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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 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."
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'.
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'.
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."
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.
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.
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.
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.
In this book, an attempt has been made by developing some
inferential methods for autoregressive models by using Internally
studentized residuals.In the Applied regression analysis, the
autoregressive models, moving average models and combined
autoregressive and moving average models have a wide number
applications. The study on autoregressive process/models is
considered to be essential to both the theoretical and applied
statisticians.The first order and higher order autoregressive
models for regressed variable and errors have been described by
giving auto covariance functions.Further, an autoregressive dynamic
model without constant term has been specified and in the presence
of lagged dependent variable, a modified durbin's h-statistic for
testing the hypthesis of no auto correlation has been developed for
first order autoregressive error process, Instrumental variable
method of estimation has been proposed to estimate the parameters
of first order autoregressive errors model with lagged dependent
variable as regressor and hence obtained estimates for
autocorrelation co-efficients based an Internally studentized
residuals.
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
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