In the Present book Chapter -I contains the general introduction about the model selection. Chapter-II speaks about the various inferential problems of linear statistical models. The distributional properties of the OLS estimators have been presented in this chapter. It also contains the procedure of testing the general linear hypothesis .Chapter-III deals with the existing criteria for model selection given in the literature. Chapter-IV proposes some new techniques for selection of linear statistical models pertaining both the nested and non-nested linear regression models. Chapter-V epitomizes the conclusions. Various selected references have been documented under a separate caption 'Bibliography'.

Biostatistics or Biometrics is a growing filed of statistics. The word 'Biometrics' derived from two Greek Words Bios (Life) and Matron (measurement). Thus Biometrics means measurement of life. Biostatistics may be defined as the quantitative analysis of biological phenomena based on the concurrent development of theory and observation related by appropriate methods of statistical inference .Chapter-I is any introductory one. It contains the general introduction about Biostatistics.Chapter-II describes the various aspects of Bioassays such as meaning, history and structure of Bioassays.Chapter-III deals with the existing univariate statistical tools in Biostatistics. It presents a brief review about basic statistical tools for Biostatistics.Chapter-IV gives a brief review about the existing Inferential Multivariate statistical tools for Biostatistics .Chapter-V proposes some advanced and new statistical techniques for Biostatistics such as modified Trend tests for Biostatistics; Chapter-VI epitomizes the conclusions based on the present book . Besides Conclusions.Several relevant research articles have been presented under the title 'BIBLIOGRAPHY'.

In this present book Chapter-I is an introductory one. Chapter-II describes the various criteria for selection of regressors in the multiple regression analysis existing in this book. Chapter-III deals with the basic stepwise regression procedures for variable selection in multiple regression analysis and The mean square error of prediction criterion has been discussed along with a similar average estimated variance criterion for the selection of variables in the general linear model. Chapter-IV presents the various methods for choosing variable subsets in multiple linear regression analysis under these methods, the mean squared prediction error has been considered as basis of the criteria. Chapter-V proposes some new criteria for selection of regressors in econometrics based on different types of residuals such as Ordinary Least Squares, Studentized and Predicted residuals. Chapter-VI depicts the main conclusions of the present research study. It also narrates the plan for future research as an extension in the lines of study. Several relevant references have been documented under a separate title "BIBLIOGRAPHY."

In the book an attempt has been made to develop some new diagnostic tests for statistical model building in the context of linear regression models. Diagnostics of outliers has been described and a test for identifying outliers by using predicted residuals has been proposed in the present study. Besides outliers, a measure of influence for diagnostics has been developed in the study. Some new modified R2 and criteria for model selection have been developed along with modified mean square prediction error criteria; and modified information criteria for model selection. A test for exogeneity in model specification by using augmented regression model; and a test for stability of regression parameters in model specification have been proposed under diagnostic tests. A new test for misspecification of the linear regression model has been derived along with a modified Rainbow Test by using Internally studentized residuals. The problem of misspecification of non-nested linear regression models, has been discussed together with a diagnostic test for functional form between loglinear and linear regression models.

This book attempts to develope some new inferential procedures for time series regression models.An inferential method for a time series linear regression model with auto correlated disturbances using quarterly data, has been developed by proposing a test based on internally studentized residuals.Two modified estimation procedures have been proposed for time series regression models involving MA (1) and MA (q) process errors.Autoregressive moving averages and autoregressive conditionally heteroscadastic (ARCH) processesses have been specified systematically with their characteristics. The generalized ARCH model is specified and the effect of error structure on ARCH model has been explained. Two modified tests for detecting the problem of ARCH errors have been developed by using Box-pierce-lying test statistics based on internally studentized residuals. A new estimation procedure has been developed for ARCH model by using an interactive technique

In this book an attempt has been made by proposing some inferential techniques for linear regression models by using various types of residuals other than OLS residuals.Chapter I contains the general introduction about the concept of residuals in regression analysis. Various types of residuals and their properties have been described in chapter II. The literature on residual analysis and regression diagnostics have been reviewed in chapter III. In particular, it is discussed about examination of residual plots diagnostics for identifying unusual data points, detection of influential subsets, until applications of residuals. Chapter IV contains the proposed methods under is the contributory one in which outliers are detected; Leverage and influential points are identified; Goldfeld-Quandt test statistics computed to know the heteroscodastocity; Chow test statistic is computed to know the structural change and Durbin-Waston test statistic is competed to know the autocorrelation using different types of residuals.

Data Envelopment Analysis (DEA) is a Mathematical Programming technique that finds a number of applications to measure the performance of similar units. The performance of these units say Decision Making Units (DMU) is assessed with DEA is obtained by using the concept of Efficiency which is the ratio of Weighted Sum of outputs to weighted sum of inputs. The efficiency obtained by using DEA are relative to best performance of Virtual DMU. In the present study, the efficiency of Production has been measured by specifying and estimating the parameters of Translog output distance function. Further, a non-parametric approach has been applied to measure the efficiency of production by constructing several Linear Programming Problem based on Translog output distance function to study efficiency variation in Indian Commercial Banks.

This book describes the analysis of transformations and their applications in regression analysis. Some new estimation procedures for estimating the parameters of the various Box and Cox transformation regression models with Autoregressive/Moving Average Process have been developed by using internally studentized residuals. The lagged dependent variable is induded as a regressor in the extended Box and Cox transformation regression model and then estimated its parameters by using the maximum likelihood estimation. In this book, it has been made to described the analysis of transformations and their applications in regression analysis.

This book has brought out some applications of linear models by using various concepts in the Linear Algebra.Most of the Applied Regression analysis techniques are based in the concept of linear model.It describes the applications of some advanced concepts in the matrix theory to linear models.The specification, estimation and various inferential aspects of linear statistical models have been discussed.The various problems of Mathematical and Statistical linear models have been presented in this book.It contains some applications of generalized Inverse matrices to the linear models

Efficiency rating of decision making units (DMUs) was long back identified as an important activity that helps both the producer and the policy maker. It requires that the DMUs are in competition, produce similar outputs combining similar inputs. Efficiency rating may be oriented or non-oriented. Twenty banks were considered to study efficiency variations pursuing 'output approach'. For given inputs, outputs are radially projected onto the data envelopment frontier for each decision making unit. Frontier output augmentation is not possible for an efficient DMU, which is a commercial bank in the present context. For inefficient decision making units peer lists exist and such a list provides role models. In The present book primarily classify commercial banks as efficient and inefficient and for inefficient banks it provides 'role models' that are always extremely efficient. Often economic data are constrained by returns to scale and this study identified for each commercial bank the sources of returns to scale as constant or increasing or decreasing. 12 out of 20 banks are found to be scale efficient and they do not experience output losses due to scale inefficiency.

In The present book Chapter - I is an introductory one. It contains the general introduction about the problem of forecasting besides objectives and organization of the research.Chapter - II describes the various basic forecasting models such as Naive, Moving averages, Simple smoothing, Double moving averages and Double smoothing, triple smoothing and adaptive smoothing forecasting models. Chapter - III deals with the Adaptive, Filtering and Combination for forecasting techniques. Chapter - IV gives the need for exponential smoothing forecasting model along with model selection criterion. Chapter - V presents the presents the various autoregressive forecasting models such as ARMA, ARIMA and STARMA models with their link with dynamic linear models .Chapter - VI proposes some new forecasting techniques in econometrics. Chapter - VII epitomizes the conclusions based on the present book..Several relevant articles regarding the forecasting techniques have been presented under a separate title 'BIBLIOGRAPHY'.

The bench mark to measure potential output is the data envelopment frontier determined by the best practice production units, which in the language of Data Envelopment Analysis (DEA) are called Decision Making Units (DMU's).In this book Chapter-I contains about the measurement of technical change in terms of total factor productivity growth and the contribution inputs growth to output growth. Chapter-II deals three important approaches namely, Parametric, Non-Parametric and Accounting approaches have been discussed for the measurement of technical change and technical progress. Chpater-III proposes some theoretical methods to decompose the Malmquist total factor productivity index into different efficiency changes. Chapter-IV presents the empirical investigation regarding the present research study. The various efficiency changes such as pure technical, output technical, scale efficiency changes have been completed for different states in India for the study periods . Chpater-V depicts the summary of results and important conclusions of the present work finaly selected references regarding present book have been given under a separate title "Bibliography."

In the present book, Chapter-I is an introductory one. It gives general introduction about the nonlinear regression models. A brief review about the existing inferential procedures for nonlinear regression models has been give in Chapter-II. It contains various nonlinear methods, of estimation based on nonlinear least squares and maximum likelihood methods, besides the methods by using some numerical analysis procedures.Chapter-II and IV describe the specification and estimation of some important nonlinear production function models such as Cobb-Douglas, Constant Elasticity of Substitution (CES), Variable Elasticity of Substitution (VES) and Transcedental Logarithmic (Translog) Production functions. Some new Inferential procedures for certain nonlinear regression models have been proposed and developed in Chapter V. The directions for further research along with the conclusions have been presented in Chapter-VI. General selected references regarding nonlinear regression models have been documented under Bibliography.

In this book, an attempt has been made to propose some new estimation procedures for the linear regression models such as elemental slopes methods, Grouping method, Hat diagonals method, and Dispersion and Correlation methods for estimating for estimating the parameters of the linear regression models. The proposed methods have been applied to two and three variables linear models for their validity.In this book Introduction given in the Chapter I, some important existing estimation procedures such as OLS, GLS, WLS, RLS and ML have been described in Chapter II. A brief about the review of the literature has been described in chapter III. In Chapter IV, some new estimation methods namely Elemental Slopes method, Grouping method, Hat diagonals method and Dispersion and Corrrelation methods have been proposed and applied to two and three variables linear models for their validity. The summary and conclusions besides the suggestions for future research, have been give in Chapter V.The slected list of research articles has been presented under Bibliography.

A cursory glance at the recent literature on criminal statistics reveals and brings to light a significant shift in the level of mathematical and statistical rigor brought to research efforts concerning Crime and Justice. Now-a-days modeling in criminology is new and fascinating. Police efficiency is an important aspect of police finding to improve police performance. This book has brought out to develop some Criminometric models based on some probability distributions to measure the efficiency of police force.A criminometric model based on a probability distribution function similar to an exponential distribution has been developed to measure the performance of police force in terms of police augmenting technological change. Two types of logistic specifications namely type I and Type II generalized half logistic probability distribution functions have been used to propose two types of criminometric models to measure the police efficiency.The relative efficiency of the police force has been decomposed two types of efficiency by using Data Envelopment Analysis (DEA). Beside these, a criminometric forecasting model has been proposed to obtain precise crime forecasts.

This book has brought out the current estimation methods, stressing the basic inferential methods and discussing the various related problems arising in applying the methods to SURE models. Firstly, the SURE model with first-order scalar autoregressive errors; secondly, an Estimation procedure has been developed for SURE model with first-order scalar autoregressive errors; thirdly, the SURE model with first-order vector autoregressive errors has been specified and a new inferential techniques has been developed for its estimation; fourthly, an adaptable Ridge Regression estimation technique has been proposed for the SURE model under the problem of multicollinearity; finally, two new test procedures have been developed for testing nested and non-nested general linear hypotheses about the parameters to the SURE modeLS

Growth Modelling is the heart of various fields of Applied Statistics such as Bio-metrics, Econometrics, Demometrics, Business and Industrial Statistics. This book brought out the mathematical and Statistical aspects of growth and developed some new statistical growth models by using the logistic and Poisson regressions, Inferential aspects of these statistical growth models have also been described in this book.Firstly, a Logistic regression model has been specified as a number of family of generalized linear models.Secondly, a Poisson regression model has been specified by using the Poisson probability model for count data.Thirdly, residuals are obtained from Logistic and Poisson regression models, to test for the adequacy of the models; Fourthly, a test procedure has been developed for assessing the fit of the Multiple Logistic regression Fifthly, new Multiple Logistic regression growth and Multiple Poisson regression growth models have been specified by using logistic and Poisson regressions. Finally, a criterion for choosing between Logistic regression growth and Poisson regression growth models has been discussed by testing the nonlinear hypotheses.

Regression analysis is one of the most widely used statistical techniques for establishing relationships between two or more variables. Regression analysis has become an increasing important powerful tool in the subject of applied statistics. In recent years the popularity of applied regression analysis has dramatically been rising up. To apply the regression analysis effectively. Statisticians need to aware and usage of several diagnostic measures for detecting violations of the assumptions about the model, model specification, detecting the presence of outliers, performance and validation of regression models. Residual analysis helps to the detect possible defects in the specification of the regression model and my suggest an improved respecification of the model.The central themes in the regression analysis are building models assessing fit, reliability and drawing conclusions. Regression analysis techniques are applied in almost every field of study, including social sciences, physical sciences, life & biological sciences, business economics, technology and humanities, engineering and management sciences