scholarly journals Copula-Based Dependence Measures For Piecewise Monotonicity

2017 ◽  
Vol 5 (1) ◽  
pp. 198-220 ◽  
Author(s):  
Eckhard Liebscher
Keyword(s):  
Regression Analysis ◽  
Convergence Rate ◽  
Asymptotic Normality ◽  
Asymptotic Behaviour ◽  
Data Points ◽  
Association Coefficients ◽  
Dependence Measures

Abstract The aim of the present paper is to develop and examine association coefficients which can be helpfully applied in the framework of regression analysis. The construction of the coeffiecients is connected with the well-known Spearman coeffiecient and extensions of it (see Liebscher [5]). The proposed coeffiecient measures the discrepancy between the data points and a function which is strictly increasing on one interval and strictly decreasing in the remaining domain.We prove statements about the asymptotic behaviour of the estimated coeffiecient (convergence rate, asymptotic normality).

Limit theorems for numbers satisfying a class of triangular arrays

2021 ◽  
Vol 56 (2) ◽  
pp. 195-223
Author(s):  
Igoris Belovas ◽  
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Convergence Rate ◽  
Asymptotic Normality ◽  
Limit Theorems ◽  
Limiting Distribution ◽  
Linear Recurrence ◽  
Triangular Arrays ◽  
Exponential Generating Function ◽  
Analytical Expressions

The paper extends the investigations of limit theorems for numbers satisfying a class of triangular arrays, defined by a bivariate linear recurrence with bivariate linear coefficients. We obtain the partial differential equation and special analytical expressions for the numbers using a semi-exponential generating function. We apply the results to prove the asymptotic normality of special classes of the numbers and specify the convergence rate to the limiting distribution. We demonstrate that the limiting distribution is not always Gaussian.

scholarly journals ON INTERCEPT ESTIMATION IN THE SAMPLE SELECTION MODEL

2002 ◽  
Vol 18 (1) ◽  
pp. 40-50 ◽  
Author(s):  
Marcia M.A. Schafgans ◽  
Victoria Zinde-Walsh
Keyword(s):  
Convergence Rate ◽  
Asymptotic Normality ◽  
Sample Selection ◽  
American Economic Review ◽  
Selection Model ◽  
Sample Selection Model ◽  
Consistency And Asymptotic Normality

We provide a proof of the consistency and asymptotic normality of the estimator suggested by Heckman (1990, American Economic Review 80, 313–318) for the intercept of a semiparametrically estimated sample selection model. The estimator is based on “identification at infinity,” which leads to nonstandard convergence rate.

scholarly journals Copula-based dependence measures

2014 ◽  
Vol 2 (1) ◽  
Author(s):  
Eckhard Liebscher
Keyword(s):  
Asymptotic Normality ◽  
Gini Coefficient ◽  
The Gini Coefficient ◽  
Close Relationship ◽  
Dependence Measures

AbstractThe aim of the present paper is to examine two wide classes of dependence coefficients including several well-known coefficients, for example Spearman’s ρ, Spearman’s footrule, and the Gini coefficient. There is a close relationship between the two classes: The second class is obtained by a symmetrisation of the coefficients in the former class. The coefficients of the first class describe the deviation from monotonically increasing dependence. The construction of the coefficients can be explained by geometric arguments. We introduce estimators of the dependence coefficients and prove their asymptotic normality.

scholarly journals A central limit theorem for numbers satisfying a class of triangular arrays associated with Hermite polynomials

2021 ◽  
Vol 61 ◽  
pp. 1-7
Author(s):  
Igoris Belovas
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Convergence Rate ◽  
Asymptotic Normality ◽  
Central Limit ◽  
Generating Function ◽  
Limit Theorems ◽  
Hermite Polynomials ◽  
Triangular Arrays ◽  
Analytical Expressions

The paper extends the investigations of limit theorems for numbers satisfying a class of triangular arrays. We obtain analytical expressions for the semiexponential generating function the numbers, associated with Hermite polynomials. We apply the results to prove the asymptotic normality of the numbers and specify the convergence rate to the limiting distribution.    

Recursive Identification of Hammerstein Systems: Convergence Rate and Asymptotic Normality

2017 ◽  
Vol 62 (7) ◽  
pp. 3277-3292 ◽  
Author(s):  
Biqiang Mu ◽  
Han-Fu Chen ◽  
Le Yi Wang ◽  
George Yin ◽  
Wei Xing Zheng
Keyword(s):  
Convergence Rate ◽  
Asymptotic Normality ◽  
Recursive Identification ◽  
Hammerstein Systems

scholarly journals Time Trend and prediction of Grade 2 Disability among new cases of leprosy in Nepal: A Statistical Modelling

2014 ◽  
Vol 4 (3) ◽  
pp. 378-383 ◽  
Author(s):  
Brijesh Sathian ◽  
Ajay Kumar ◽  
Jayadevan Sreedharan ◽  
Indrajit Banerjee ◽  
Bedanta Roy ◽  
...  
Keyword(s):  
Regression Analysis ◽  
Time Trends ◽  
Time Trend ◽  
Constant Term ◽  
Statistical Modelling ◽  
Inverse Model ◽  
Descriptive Statistics ◽  
Health Ministry ◽  
Data Points ◽  
Best Fit

Background  It is estimated that globally there are around 2 million people with grade 2 disabilities attributed to leprosy. Objective of the study was to find out the time trends of Grade 2 Disability among the new cases of Leprosy in Nepal. Materials and Methods A retrospective study was carried out on the data collected from the Health ministry records of Nepal, between 2009 and 2013. The annual reported numbers of Grade 2 Disability among new cases of leprosy plotted in y-axis against the corresponding year in the x-axis. Curve fitting, also known as regression analysis, was used to find the "best fit" line or curve for a series of data points. Linear, Logarithmic, Inverse, Quadratic, and Cubic were chosen to fit to the obtained curve. Descriptive statistics and statistical modelling were used for the analysis and forecasting of data. Results Including the constant term from the equation, the inverse model was the best fit, for the forecasting of the Grade 2 Disability among new cases of leprosy in Nepal [R2=0.739, p=0.062]. Using inverse model, it is estimated that 78 with CI [0, 170] of Grade 2 Disability among new cases of leprosy can be expected in Nepal by the year 2020. Conclusion Our study proves Inverse model is the best fit for epidemiological modelling of Grade 2 Disability among the new cases of Leprosy in Nepal. Prevention of disabilities should begin with diagnosing leprosy.DOI: http://dx.doi.org/10.3126/nje.v4i3.10668 Nepal Journal of Epidemiology 2014; 4(3): 378-383

The Influence of Capacity on Prison Population: A Critical Review of Some Recent Evidence

1983 ◽  
Vol 29 (1) ◽  
pp. 1-51 ◽  
Author(s):  
Alfred Blumstein ◽  
Jacqueline Cohen ◽  
William Gooding
Keyword(s):  
Regression Analysis ◽  
Critical Review ◽  
Prison Population ◽  
Regression Equation ◽  
Coefficient Estimate ◽  
Widespread Acceptance ◽  
Data Points ◽  
Prison Capacity ◽  
Computation Error ◽  
Simple Regression

A recent study by Abt Associates (Abt/Carlson) purported to show that increments to prison capacity would lead to growth in prison population to fill that added capacity two years later. That finding has rapidly attained broad circulation and widespread acceptance. The original conclusion was based on a coefficient of 1.02 in a simple regression equation that represents change in prison population as a function of lagged changes in prison population and capacity. Reanalysis of the data shows that the original estimates resulted from a computation error; when that error is corrected the coefficient estimate is reduced to .264. Furthermore, two data points were particularly influential in the regression analysis, and omitting them results in a coefficient of .095 which is not statistic ally significant. Thus, the coefficient on which the original conclusion was based is eliminated in importance.

Determining School Effectiveness Following a Regression Analysis

1977 ◽  
Vol 2 (1) ◽  
pp. 27-39 ◽  
Author(s):  
John J. Convey
Keyword(s):  
Regression Analysis ◽  
School Effectiveness ◽  
Relative Effectiveness ◽  
Confidence Bands ◽  
Multivariate Normal ◽  
Conservative Strategy ◽  
Confidence Levels ◽  
Hypothetical Data ◽  
Data Points ◽  
The Mean

Three methods that can be used subsequent to a regression analysis to determine the relative effectiveness of schools are Dyer’s performance indicators (PIs), Scheffé’s hyperbolic confidence bands, and Gafarian’s linear confidence bands. The purpose of this paper is to investigate the relative usefulness of the three methods under various conditions. The three methods were applied to hypothetical data from 54 schools randomly generated from a multivariate normal distribution using parameters from previous studies. Data points having PIs of 1 and 5 generally fell outside of the Scheffé confidence bands. The linear confidence bands were much wider than the Scheffé bands near the mean and slightly narrower at the extremes. The results indicated that extreme PIs seem to be appropriate for identifying schools which are achieving above and below expectation. Fine discriminations using PIs as defined by Dyer may not be warranted. Gafarian bands tend to be so wide as to limit their applicability to most settings. The choice of a particular technique to determine school effectiveness is dictated somewhat by the intent of the investigator. A conservative strategy would dictate employing the Scheffé technique with high confidence levels or adopting a decision rule of a difference of four PIs between two schools. Use of lower confidence levels or less stringent differences in PIs would result in a more liberal strategy.

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