In regression models, the existence of multicollinearity problem and its effect on the results of regression analysis has led to the use of other estimators instead of the ordinary least squares estimation. One of these estimators is Lasso estimator, which has some of the features of least squares estimate. In addition to the shrinkage of estimates, Lasso's method eliminates coefficients whose corresponding variables have a small effect on the response variable. Also, if the number of explanatory variables is high and exceeds the number of observations, we use Fused Lasso, which increases the efficiency of the resulting estimator. This estimator tends to be aligned when the explanatory variables are highly correlated with a better performance than that of Lasso estimate, and so-called have group effects. we first study a number of methods, including Lasso and Ridge, which are used to solve the multicollinearity problem in estimating the coefficients, and then we focus on the estimator of Lasso and some generalizations such as the Fused Lasso, and then estimate using these methods the coefficients for data on the productivity of industrial power plants in Iran (2006). Lastly, with the simulation example, we examine the performance of these estimators.

 In linear regression analysis, the presence of collinearity among regressor variables may cause highly unstable least squares estimates of the regression parameters.When
prior information about coefficients are available, the application of this informations
into estimate will increase efficiency of resulting estimator and also decrease collinearity effects. A subset of the data can have a disproportionate influence on the different aspects models So, it is necessary to identify these kind of data. Among unusual observations in models one can refer to the outliers, leverage point and influential observation. Diffrrent measures including matrix prediction, standardized residuals, DFBETAS, DFFITSS, Cook’s distance and mean-shift have proposed, to detect these kind of observations. In this dissertation, we first study an approximate version of lasso estimate and some its propeties. Then we proposed a new estimator by applying mix procedure to approximate version of lasso estimate when stochastic restrictions are assumed. Then, we extend diagnostics methods under this estimators. As analogues to those given in OLSE estimators. Finally, a numerical example is given to illustrate some of the theoretical results.

In the presence of multicollinearity, the OLS estimate will be challenged. In fact
this estimator still unbiased but because of large variance and its MSE this estimator
will be far from its true value. In order to decreasing multicollinearity effects, biased
estimators such as r-d calss estimator and or r-d class estimator under stochastic linear
restrictions can be used. These estimators by accepting a little bit biase and decreasing
variance of regression coeficients, will produce stable coeficients. To compare these
biased estimator, MSE criterion will be used.
Sometime a small group of data have large effect on fitting a regression model, and
will influnce on some aspect of model, so these data must be identified. Detection such
observations by methodes and criterions base on sensibility analys is introduced. By
considering detection of influential and outliers observation as a goal, criterions such
as prediction matrix (Hat matrix), standard residuals, DFBETAS, DFFITS and mean
shift procedure are proposed.
In this disertation r-d class estimate and r-d class estimate under stochastic linear
restriction will be study, then some diagnostics for these estimates are generalized.
Finally by using a real data set the resulting conclusions are investigated.

The existence of collinearity in linear regression models and its effects on results of regression analysis has caused using other estimators instead of least squares estimates‎. ‎When prior information about coefficients are available‎, ‎the application of this information into estimate will increase efficiency of resulting estimator and also decrease collinearity effects‎. ‎Identifying influential observation is an important part of the model building process in linear regression‎. ‎Therefor numerous diagnostic measures based on different approaches in linear regression analysis are proposed‎. ‎In this dissertation‎, ‎we first study two parameter ridge estimate and some its properties‎. ‎Then we proposed a new estimator by applying mix procedure to two parameter ridge estimate when stochastic restrictions are assumed‎. ‎Thus by a simulation study we compare the performance of this new estimate with other estimators‎. ‎Also we extend diagnostics methods under generalized two parameter ridge and mixed two parameter ridge estimators‎. ‎A statistic for mean shift test is proposed‎, ‎which its empirical distribution is obtained by application of bootstrap procedure in a simulation study.

The homogeneity of the variances of errors is one of the assumptions of the classical linear regression model. If this assumption does not hold, generalized least squares method is used to estimute the parameters. On the other hand, some of the observations can have a significant effect on the parameter estimates and it is important to identify these observations. In this thesis we deal with the multiple linear regression models with the heteroscedasticity error variances and the weighted method has been used to fix the error variance. We study the effect of simultaneous deleting of an observation and an independent variable on the ordinary and weighted least square regression models and derive the influential Observations, Outliers and Leverage points with using deleting method in the ordinary and weighted least square regression models. Next we examine the effects of simultaneous deleting multiple observations and a subset of independent variables on the weighted least square regression models. Finally, an example of real data set is used to illustrate the proposed methods.

In linear regression analysis, the presence of collinearity among regressor variables may cause highly unstable least squares estimates of the regression parameters. When faced with collinearity, we use the biased estimators such as, the principal components regression or the stochastic restricted principal components regression to combat collinearity. On the other hand, study of the diagnostics methods and identifing unusual observations is an important step in the process of model building. Sometimes, A subset of the data can have a disproportionate influence on the different aspects models So, it is necessary to identify these kind of data. Among unusual observations in models one can refer to the outliers, leverage point and influential observation. Diffrrent measures including matrix prediction, standardized residuals, DFBETAS, DFFITSS, Cook’s distance and mean-shift have proposed, to detect these kind of observations. In this dissertation, we first study the principal components regression and the stochastic restricted principal components regression estimators. Then, we extend diagnostics methods under this estimators. As analogues to those given in OLSE estimators. Finally, a numerical example is given to illustrate some of the theoretical results.

Among themethodsused inregression, one can use the least squares method toestimate the parameters of the model. But sometimes we faced withcollinearityamongthe independent variables.Consequently, theresults of the least squares method will not be reliable.Many methods have been proposed to deal with this phenomenon by researchers. Among those one can refer to the ridgeregressionmethods, principal componentregressionandpartialleast squares. In this thesis theridgeregressionmethodis usedto deal withthis phenomenon. Thehomogeneity ofthe variancesof errors, is one of theassumptions ofthe classicallinear regressionmodel.If this assumption does not hold, generalized least square used to estimation parameters.In this thesis we deal with multiple linear regression models in which the disturbancesare heteroscedasticity and the explanatory variables are collinear.
On the other hand, someof the observations canhavea significant effect onthe parameter estimates and it is important toidentifytheseobservations.
Inthisthesis, westudyseemingly unrelatedregressionmodelto estimatetheridge, ridgeregression modelwithautocorrelatederrors, ridgeregression modelwithheteroscedasticity errors and to evaluate influential Observations, usingdeleting merthod. Then,weextendthisapproachtostudythe models and to find effectiveobservationonthesemodels. Finally, examples of real data set are used to illustrate the proposed methods.
 

In regression analysis, a small subset of the data sets can have a disproportionate influence on the estimate of parameters or predictions. Accordingly, detecting this kind of data is one of the important steps in regression analysis and model building process. The situation will be more complicated when there are influential observations in the presence of collinearity. In this case it is suggested that first reducing collinearity and then detecting anomalous data. On the other hand, collinearity can increase the variance of the least squares estimates regression coefficients and build unstable estimates. One can use the biased estimators to mitigate the effects of collinearity. The biased estimators decrease the variance of regression coefficients and building stabilized coefficients. An estimator with minimum mean square error is more efficient among several estimators. Reducing the bias can be one of the enhancement efficiency methods in biased estimator. In this thesis, we study the Jackknife Liu and Modify Jackknife Liu estimators. Then we generalize diagnostic methods for these estimates. Generalized diagnostics involve: DFFITS, DFBETAS, and COVRATIO, COOK distance and mean shift outliers. Finally, real data sets are used to illustrate the methodologies proposed.

 The birth interval is one of the main criterion about reproduction subject. Although pairʼs decision is very important in this matter, but economic, cultural and public factors are also affective. In this thesis, panel data models have been considered. Panel data are combinations of time series and cross section data. In other words, information about cross section data have been noticed during a certain period of time. Therefore; these kind of data have two dimension. One of these dimension correspond to various units in every particular time section and the other dimension correspond to time subject and allow us to analysis topics which can not be considered as time series or cross section data. Panel data have many applications in econometrics and also they have more advantages then cross section or time series data. Morever; these data are more informative and variability and less collinearity among the variables. Also, these data have more degrees of freedom and efficiency. In this thesis uses balanced, unbalanced and dynamic panel models, the effective factors in birth intervals of womenʼs children attending to clinical-healthy centers in Ahwaz have been studied.

 Survival analysis is the perhaps used to describe analysis of the data in the from times from a well defined time origin untile the occurrence of some particular event or end points. One of the main goals in the analysis of survival data, is to find a relationship between the dependent variable and independent variables. For to achieve this goal using the regressions accelerated failure time model. In the regression models one of the basic assumptions is that the independent variables are fixed and known. But covariate measurement error is often present in survival data for various reasons. When the main objective of the model is relationships between dependent and independent variables and examine the relationship between them, attention to measurement error is a serious problem. Since ignoring measurement error may result in substantially biased estimates in many context including linear and nonlinear regression.
Using of this method for modeling birth intervals in Ahvaz is an issue that has been considered in this study. The data source for this study is the birth intervals woman referred to health centers in Ahvaz. Since there are some factors that seems may be difficult to observe precisely, using the simulation extrapolation method seems to be appropriate. The results shown that estimates for birth intervals models in two methods Naïve that ignoring measurement error and simulation extrapolation method are different.