Statistical inference from complete and incomplete data

Download

index.pdf

Date

2010

Author

Can Mutan, Oya

Metadata

Show full item record

Item Usage Stats

177
views

75
downloads

Let X and Y be two random variables such that Y depends on X=x. This is a very common situation in many real life applications. The problem is to estimate the location and scale parameters in the marginal distributions of X and Y and the conditional distribution of Y given X=x. We are also interested in estimating the regression coefficient and the correlation coefficient. We have a cost constraint for observing X=x, the larger x is the more expensive it becomes. The allowable sample size n is governed by a pre-determined total cost. This can lead to a situation where some of the largest X=x observations cannot be observed (Type II censoring). Two general methods of estimation are available, the method of least squares and the method of maximum likelihood. For most non-normal distributions, however, the latter is analytically and computationally problematic. Instead, we use the method of modified maximum likelihood estimation which is known to be essentially as efficient as the maximum likelihood estimation. The method has a distinct advantage: It yields estimators which are explicit functions of sample observations and are, therefore, analytically and computationally straightforward. In this thesis specifically, the problem is to evaluate the effect of the largest order statistics x(i) (i>n-r) in a random sample of size n (i) on the mean E(X) and variance V(X) of X, (ii) on the cost of observing the x-observations, (iii) on the conditional mean E(Y

Subject Keywords

Statistics., Modified maximum likelihood (MML)

URI

http://etd.lib.metu.edu.tr/upload/3/12611531/index.pdf
https://hdl.handle.net/11511/19351

Collections

Graduate School of Natural and Applied Sciences, Thesis

Suggestions

OpenMETU
Core

Nonnormal regression. I. Skew distributions İslam, Muhammed Qamarul; Yildirim, F (2001-01-01) In a linear regression model of the type y = thetaX + e, it is often assumed that the random error e is normally distributed. In numerous situations, e.g., when y measures life times or reaction times, e typically has a skew distribution. We consider two important families of skew distributions, (a) Weibull with support IR: (0, infinity) on the real line, and (b) generalised logistic with support IR: (-infinity, infinity). Since the maximum likelihood estimators are intractable in these situations, we deriv...
Asymptotic integration of second-order nonlinear differential equations via principal and nonprincipal solutions Ertem, T.; Zafer, Ağacık (2013-02-01) Let u and v denote respectively the principal and nonprincipal solutions of the second-order linear equation (p(t)x')' + q(t)x = 0 defined on some half-line of the form [t(*), infinity).
Non-normal bivariate distributions: estimation and hypothesis testing Qunsiyeh, Sahar Botros; Tiku, Moti Lal; Department of Statistics (2007) When using data for estimating the parameters in a bivariate distribution, the tradition is to assume that data comes from a bivariate normal distribution. If the distribution is not bivariate normal, which often is the case, the maximum likelihood (ML) estimators are intractable and the least square (LS) estimators are inefficient. Here, we consider two independent sets of bivariate data which come from non-normal populations. We consider two distinctive distributions: the marginal and the conditional dist...
Value sets of folding polynomials over finite fields Küçüksakallı, Ömer (2019-01-01) Let k be a positive integer that is relatively prime to the order of the Weyl group of a semisimple complex Lie algebra g. We find the cardinality of the value sets of the folding polynomials P-g(k)(x) is an element of Z[x] of arbitrary rank n >= 1, over finite fields. We achieve this by using a characterization of their fixed points in terms of exponential sums.
Polynomial solutions of the Mie-type potential in the D-dimensional Schrodinger equation IKHDAİR, SAMEER; Sever, Ramazan (2008-04-30) The polynomial solution of the D-dimensional Schrodinger equation for a special case of Mie potential is obtained with an arbitrary l not equal 0 states. The exact bound state energies and their corresponding wave functions are calculated. The bound state (real) and positive (imaginary) cases are also investigated. In addition, we have simply obtained the results from the solution of the Coulomb potential by an appropriate transformation.

Citation Formats

O. Can Mutan, “Statistical inference from complete and incomplete data,” Ph.D. - Doctoral Program, Middle East Technical University, 2010.