In this paper, the problem of Nonparametric Estimation of Finite Population Totals in high dimensional datasets is considered. A robust estimator of the Finite Population Total based on Feedforward Backpropagation Neu...In this paper, the problem of Nonparametric Estimation of Finite Population Totals in high dimensional datasets is considered. A robust estimator of the Finite Population Total based on Feedforward Backpropagation Neural Network is derived with the aid of a Super-Population Model. This current study is motivated by the fact that Local Polynomials and Kernel methods have in preceding related studies, been shown to provide good estimators for Finite Population Totals but in low dimensions. Even in these situations however, bias at boundary points presents a big challenge when using these estimators in estimating Finite Population parameters. The challenge worsens as the dimension of regressors increase. This is because as the dimension of the Regressor Vectors grows, the Sparseness of the Regressors’ values in the design space becomes unfeasible, resulting in a decrease in the fastest achievable rates of convergence of the Regression Function Estimators towards the target curve, rendering Kernel Methods and Local Polynomials ineffective to address these challenges. This study considers the technique of Artificial Neural Networks which yields robust estimators in high dimensions and reduces the estimation bias with marginal increase in variance. This is due to its Multi-Layer Structure, which can approximate a wide range of functions to any required level of precision. The estimator’s properties are developed, and a comparison with existing estimators was conducted to evaluate the estimator’s performance using real data sets acquired from the United Nations Development Programme 2020. The estimation approach performs well in an example using data from a United Nations Development Programme 2020 on the study of Human Development Index against other factors. The theoretical and practical results imply that the Neural Network estimator is highly recommended for survey sampling estimation of the finite population total.展开更多
The problem of classification in situations where the assumption of normality in the data is violated, and there are non-linear clustered structures in the dataset is addressed. A robust nonparametric kernel discrimin...The problem of classification in situations where the assumption of normality in the data is violated, and there are non-linear clustered structures in the dataset is addressed. A robust nonparametric kernel discriminant classification function, which is able to address this challenge, has been developed and the misclassification rates computed for various bandwidth matrices. A comparison with existing parametric classification functions such as the linear discriminant and quadratic discriminant is conducted to evaluate the performance of this classification function using simulated datasets. The results presented in this paper show good performance in terms of misclassification rates for the kernel discriminant classifier when the correct bandwidth is selected as compared to other identified existing classifiers. In this regard, the study recommends the use of the proposed kernel discriminant classification rule when one wishes to classify units into one of several categories or population groups where parametric classifiers might not be applicable.展开更多
Statelessness is the absence of any Nationality. These include the Pemba, Shona, Galjeel, people of Burundi and Rwanda descent, and children born in Kenya to British Overseas Citizens after 1983. Frequently, they are ...Statelessness is the absence of any Nationality. These include the Pemba, Shona, Galjeel, people of Burundi and Rwanda descent, and children born in Kenya to British Overseas Citizens after 1983. Frequently, they are not only undocumented but also often overlooked and not included in National Administrative Registers. Accordingly, find it hard to participate in Social and Economic Affairs. There has been a major push by UNHCR and international partners to “map” the size of stateless populations and their demographic profile, as well as causes, potential solutions and human rights situation. One of the requirements by the UNHCR in their push is for countries to find a potential solution to statelessness which starts with classifying/associating a person from these communities to a particular local community that is recognized in Kenya. This paper addresses this problem by adopting a Robust Nonparametric Kernel Discriminant function to correctly classify the stateless communities in Kenya and compare the performance of this method with the existing techniques through their classification rates. This is because Non-parametric functions have proven to be more robust and useful especially when there exists auxiliary information which can be used to increase precision. The findings from this paper indicate that Nonparametric discriminant classifiers provide a good classification method for classifying the stateless communities in Kenya. This is because they exhibit lower classification rates compared to the parametric methods such as Linear and Quadratic discriminant functions. In addition, the finding shows that based on certain similarities in characteristics that exist in these communities that surround the Pemba Community, the Pemba community can be classified as Giriama or Rabai in which they seem to have a strong link. In this regard, the study recommends the use of the Kernel discriminant classifiers in classifying the stateless persons and that the Government of Kenya consider integrating/recognizing the Pemba community into Giriama or Rabai so that they can be issued with the National Identification Cards and be recognized as Kenyans.展开更多
文摘In this paper, the problem of Nonparametric Estimation of Finite Population Totals in high dimensional datasets is considered. A robust estimator of the Finite Population Total based on Feedforward Backpropagation Neural Network is derived with the aid of a Super-Population Model. This current study is motivated by the fact that Local Polynomials and Kernel methods have in preceding related studies, been shown to provide good estimators for Finite Population Totals but in low dimensions. Even in these situations however, bias at boundary points presents a big challenge when using these estimators in estimating Finite Population parameters. The challenge worsens as the dimension of regressors increase. This is because as the dimension of the Regressor Vectors grows, the Sparseness of the Regressors’ values in the design space becomes unfeasible, resulting in a decrease in the fastest achievable rates of convergence of the Regression Function Estimators towards the target curve, rendering Kernel Methods and Local Polynomials ineffective to address these challenges. This study considers the technique of Artificial Neural Networks which yields robust estimators in high dimensions and reduces the estimation bias with marginal increase in variance. This is due to its Multi-Layer Structure, which can approximate a wide range of functions to any required level of precision. The estimator’s properties are developed, and a comparison with existing estimators was conducted to evaluate the estimator’s performance using real data sets acquired from the United Nations Development Programme 2020. The estimation approach performs well in an example using data from a United Nations Development Programme 2020 on the study of Human Development Index against other factors. The theoretical and practical results imply that the Neural Network estimator is highly recommended for survey sampling estimation of the finite population total.
文摘The problem of classification in situations where the assumption of normality in the data is violated, and there are non-linear clustered structures in the dataset is addressed. A robust nonparametric kernel discriminant classification function, which is able to address this challenge, has been developed and the misclassification rates computed for various bandwidth matrices. A comparison with existing parametric classification functions such as the linear discriminant and quadratic discriminant is conducted to evaluate the performance of this classification function using simulated datasets. The results presented in this paper show good performance in terms of misclassification rates for the kernel discriminant classifier when the correct bandwidth is selected as compared to other identified existing classifiers. In this regard, the study recommends the use of the proposed kernel discriminant classification rule when one wishes to classify units into one of several categories or population groups where parametric classifiers might not be applicable.
文摘Statelessness is the absence of any Nationality. These include the Pemba, Shona, Galjeel, people of Burundi and Rwanda descent, and children born in Kenya to British Overseas Citizens after 1983. Frequently, they are not only undocumented but also often overlooked and not included in National Administrative Registers. Accordingly, find it hard to participate in Social and Economic Affairs. There has been a major push by UNHCR and international partners to “map” the size of stateless populations and their demographic profile, as well as causes, potential solutions and human rights situation. One of the requirements by the UNHCR in their push is for countries to find a potential solution to statelessness which starts with classifying/associating a person from these communities to a particular local community that is recognized in Kenya. This paper addresses this problem by adopting a Robust Nonparametric Kernel Discriminant function to correctly classify the stateless communities in Kenya and compare the performance of this method with the existing techniques through their classification rates. This is because Non-parametric functions have proven to be more robust and useful especially when there exists auxiliary information which can be used to increase precision. The findings from this paper indicate that Nonparametric discriminant classifiers provide a good classification method for classifying the stateless communities in Kenya. This is because they exhibit lower classification rates compared to the parametric methods such as Linear and Quadratic discriminant functions. In addition, the finding shows that based on certain similarities in characteristics that exist in these communities that surround the Pemba Community, the Pemba community can be classified as Giriama or Rabai in which they seem to have a strong link. In this regard, the study recommends the use of the Kernel discriminant classifiers in classifying the stateless persons and that the Government of Kenya consider integrating/recognizing the Pemba community into Giriama or Rabai so that they can be issued with the National Identification Cards and be recognized as Kenyans.
