中国要素替代弹性估计

要素替代弹性是经济研究中的重要参数,对经济增长和要素分配研究至关重要。本文基于一般要素增强型CES生产函数,利用1978-2011年省级面板数据,以变系数面板模型估计我国替代弹性时间序列。主要发现为：我国替代弹性明显小于1（0.23-0.55之间）,改革时期基本呈上升趋势;此时劳动增强型技术表现出资本偏向,构成近期我国劳动份额持续下降的重要原因。最后,对该领域未来发展方向进行展望。     

Unverfälschte Variablenprüfpläne für exponentialverteilte Merkmale mit zweiseitigen Toleranzgrenzen

As a well known fact the standard X²-procedures (e.g. confidence intervals for σ², tests of the hypothesis H:″σ=σ_o″ in the case of normal population with variance σ²) are biased. We refer to some useful tables which enable in the case of normal population to procure unbiased confidence intervals or confidence intervals with minimal length for σ², control charts for σ with minimal distance between the limit lines, and unbiased tests of H:″σ=σ_o″. Another important application yields—as main result of the present paper—unbiased sampling plans in the case of an exponential distributed attribute with upper and lower specification limit (two-way-protection). It turns out to be possible, also in the case of exponential distribution, to reduce the sample size by using incomplete prior information about the proportion p of defectives.     

PROPERTIES OF THE PATTERNED VECH OPERATOR

The vec operator arranges the columns of a matrix one below the other. When the matrix is symmetric such elements are not distinct but an extraction of only the distinct elements on or below the diagonal forms the operation denoted by vech. For other types of patterned matrices a ‘patterned vech’ operator is defined. The transformations from vech to vec are not uniquely defined. Here we examine properties of linear transformations which overcome the lack of uniqueness and develop properties of such linear transformations.     

Choice of best linear in the guass-markoff model with a singular dispersion matrix

In this paper we obtain the complete class of representations and useful subclasses of MV-UB-LE and MV-MB-LE (minimum variance unbiased and minimum bias linear estimators) of linear parametric functions in the Gauss-Markoff model (Y,Xβ, σ ²V) when V is possibly singular.     

Optimality of blue's in a general linear model with incorrect design matrix

We consider the Gauss-Markoff model (Y,X₀β,σ²V) and provide solutions to the following problem: What is the class of all models (Y,Xβ,σ²V) such that a specific linear representation/some linear representation/every linear representation of the BLUE of every estimable parametric functional p'β under (Y,X₀β,σ²V) is (a) an unbiased estimator, (b) a BLUE, (c) a linear minimum bias estimator and (d) best linear minimum bias estimator of p'β under (Y,Xβ,σ²V)? We also analyse the above problems, when attention is restricted to a subclass of estimable parametric functionals.     

A Bayesian Time Series Model of Multiple Structural Changes in Level,Trend, and Variance

We investigate whether seasonal-adjustment procedures are, at least approximately, linear data transformations. This question was initially addressed by Young and is important with respect to many issues including estimation of regression models with seasonally adjusted data. We focus on the X-11 program and rely on simulation evidence, involving linear unobserved component autoregressive integrated moving average models. We define a set of properties for the adequacy of a linear approximation to a seasonal-adjustment filter. These properties are examined through statistical tests. Next, we study the effect of X-11 seasonal adjustment on regression statistics assessing the statistical significance of the relationship between economic variables. Several empirical results involving economic data are also reported.     

A REGRESSION CHARACTERISATION OF THE MEIXNER HYPERGEOMETRIC DISTRIBUTION

The paper describes the Meixner hypergeometric distribution, characterised by properties of the regression of products of linear transformations of random variables with respect to residuals.     

Estimation of a standard measuring error by repeated measurements and sortings

A sorting-and-measuring machine (SMM) measures and sorts (classifies) on-line produced items into several groups according to their size. The measuring devices of the SMM perceive the actual item size with a random error ε and classify the item as being smaller than b iff z+ε<b. Here ε is a normal zero-mean r.v. with unknown standard deviation σ which is the main parameter characterizing the precision and technical condition of an SMM. The paper gives the following method of estimating σ. N₀ items are measured and N₁ of them are recognized by the SMM as belonging to the group a<z≤b. These N₁ items are sorted again and N₂ of them return to this group, these are sorted again, and so on. The estimation of σ is based on the statistics N_m/N_n. Moments of the ratio statistics N_m/N_n and their distributional properties are investigated. It turns out that the expected value of N_m/N_n depends almost linearly on σ which allows us to construct ‘almost’ unbiased estimators of type $\text{σ}\text{?}{}_{\mathrm{mn}}\text{=A}\textcolor{red}{}\text{N}{}_{\mathrm{m}}\text{/N}{}_{\mathrm{n}}\text{+B}$ with good propert including robustness with respect to the distribution of item size. Convex combinations of $\text{σ}\text{?}{}_{\mathrm{mn}}$ statistics are considered to obtain an estimator with minimal variance.     

Designing and construction of tightened-normal-tightened variables sampling scheme

The tightened-normal-tightened (TNT) attributes sampling scheme was devised by Calvin (1977). In this paper, a TNT Scheme with variables sampling plan as the reference plan, designated as TNTVSS (n_σ; k_T, k_N) is introduced, where n_σ is the sample size under the reference plan, and k_T and k_N are the acceptance constants corresponding to tightened and normal plans respectively. The behaviour of OC curves of the TNTVSS (n_σ; k_T, k_N) is studied. The efficiency of TNTVSS (n_σ; k_T, k_N) with respect to smaller sample sizes has been established over the attributes scheme. The TNTVSS is matched with the TNT (n; c_N, c_T) of Vijayaraghavan and Soundararajan (1996), for the specified points on the OC curves, namely (p₁, α) and (p₂, β) and it is shown that the sample size of the variables scheme is much smaller than that of the attributes scheme. The TNT scheme with an unknown σ variables plan as the reference plan is also introduced along with the procedure of selection of the parameters. The method of designing the scheme based on the given AQL (Acceptable Quality level), α (producer's risk), LQL (Limiting Quality Level) and β (consumer's risk) is indicated. Among the class of TNTVSS which exists, for a given (p₁,α) and (p₂, β), a scheme, which will have a more steeper OC curve than that of any other scheme, is identified and given.     

Invariant properties of logistic regression model in credit scoring under monotonic transformations

Monotonic transformations of explanatory continuous variables are often used to improve the fit of the logistic regression model to the data. However, no analytic studies have been done to study the impact of such transformations. In this paper, we study invariant properties of the logistic regression model under monotonic transformations. We prove that the maximum likelihood estimates, information value, mutual information, Kolmogorov–Smirnov (KS) statistics, and lift table are all invariant under certain monotonic transformations.     

Simplified estimation of the parameters of exponential distribution from samples censored in the middle

This paper presents the small sample optimum choice of k ≤n + r₁ ? r₂ + 1) order statistics for the best linear unbiased estimates (BLUES) of the parameters μ and σ or σ alone ( μ known) when the sample is Type II censored in the middle retaining only r₁ lower and n - r₂ + 1 upper order statistics. For n = 3(1)10, k = 2(1)4, r₁ = O(1) (n?2) and r₂ = (r₁ +2) (l)n, the optimum ranks, the coefficients of the BLUEs have been presented in Table I     

On the normality of transformed beta and unit- gamma random variables

In this paper we consider properties of the logarithmic and Tukey's lambda-type transformations of random variables that follow beta or unit-gamma distributions. Beta distributions often arise as models for random proportions, and unit-gamma distributions, although not well- known, may serve the same purpose. The latter possess many properties similar to those of beta distributions. Some transformations of random variables that follow a beta distribution are considered by Johnson (1949) and Johnson and Kotz (1970,1973). These are used to obtain a -new"random variable that potentially approximately follows a normal distribution, so that practical analyses become possible. We study normality -related properties of the above transformations. This is done for the first time for unit-gamma distributions. Under the logarithmic transformation the beta and unit-gamma distributions become, respectively, the logarithmic F and generalized logistic distributions. The distributions of the transformed beta and unit-gamma distributions after application of Tukey's lambda-type transformations cannot be derived easily; however, we obtain the first four moments and expressions for the skewness and kudos is of the transformed variables. Values of skewness and kurtosis for a variety of different parameter values are calculated, and in consequence, the near (or not near) normality of the transformed variables is evaluated. Comments on the use of the various transformations are provided..     

On generalized exponential transformations for proportions

ABSTRACT

Transformation of the response is a popular method to meet the usual assumptions of statistical methods based on linear models such as ANOVA and t-test. In this paper, we introduce new families of transformations for proportions or percentage data. Most of the transformations for proportions require 0 < x < 1 (where x denotes the proportion), which is often not the case in real data. The proposed families of transformations allow x = 0 and x = 1. We study the properties of the proposed transformations, as well as the performance in achieving normality and homoscedasticity. We analyze three real data sets to empirically show how the new transformation performs in meeting the usual assumptions. A simulation study is also performed to study the behavior of new families of transformations.     

De l'unicité des estimateurs robustes en régression lorsque le paramètre d'échelle et le paramètre de la régression sont estimés simultanément

Several methods have been suggested to calculate robust M- and G-M -estimators of the regression parameter β and of the error scale parameter σ in a linear model. This paper shows that, for some data sets well known in robust statistics, the nonlinear systems of equations for the simultaneous estimation of β, with an M-estimate with a redescending ψ-function, and σ, with the residual median absolute deviation (MAD), have many solutions. This multiplicity is not caused by the possible lack of uniqueness, for redescending ψ-functions, of the solutions of the system defining β with known σ; rather, the simultaneous estimation of β and σ together creates the problem. A way to avoid these multiple solutions is to proceed in two steps. First take σ as the median absolute deviation of the residuals for a uniquely defined robust M-estimate such as Huber's Proposal 2 or the L₁-estimate. Then solve the nonlinear system for the M-estimate with σ equal to the value obtained at the first step to get the estimate of β. Analytical conditions for the uniqueness of M and G-M-estimates are also given.     

Weighted extensions of generalized cumulative residual entropy and their applications

Abstract

In this paper, we consider weighted extensions of generalized cumulative residual entropy and its dynamic(residual) version. Our results include linear transformations, stochastic ordering, bounds, aging class properties and some relationships with other reliability concepts. We also define the conditional weighted generalized cumulative residual entropy and discuss some properties of its. For these concepts, we obtain some characterization results under some assumptions. Finally, we provide an estimator of the new information measure using empirical approach. In addition, we study large sample properties of this estimator.     

Variance Reduction Using Nonlinear Controls and Transformations

Nonlinear regression-adjusted control variables are investigated for improving variance reduction in statistical and system simulations. To this end, simple control variables are piecewise sectioned and then transformed using linear and nonlinear transformations. Optimal parameters of these transformations are selected using linear or nonlinear least-squares regression algorithms. As an example, piecewise power-transformed variables are used in the estimation of the mean for the twovariable Anderson-Darling goodness-of-fit statistic W ₂ ². Substantial variance reduction over straightforward controls is obtained. These parametric transformations are compared against optimal, additive nonparametric transformations obtained by using the ACE algorithm and are shown, in comparison to the results from ACE, to be nearly optimal.     

Pitman closeness for hierarchical bayes predictors in mixed linear models

The present article considers the Pitman Closeness (PC) criterion of certain hierarchical Bayes (HB) predictors derived under a normal mixed linear models for known ratios of variance components using a uniform prior for the vector of fixed effects and some proper or improper prior on the error variance. For a generalized Euclidean error, simultaneous HB predictors of several linear combinations of vector of effects are shown to be the Pitman-closest in the frequentist sense in the class of equivariant predictors for location group of transformations. The normality assumption can be relaxed to show that these HB predictors are the Pitman-closest for location-scale group of transformations for a wider family of elliptically symmetric distributions. Also for this family, the HB predictors turn out to be Pitman-closest in the class of all linear unbiased predictors (LUPs). All these results are extended for the HB predictor of finite population mean vector in the context of finite population sampling.     

Geometric ergodicity of nonlinear autoregressive models with changing conditional variances

The authors give easy‐to‐check sufficient conditions for the geometric ergodicity and the finiteness of the moments of a random process x_t = ?(x_t‐1,…, x_t‐p) + ?_tσ(x_t‐1,…, x_t‐q) in which ?: R^p → R, σ R^q → R and (?_t) is a sequence of independent and identically distributed random variables. They deduce strong mixing properties for this class of nonlinear autoregressive models with changing conditional variances which includes, among others, the ARCH(p), the AR(p)‐ARCH(p), and the double‐threshold autoregressive models.     

Linear Transformations of Linear Mixed-Effects Models

A number of articles have discussed the way lower order polynomial and interaction terms should be handled in linear regression models. Only if all lower order terms are included in the model will the regression model be invariant with respect to coding transformations of the variables. If lower order terms are omitted, the regression model will not be well formulated. In this paper, we extend this work to examine the implications of the ordering of variables in the linear mixed-effects model. We demonstrate how linear transformations of the variables affect the model and tests of significance of fixed effects in the model. We show how the transformations modify the random effects in the model, as well as their covariance matrix and the value of the restricted log-likelihood. We suggest a variable selection strategy for the linear mixed-effects model.     

Linear Transformations and the k-Means Clustering Algorithm: Applications to Clustering Curves

Functional data can be clustered by plugging estimated regression coefficients from individual curves into the k-means algorithm. Clustering results can differ depending on how the curves are fit to the data. Estimating curves using different sets of basis functions corresponds to different linear transformations of the data. k-means clustering is not invariant to linear transformations of the data. The optimal linear transformation for clustering will stretch the distribution so that the primary direction of variability aligns with actual differences in the clusters. It is shown that clustering the raw data will often give results similar to clustering regression coefficients obtained using an orthogonal design matrix. Clustering functional data using an L(2) metric on function space can be achieved by clustering a suitable linear transformation of the regression coefficients. An example where depressed individuals are treated with an antidepressant is used for illustration.