الفهرس 
Introduction and Review of LiteratureOnly 14 pages are availabe for public view
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Abstract
Nonparametric estimation is a methodology for estimating density functions or conditional moments of distributions without making any prior assumptions about functional forms. The data are allowed to speak for themselves in determining the shape of the unknown functions (Silverman 1986). In this thesis, we studied some of nonparametric estimation techniques such as the kernel estimator, the local linear estimator and the maximum penalized likelihood estimator.
The thesis consists of four chapters:
Chapter I, is an introduction and literature review for nonparametric estimation technique.
Chapter II, the nonparametric approach is considered to estimate probability density function (pdf) which have support on . This approach is the inverse gamma kernel. We show that it has the same properties as gamma, reciprocal inverse Gaussian and inverse Gaussian kernels such as being free of the boundary bias, non-negative, and achieves the optimal rate of convergence for the mean integrate squared error. Also some properties of the estimator were established such as bias and variance. Comparison of the bandwidth selection methods for inverse gamma kernel estimation of probability density function is introduced. Some results of this chapter are accepted to be published in the journal of Communications in Statistics – Theory and Methods, vol. 45, No. 23, 7002-7010, (2016).
Chapter III, considers the problem of estimating the regression curve with bounded support by using asymmetric kernels in local linear smoothing. The used asymmetric kernels are inverse gamma, inverse gaussian and reciprocal inverse gaussian kernels for which the curve is bounded from one end only. The local linear smoothers using the previous kernels offers some extra advantages in aspects of having finite variance and resistance to sparse design. This is because of their flexible kernel shape and the support of the kernel matching the support of the regression curve. In addition to compare between the local linear smoothers using the gamma, inverse gamma, inverse gaussian and reciprocal inverse gaussian kernels using simulation study. Some results of this chapter were submitted to ” ESAIM Probability and Statistics Journal ”.
Chapter IV, considers the problem of estimating the probability density function based on maximum penalized likelihood estimation. We will, review some of the previous studies on maximum penalized likelihood estimation (MPLE) approaches. We show the maximum penalized likelihood estimation in reliability parameter based on two-parameter exponential distribution and the maximum likelihood estimation in reliability parameter based on two-parameters exponential distribution. In addition to compare between the two methods using simulation study.
Some results of this chapter were submitted to ”The Egyptian Statistical Journal”.
Nonparametric estimation is a methodology for estimating density functions or conditional moments of distributions without making any prior assumptions about functional forms. The data are allowed to speak for themselves in determining the shape of the unknown functions (Silverman 1986). In this thesis, we studied some of nonparametric estimation techniques such as the kernel estimator, the local linear estimator and the maximum penalized likelihood estimator.
The thesis consists of four chapters:
Chapter I, is an introduction and literature review for nonparametric estimation technique.
Chapter II, the nonparametric approach is considered to estimate probability density function (pdf) which have support on . This approach is the inverse gamma kernel. We show that it has the same properties as gamma, reciprocal inverse Gaussian and inverse Gaussian kernels such as being free of the boundary bias, non-negative, and achieves the optimal rate of convergence for the mean integrate squared error. Also some properties of the estimator were established such as bias and variance. Comparison of the bandwidth selection methods for inverse gamma kernel estimation of probability density function is introduced. Some results of this chapter are accepted to be published in the journal of Communications in Statistics – Theory and Methods, vol. 45, No. 23, 7002-7010, (2016).
Chapter III, considers the problem of estimating the regression curve with bounded support by using asymmetric kernels in local linear smoothing. The used asymmetric kernels are inverse gamma, inverse gaussian and reciprocal inverse gaussian kernels for which the curve is bounded from one end only. The local linear smoothers using the previous kernels offers some extra advantages in aspects of having finite variance and resistance to sparse design. This is because of their flexible kernel shape and the support of the kernel matching the support of the regression curve. In addition to compare between the local linear smoothers using the gamma, inverse gamma, inverse gaussian and reciprocal inverse gaussian kernels using simulation study. Some results of this chapter were submitted to ” ESAIM Probability and Statistics Journal ”.
Chapter IV, considers the problem of estimating the probability density function based on maximum penalized likelihood estimation. We will, review some of the previous studies on maximum penalized likelihood estimation (MPLE) approaches. We show the maximum penalized likelihood estimation in reliability parameter based on two-parameter exponential distribution and the maximum likelihood estimation in reliability parameter based on two-parameters exponential distribution. In addition to compare between the two methods using simulation study.
Some results of this chapter were submitted to ”The Egyptian Statistical Journal”.
Nonparametric estimation is a methodology for estimating density functions or conditional moments of distributions without making any prior assumptions about functional forms. The data are allowed to speak for themselves in determining the shape of the unknown functions (Silverman 1986). In this thesis, we studied some of nonparametric estimation techniques such as the kernel estimator, the local linear estimator and the maximum penalized likelihood estimator.
The thesis consists of four chapters:
Chapter I, is an introduction and literature review for nonparametric estimation technique.
Chapter II, the nonparametric approach is considered to estimate probability density function (pdf) which have support on . This approach is the inverse gamma kernel. We show that it has the same properties as gamma, reciprocal inverse Gaussian and inverse Gaussian kernels such as being free of the boundary bias, non-negative, and achieves the optimal rate of convergence for the mean integrate squared error. Also some properties of the estimator were established such as bias and variance. Comparison of the bandwidth selection methods for inverse gamma kernel estimation of probability density function is introduced. Some results of this chapter are accepted to be published in the journal of Communications in Statistics – Theory and Methods, vol. 45, No. 23, 7002-7010, (2016).
Chapter III, considers the problem of estimating the regression curve with bounded support by using asymmetric kernels in local linear smoothing. The used asymmetric kernels are inverse gamma, inverse gaussian and reciprocal inverse gaussian kernels for which the curve is bounded from one end only. The local linear smoothers using the previous kernels offers some extra advantages in aspects of having finite variance and resistance to sparse design. This is because of their flexible kernel shape and the support of the kernel matching the support of the regression curve. In addition to compare between the local linear smoothers using the gamma, inverse gamma, inverse gaussian and reciprocal inverse gaussian kernels using simulation study. Some results of this chapter were submitted to ” ESAIM Probability and Statistics Journal ”.
Chapter IV, considers the problem of estimating the probability density function based on maximum penalized likelihood estimation. We will, review some of the previous studies on maximum penalized likelihood estimation (MPLE) approaches. We show the maximum penalized likelihood estimation in reliability parameter based on two-parameter exponential distribution and the maximum likelihood estimation in reliability parameter based on two-parameters exponential distribution. In addition to compare between the two methods using simulation study.
Some results of this chapter were submitted to ”The Egyptian Statistical Journal”.
Nonparametric estimation is a methodology for estimating density functions or conditional moments of distributions without making any prior assumptions about functional forms. The data are allowed to speak for themselves in determining the shape of the unknown functions (Silverman 1986). In this thesis, we studied some of nonparametric estimation techniques such as the kernel estimator, the local linear estimator and the maximum penalized likelihood estimator.
The thesis consists of four chapters:
Chapter I, is an introduction and literature review for nonparametric estimation technique.
Chapter II, the nonparametric approach is considered to estimate probability density function (pdf) which have support on . This approach is the inverse gamma kernel. We show that it has the same properties as gamma, reciprocal inverse Gaussian and inverse Gaussian kernels such as being free of the boundary bias, non-negative, and achieves the optimal rate of convergence for the mean integrate squared error. Also some properties of the estimator were established such as bias and variance. Comparison of the bandwidth selection methods for inverse gamma kernel estimation of probability density function is introduced. Some results of this chapter are accepted to be published in the journal of Communications in Statistics – Theory and Methods, vol. 45, No. 23, 7002-7010, (2016).
Chapter III, considers the problem of estimating the regression curve with bounded support by using asymmetric kernels in local linear smoothing. The used asymmetric kernels are inverse gamma, inverse gaussian and reciprocal inverse gaussian kernels for which the curve is bounded from one end only. The local linear smoothers using the previous kernels offers some extra advantages in aspects of having finite variance and resistance to sparse design. This is because of their flexible kernel shape and the support of the kernel matching the support of the regression curve. In addition to compare between the local linear smoothers using the gamma, inverse gamma, inverse gaussian and reciprocal inverse gaussian kernels using simulation study. Some results of this chapter were submitted to ” ESAIM Probability and Statistics Journal ”.
Chapter IV, considers the problem of estimating the probability density function based on maximum penalized likelihood estimation. We will, review some of the previous studies on maximum penalized likelihood estimation (MPLE) approaches. We show the maximum penalized likelihood estimation in reliability parameter based on two-parameter exponential distribution and the maximum likelihood estimation in reliability parameter based on two-parameters exponential distribution. In addition to compare between the two methods using simulation study.
Some results of this chapter were submitted to ”The Egyptian Statistical Journal”.
Nonparametric estimation is a methodology for estimating density functions or conditional moments of distributions without making any prior assumptions about functional forms. The data are allowed to speak for themselves in determining the shape of the unknown functions (Silverman 1986). In this thesis, we studied some of nonparametric estimation techniques such as the kernel estimator, the local linear estimator and the maximum penalized likelihood estimator.
The thesis consists of four chapters:
Chapter I, is an introduction and literature review for nonparametric estimation technique.
Chapter II, the nonparametric approach is considered to estimate probability density function (pdf) which have support on . This approach is the inverse gamma kernel. We show that it has the same properties as gamma, reciprocal inverse Gaussian and inverse Gaussian kernels such as being free of the boundary bias, non-negative, and achieves the optimal rate of convergence for the mean integrate squared error. Also some properties of the estimator were established such as bias and variance. Comparison of the bandwidth selection methods for inverse gamma kernel estimation of probability density function is introduced. Some results of this chapter are accepted to be published in the journal of Communications in Statistics – Theory and Methods, vol. 45, No. 23, 7002-7010, (2016).
Chapter III, considers the problem of estimating the regression curve with bounded support by using asymmetric kernels in local linear smoothing. The used asymmetric kernels are inverse gamma, inverse gaussian and reciprocal inverse gaussian kernels for which the curve is bounded from one end only. The local linear smoothers using the previous kernels offers some extra advantages in aspects of having finite variance and resistance to sparse design. This is because of their flexible kernel shape and the support of the kernel matching the support of the regression curve. In addition to compare between the local linear smoothers using the gamma, inverse gamma, inverse gaussian and reciprocal inverse gaussian kernels using simulation study. Some results of this chapter were submitted to ” ESAIM Probability and Statistics Journal ”.
Chapter IV, considers the problem of estimating the probability density function based on maximum penalized likelihood estimation. We will, review some of the previous studies on maximum penalized likelihood estimation (MPLE) approaches. We show the maximum penalized likelihood estimation in reliability parameter based on two-parameter exponential distribution and the maximum likelihood estimation in reliability parameter based on two-parameters exponential distribution. In addition to compare between the two methods using simulation study.
Some results of this chapter were submitted to ”The Egyptian Statistical Journal”.
Nonparametric estimation is a methodology for estimating density functions or conditional moments of distributions without making any prior assumptions about functional forms. The data are allowed to speak for themselves in determining the shape of the unknown functions (Silverman 1986). In this thesis, we studied some of nonparametric estimation techniques such as the kernel estimator, the local linear estimator and the maximum penalized likelihood estimator.
The thesis consists of four chapters:
Chapter I, is an introduction and literature review for nonparametric estimation technique.
Chapter II, the nonparametric approach is considered to estimate probability density function (pdf) which have support on . This approach is the inverse gamma kernel. We show that it has the same properties as gamma, reciprocal inverse Gaussian and inverse Gaussian kernels such as being free of the boundary bias, non-negative, and achieves the optimal rate of convergence for the mean integrate squared error. Also some properties of the estimator were established such as bias and variance. Comparison of the bandwidth selection methods for inverse gamma kernel estimation of probability density function is introduced. Some results of this chapter are accepted to be published in the journal of Communications in Statistics – Theory and Methods, vol. 45, No. 23, 7002-7010, (2016).
Chapter III, considers the problem of estimating the regression curve with bounded support by using asymmetric kernels in local linear smoothing. The used asymmetric kernels are inverse gamma, inverse gaussian and reciprocal inverse gaussian kernels for which the curve is bounded from one end only. The local linear smoothers using the previous kernels offers some extra advantages in aspects of having finite variance and resistance to sparse design. This is because of their flexible kernel shape and the support of the kernel matching the support of the regression curve. In addition to compare between the local linear smoothers using the gamma, inverse gamma, inverse gaussian and reciprocal inverse gaussian kernels using simulation study. Some results of this chapter were submitted to ” ESAIM Probability and Statistics Journal ”.
Chapter IV, considers the problem of estimating the probability density function based on maximum penalized likelihood estimation. We will, review some of the previous studies on maximum penalized likelihood estimation (MPLE) approaches. We show the maximum penalized likelihood estimation in reliability parameter based on two-parameter exponential distribution and the maximum likelihood estimation in reliability parameter based on two-parameters exponential distribution. In addition to compare between the two methods using simulation study.
Some results of this chapter were submitted to ”The Egyptian Statistical Journal”.