In this present book Chapter I is an introductory one. It contains the general introduction about the importance of hypotheses testing in econometrics. Chapter II deals with the inferential aspects of linear models. It describes the various problems of the theory of Econometrics. Chapter III describes the existing criteria for testing general linear hypotheses in the linear models. It contains the derivation and applications of Restricted Least Squares estimation in the theory of Econometrics.Chapter IV proposes same alternative criteria for testing general linear hypotheses in the generalized linear models. Mean Squared Error (MSE) criteria have been explained for testing general linear hypotheses in the generalized linear models under the problems of heteroscedasticity and singular linear models.Chapter V gives the conclusions of the book .Several relavant articles regarding the Hypotheses testing in linear regression models have been presented under a title 'BIBLIOGRAPHY'

In the present book Chapter-I is an introductory one. It states the main aims of the study and source of data about different variables . Chapter-II gives a survey of the literature about all the existing alternative methods of estimation of CES production function. It clearly shows how considerable research has been reported on the estimation of CES function. Chapter-III proposes an alternative method of estimation of CES production function using Kmenta's (1967) approach to the production function. Chapter-IV deals with the empirical investigation of the present study. It includes the empirical results about the estimates of parameters of CES production function using a time series data. Several References are listed in separate title of Bibilography.

In the Present Book Chapter-I is an introductory one.Chapter-II describes the concept and causal relations by econometric models. It presents the different representations such as autoregressive, Moving - average and univariate representation of causality. Chapter-III explore lucidly the various tests for causality, we come across in econometrics. In regression analysis, researchers are interested in testing for the exogenity of variables this testing is closely related to the causality test proposed by Granger, which is explained in detail in this chapter. Chapter-IV gives the conclusions about the present study.The various relevant research articles have been presented under the title BIBLIOGRAPHY.

In the Present Book Chapter-I is an introductory one. It contains the general introduction about the problem of autocorrelation . Chapter-II presents statistical inferential problems in linear models. It explains the specification of classical linear regression model together with its estimation. Chapter-III describes the review about inferential methods in linear models under the problem of autocorrelation. Chapter-IV proposes some alternative inferential methods for linear model with autocorrelated disturbances. It uses the various types of residuals such as ordinary least squares, studentized and predicted residuals to develop alternative iterative estimation methods and tests for the autocorrelation. Chapter-V depicts the conclusions. Several selected references for the present book are given under the title 'BIBLIOGRAPHY'

Technical change and its measurement is a fascinating subject. The various procedures to measure technical change fall into two categories (i).The parametric approach and (ii). The non-parametric approach. In theformer case, a parametric production function is postulated a priori, using it as basic tool, technical change is estimated. The present book aims at presenting a method to measure technicalprogress relaxing the assumptions of full profit efficiency and constant returns to scale. The method is essentially non-parametric, in which wesolve a number of linear programming problems, first to measure frontier technical change and hence, to estimate average technical change.The rate of shift of frontier production function is attributed to technical progress or innovation and rate of change in profit efficiency is assumed to be due to the CATCHING UP effort of the producer to reach the frontier.

In the present book Chapter - I is an introductory one. It contains the general introduction about the problem of distributed lag models. Chapter - II deals with the specification of the distributed lag models through expectations models.Chapter - III describes the estimation methods for different finite distributed lag models existing in the literature.Chapter - IV gives the details about the various infinite distributed lag models existing in the literature along with the estimation of their parameters.Chapter - V develops a new estimation procedure for a finite distributed lag model by using Bernstein polynomial approximation to a function on which the lag weights are assumed to lie. Chapter - VI depicts the conclusions Several relevant articles regarding the distributed lag models have been presented under the title 'BIBLIOGRAPHY'.

In the Present Book Chapter-I is an introductory one. Chapter - II deals the various types of residuals discussed in the literature for the linear regression analysis. Different types of residuals such as OLS, BLUS, Recursive, Internally and Externally studentized, predicted, and weighted residuals have been explained with their properties. Chapter - III presents some new applications of residuals in linear regression models under the problem of heteroscedasticity.Chapter - IV proposes some criteria for testing the equality between sets of regression coefficients in two linear models under two different specifications of error variance using studentized residuals. Chapter - V depicts the conclusion of the present research study. Various selected references regarding present study have been documented under a separate title "BIBLIOGRAPHY."

In the Present book Chapter I is an introductory one. It contains the general introduction about the problem of heteroscedasticity. Chapter II describes some aspects of linear models with their inferential problems. It deals with some basic statistical results about Gauss-Markov linear model besides the restricted least squares estimation and its application to the tests of general linear hypotheses. Chapter III presents a brief review on the existing estimation methods for linear models under the various specifications of heteroscedastic variances. Chapter IV deals with the analysis and examination of different types of residuals with their applications in the regression analysis. It also contains the restricted residuals in 'Seemingly Unrelated Regression' (SUR) systems. Chapter V proposes some new estimation procedures for linear models under heteroscedasticity. Chapter VI depicts the conclusions .Several references articles regarding the estimation for linear models under heteroscedasticity have been presented under a title "BIBLIOGRAPHY."

In the Present Book Chapter-I is an introductory one. It contains the general introduction about the problem of nonnormal disturbances in linear statistical models, Chapter-II deals with the consequences of nonnormal disturbances in linear statistical models under finite and infinite variances of disturbances and It explains a few Robust estimators.Chapter-III describes the review about the various existing tests for normality of observations. It deals with Shapiro-Wilk 'W' test for normality and it's extensions along with the comparative study of various statistical procedures for evaluating the normality of a complete sample. Chapter - IV proposes some new test procedures for testing the normality of disturbances in linear statistical models by using the various types of residuals namely, studentized, predicted, recursive and Best Linear Unbiased Scalar (BLUS) residuals.Chapter -V presents the conclusions.Several selected references have been documented under a separate caption 'BIBLIOGRAPHY'.

Measurement of technical progress dates back to Solow (1957) who expressed technical change as residual, obtained by subtracting weighed input growth from output growth. There were studies of measuring technical change based on factor minimal cost function, assuming technical change is Hicks neutral, producer was at equilibrium. There existed studies which assumed technical change was non-neutral. The present study assumed technical change is Hicks neutral. To measure technical change input-output quantities alone can be used; or input-output quantities and their prices can be utilized; or accounting approach can be used to decompose output growth into their sources; further, production approach can be used; cost function approach can also be used.The various models have been specified in the form of Linear Programming Problems to measure technical changes based on Returns to scale and Input technical efficiencies.

The commercial banking sector in India is constituted by public, private and foreign sector banks. Public sector banks operate at a larger scale than private and foreign sector banks. Before nationalization of Banks they played the role of financial intermediaries whose objectives were deposit collection and lending. Though the Public and Private sector banks are regulated by RBI and Govt. of India, these two sectors are different in their objectives and activities. The public sector banks supply huge credit to priority sectors below the market rate of credit. Therefore, it is desirable to compare the production efficiency of the two sectors of banks. The parameters of comparison are input over all, pure, scale, allocative and cost efficiencies. In several cases actual prices are not known, in some other cases it is required to find potential (minimum) prices and the extent of deviation of actual prices from potential prices. One can also find the prices that can make the producer allocatively efficient. In this book We concentrate on the prices that induce the production unit allocatively efficient and we call them as our shadow prices.

In this book, an attempt has been made by proposing some new inferential procedures for linear regression models with different autoregressive schemes for disturbances. These estimation procedures have used iterative methods based on studentized residuals. It proposes some new inferential methods for linear statistical models with first, second and fourth order autoregressive disturbances. A new estimated iterative restricted GLS estimator has been derived for linear regression model with first order autoregressive disturbances. Later it has been applied for testing the general linear hypothesis. The linear statistical models have been specified with AR (1), AR (2) and AR (4) disturbances. The EGLS methods of estimation have been developed with particular AR (2) and AR (4) disturbances by using Iterative procedures. Here, Studentized residuals have been used in the place of OLS residuals. The parametric tests for particular second order and fourth order autocorrelations also have been discussed in this book

In the Present book Chapter - I is an introductory one. It contains the general introduction and statement of the problem of Latin squares. Chapter - II presents the Latin square theory along with the construction of different types of Latin squares. It also gives the description about the layout, analysis and various problems of Latin square design. Chapter - III describes the concept, construction and important application of orthogonal Latin squares. It contains the use of Galois filed in the construction of mutual orthogonal Latin squares. Chapter - IV depicts the various applications of Latin squares in the analysis of design of experiments. It gives the applications of Latin squares, in particular, orthogonal Latin squares in the construction of incomplete block designs such as BIBD, PBIBD., and Latin design. Chapter - V gives the conclusions .study. Some selected references are listed under title 'BIBLIOGRAPHY'.

India was the first country to start a systematic development of long range forecasting techniques for estimating in advance the seasonal monsoon rainfall over the country. For forecasting rainfall on the basis of past values, a variety of time series models are available these are referred as Box-Jenkins methodology Box and Jenkins.Chief objectives of this book is many folds as listed as to compare and predict the nature of rainfall in three taluks of Khammam district using various statistical methods; Critically comparing the behavior of rainfall in Sathupally, Vemsoor and Aswaraopet taluks of Khammam district through ANOM's;To study the Steady State behavior of rainfall in three taluks through Markov Chain.;Predicting the bahaviour of rainfall in three taluks of Khammam district through Moving Average forecasting methods;Estimation of Assured availability of rainfall through Multivariate approach and Distribution free approach of three taluks of Khammam district.

The study estimates efficiency magnitudes by applying LPP technic and compare them with their Stochastic Counterparts. The proposed study combines timeseries, cross section observations on Inputs, Input prices, outputs, derives factor minimal cost functions and formulates the Likelihood functions and maximise them to find MLEs of known parameters. This kind of research study can be further extended to any other functional forms like CES and TRANSLOG production functions etc., with comfortable ease.

In this some new estimation methods and testing procedures for the linear regression models with heteroscedastic disturbances. A Minimum Norm Quadratic Unbiased (MINQU) estimation method has been developed for estimating the unknown heteroscedastic error variances by using the weighted studentized residuals. A multiplicative heteroscedastic linear regression model has been specified and a method of estimating the parameters of linear regression model along with the in the heteroscedastic error variance has been given by using the predicted residuals. Three types of modified estimators have been proposed for the parameter of multiplicative heteroscedastic error variance by using internally studentized residuals.an adaptive method of estimation has been suggested to estimate the heteroscedastic error variances based on Bartlett's test by using the internally studentized residuals. Besides these new estimation methods, the testing procedures for testing the equality between the regression coefficients in two/sets of linear regression models under heteroscedasticity have been suggested by using the studentized residuals.

In the Present Book Chapter - I is an introductory one. It contains the general introduction about the problem of testing linear restrictions on the parameters of the linear regression models, Chapter - II describes the concept and the estimation of parameters of linear model subject to the linear restrictions. Chapter - III deals with the review about the various tests for linear restrictions in the linear statistical models including Wald, Likelihood Ratio and Lagrange Multiplier tests. Chapter - IV gives the details about the various problems of testing equality between sets of regression coefficients in linear regression models, Chapter - V proposes some new criteria for testing linear restrictions on parameters in linear statistical models. Chapter - VI presents the conclusions. Several selected references for the present research work have been given under the title "BIBLIOGRAPHY."

The concept of cost efficiency was introduced by Farrell (1957) as the ratio of factor minimal cost to the actual cost. Unlike technical efficiency, the cost efficiency measure takes into consideration changes in input mix also. The Farrell cost efficiency measure was extended by Fare et.al (1984) for the case of multiple inputs and outputs. Solving one linear programming problem for one production unit, the factor minimal cost can be calculated which is called in this study as 'Farrell Cost Efficiency'. This is a very restrictive measure since it requires the knowledge of input prices and these prices are assumed to be constant.This book describes the concepts of various types of market efficiencies of decision making units (DMU's) such as price efficiency, Farrell cost efficiency, Economic efficiency, Input technical efficiency and Input Associative efficiencies. The study aims at evaluating the cost efficiencies of 77 Indian commercial Banks employing a wide variety of inputs in order to produce a spectrum of outputs.

In this Present book Chapter - I is an introductory one. It contains general introduction about the selection of regressors for the linear models. Chapter - II deals with the model selection measures using R square and statistics. It explains properties of these statistics and the relationships between them. Chapter - III describes the criteria for model selection proposed by Mallows (1973) and Amemiya (1990). The generalized mean squared error criterion is also explained in this chapter. Chapter - IV presents different measures for selecting regressors. It deals with step wise regression methods and stopping rules. Several references regarding the criteria for model selection have been presented under a title "BIBLIOGRAPHY."

In this book some mathematical and statistical models have been specified for forecasting and proposed certain criteria for choosing an appropriate forecasting model.the general method of forecasting by using regression model with the estimates of the parameters of the general linear statistical model has been described along with the estimates of the parameters of the general linear statistical model has been described along with the properties of the forecasts.Different stationary and non stationary autoregressive and moving averege processes such as AR(1), AR(2), ARMA(p, q) and ARMA(p, d, q) models have been proposed forecasting in this book.A new statistical forecasting errors to obtain good forecasts.A goodness of fit criterion for ARMA model has been suggested by using the variance ratio test statistics.Further a Modified selection criterion for selecting a forecasting model has been proposed in the book, Here, two modified criteria namely Akaike Information criterion and Schwartz Bayesian Criterion have been considered for selecting the best forecasting m

This book proposes the various types of new Ridge regression estimators to deal with the problem of multicollinearity in multiple linear regression analysis.An Ordinary ridge regression estimators and an orthonormal( ridge regression estimators have been derived by selecting the values for ridge parameter based on studentized residuals.A partitioned linear regression model has been specified and the ridge regression estimator has been developed by using Internally studentized residual sum of squares.besides these, an Adaptive General Ridge regression estimator's and a new combined restricted ridge regression estimators have been proposed along with iterative procedures for the solutions of elements of ridge parameters matrix.

In the present book, Chapter I gives the introduction about the concept of outliers along with the statistical inference in linear regression model. The various test statistics for detecting outliers such as Maximum Normed Residual, Extreme Studentized Deviation, Studentized Range, Kurtosis, R-Statistic, Maximum Eigen differences Least Medium Squares (LMS) estimator, Mahalanobis Distance, Cooks Distance, DFFITS, DF BETAS, COVRATIO, Scale ratio, Gap Test Statistic and 2-sigma Region have been described in Chapter II. Different test procedures to detect the outliers have been reviewed in brief in Chapter III. In Chapter IV some new tests for detecting outliers have been suggested based on different types of residuals and dummy variables.The summary and conclusions along with plan for the future research have been in Chapter V. Several research articles and related books are presented under BIBLIOGRAPHY.

Forecasting is an important aid in effective and efficient planning. It is a current topic of growing important in business and economic analysis. It is an attempt is predict the future by examining the past. It consists of generating unbiased estimates of future magnitude of some variable, on the basis of past and present knowledge and experience. The present work of the reasearch is focused on development of some forecasting methods with special reference to Auto Regressive Integrated Moving Average (ARIMA) and Artificial Neural Network (ANN) methods along with residual measures. The empirical study is analyzed based on residual measures like MSE, RMSE and MAPE. It is shown that ANN out performs ARIMA in Forecasting stock market indices.

In Statistics, as any other scientific discipline, a research worker is certainly faced with the problem of specification of the model. This book brings out some inferential methods for model specification in Statistics. It uses the various types of residuals such as ordinary least squares, studentized and predicted residuals to develop tests for misspecification of the linear statistical models. It deals with various advanced problems on Statistics and Econometrics