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A Note on the Small-Sample Power Functions for Nonparametric Tests of Location in the Double Exponential Family
双指数分布族中非参数位置检验的小样本功效
Eight nonparametric tests are examined in a small-sample setting. Their power functions are compared with the locally most powerful (LMP) linear rank test, primarily to see over which range the LMP test retains good power. All tests are two-sample tests, the populations are governed by the double exponential distribution, and the sample sizes are m = 5, n = 5, and m = 5, n = 4. The LMP test performs uniformly well, even under nonlocal alternatives, while its asymptotically…
Likelihood Methods and Nonparametric Tests
似然方法与非参数检验
Standard techniques of nonparametric statistics are related to likelihood procedures. In particular, rank tests and permutation tests in the regression problem are shown to be directly related to score function tests based on marginal and conditional likelihoods, respectively. The problem of estimating a population percentile is also examined from the viewpoint of marginal likelihood. These calculations tend to bring nonparametric procedures more closely in line with…
Size and Power Assessments of Tests of Hypotheses on Survival Parameters
生存模型参数假设检验的尺寸与功效评估
Assuming the time-dependent component of Cox's form of the hazard function to be specified by the constant, Weibull, and Gompertz, produces three failure density models. Using simulation techniques, size and power comparisons between tests of hypotheses (concerning the regression parameters) arising from Cox's nonparametric method and tests arising from the three parametric models are made. The test statistics arise from the likelihood ratio criterion and the asymptotic…
Estimating the Order of Autoregressive Models: The Max χ 2 Method
Evolution Times of Languages
语言分化时间的统计估计
A problem in anthropological linguistics is to reconstruct, from present-day linguistic data, a family tree depicting the ancestry of a family of languages. There are two parts to the problem. The first is to construct the family tree showing the sequence of language separations; this is analogous to classifying biological species by degree of similarity. The second is to estimate when the separations occurred. In this article, a stochastic model is given for the process of…
Small-Area Estimation with Application to Unemployment and Housing Estimates
小区域估计及其在失业与住房估计中的应用
The purpose of this study is to investigate methodologies for constructing intercensal estimates of various characteristics of the population for small areas. The proposed methodology is illustrated mainly in the context of unemployment estimates, with one section utilizing dilapidated housing estimates. Alternative synthetic estimates of unemployment based on the 1970 Census 20-percent sample are investigated and their relative error is analyzed. The reliability of the…
Essays in Economics, Volume 2: Consumption and Econometrics.
Maximum Likelihood Estimates of the Parameters of the Cauchy Distribution for Samples of Size 3 and 4
样本量为 3 和 4 时柯西分布参数的最大似然估计
Expressions are given for the joint maximum likelihood estimates of the location and scale parameters of a Cauchy distribution based on samples of size 3 and 4.
A Note on the Efficient Estimation of the Linear Expenditure System
线性支出系统高效估计札记
An efficient method of estimating the linear expenditure system (LES) by maximum likelihood is introduced. A test for insuring that parameter estimates obtained by numerical maximization satisfy the first-order conditions is given. In some experiments the new method of estimating the LES is compared to the more conventional method of estimation and is found to use significantly less computer time than the conventional method.