure the relative contribution of families in these classes to the over-all per cent saturation of the dependent variable in the tract. The coefficients were estimated by techniques developed in the first portion of the paper; estimation by classical regression methods would have been impossible because of multicollinearity. The empirical results are in substantial agreement with findings from regressions of the dependent variables upon the mean values of income and education, and their squares. The statistical devices appear to be useful in exploratory empirical research.

ISSN:0162-1459    

DOI:10.1080/01621459.1965.10480787

出版商:Taylor & Francis Group    

年代:1965

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1965.10480788

出版商:Taylor & Francis Group    

年代:1965

数据来源: Taylor

摘要:

Usually auxiliary information based on just one variate is used to improve the precision of estimators of population totals, means, etc. In this paper a method is proposed of using information on several variates to achieve higher precision. The technique of difference estimation is employed throughout. It is shown that the variances of difference estimators are comparable to those of ratio estimators. The results are extended to double sampling procedures and sampling over two occasions.

ISSN:0162-1459    

DOI:10.1080/01621459.1965.10480789

出版商:Taylor & Francis Group    

年代:1965

数据来源: Taylor

摘要:

Approximate expressions are given for the variance of two commonly used variance estimators when two units are selected from a stratum systematically with probability proportionate to size. The stability of the variance estimators is examined with the help of an example.

ISSN:0162-1459    

DOI:10.1080/01621459.1965.10480790

出版商:Taylor & Francis Group    

年代:1965

数据来源: Taylor