The parameter estimation problem for an economic model called Constantinides-Ingersoll model is investigated based on discrete observations. Euler-Maruyama scheme and iterative method are applied to getting the joint ...The parameter estimation problem for an economic model called Constantinides-Ingersoll model is investigated based on discrete observations. Euler-Maruyama scheme and iterative method are applied to getting the joint conditional probability density function. The maximum likelihood technique is employed for obtaining the parameter estimators and the explicit expressions of the estimation error are given. The strong consistency properties of the estimators are proved by using the law of large numbers for martingales and the strong law of large numbers. The asymptotic normality of the estimation error for the diffusion parameter is obtained with the help of the strong law of large numbers and central-limit theorem. The simulation for the absolute error between estimators and true values is given and the hypothesis testing is made to verify the effectiveness of the estimators.展开更多
The normal distribution, which has a symmetric and middle-tailed profile, is one of the most important distributions in probability theory, parametric inference, and description of quantitative variables. However, the...The normal distribution, which has a symmetric and middle-tailed profile, is one of the most important distributions in probability theory, parametric inference, and description of quantitative variables. However, there are many non-normal distributions and knowledge of a non-zero bias allows their identification and decision making regarding the use of techniques and corrections. Pearson’s skewness coefficient defined as the standardized signed distance from the arithmetic mean to the median is very simple to calculate and clear to interpret from the normal distribution model, making it an excellent measure to evaluate this assumption, complemented with the visual inspection by means of a histogram and a box-and-whisker plot. From its variant without tripling the numerator or Yule’s skewness coefficient, the objective of this methodological article is to facilitate the use of this latter measure, presenting how to obtain asymptotic and bootstrap confidence intervals for its interpretation. Not only are the formulas shown, but they are applied with an example using R program. A general rule of interpretation of ∓0.1 has been suggested, but this can only become relevant when contextualized in relation to sample size and a measure of skewness with a population or parametric value of zero. For this purpose, intervals with confidence levels of 90%, 95% and 99% were estimated with 10,000 draws at random with replacement from 57 normally distributed samples-population with different sample sizes. The article closes with suggestions for the use of this measure of skewness.展开更多
基金National Nature Science Foundation of China(No.60974030)the Chinese Universities Scientific Fund(No.CUSF-DH-D-2014059)
文摘The parameter estimation problem for an economic model called Constantinides-Ingersoll model is investigated based on discrete observations. Euler-Maruyama scheme and iterative method are applied to getting the joint conditional probability density function. The maximum likelihood technique is employed for obtaining the parameter estimators and the explicit expressions of the estimation error are given. The strong consistency properties of the estimators are proved by using the law of large numbers for martingales and the strong law of large numbers. The asymptotic normality of the estimation error for the diffusion parameter is obtained with the help of the strong law of large numbers and central-limit theorem. The simulation for the absolute error between estimators and true values is given and the hypothesis testing is made to verify the effectiveness of the estimators.
文摘The normal distribution, which has a symmetric and middle-tailed profile, is one of the most important distributions in probability theory, parametric inference, and description of quantitative variables. However, there are many non-normal distributions and knowledge of a non-zero bias allows their identification and decision making regarding the use of techniques and corrections. Pearson’s skewness coefficient defined as the standardized signed distance from the arithmetic mean to the median is very simple to calculate and clear to interpret from the normal distribution model, making it an excellent measure to evaluate this assumption, complemented with the visual inspection by means of a histogram and a box-and-whisker plot. From its variant without tripling the numerator or Yule’s skewness coefficient, the objective of this methodological article is to facilitate the use of this latter measure, presenting how to obtain asymptotic and bootstrap confidence intervals for its interpretation. Not only are the formulas shown, but they are applied with an example using R program. A general rule of interpretation of ∓0.1 has been suggested, but this can only become relevant when contextualized in relation to sample size and a measure of skewness with a population or parametric value of zero. For this purpose, intervals with confidence levels of 90%, 95% and 99% were estimated with 10,000 draws at random with replacement from 57 normally distributed samples-population with different sample sizes. The article closes with suggestions for the use of this measure of skewness.
