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Chaudhary Charan Singh Haryana Agricultural University, Hisar

Chaudhary Charan Singh Haryana Agricultural University popularly known as HAU, is one of Asia's biggest agricultural universities, located at Hisar in the Indian state of Haryana. It is named after India's seventh Prime Minister, Chaudhary Charan Singh. It is a leader in agricultural research in India and contributed significantly to Green Revolution and White Revolution in India in the 1960s and 70s. It has a very large campus and has several research centres throughout the state. It won the Indian Council of Agricultural Research's Award for the Best Institute in 1997. HAU was initially a campus of Punjab Agricultural University, Ludhiana. After the formation of Haryana in 1966, it became an autonomous institution on February 2, 1970 through a Presidential Ordinance, later ratified as Haryana and Punjab Agricultural Universities Act, 1970, passed by the Lok Sabha on March 29, 1970. A. L. Fletcher, the first Vice-Chancellor of the university, was instrumental in its initial growth.

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2008 - 20095
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Subject: Statistics × End date: 2009 × Start date: 2008 × Type: Thesis ×
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    ThesisItemOpen Access
    Robust estimation for multiple linear regression
    (CCSHAU, 2008) Shekhar, Shashi; Grover, Deepak
    The search for better method of estimation is everlasting. Assumptions of ordinary least squares provided numerous opportunities of study when its assumptions are violated in multiple linear regression. The present study is related to the violation of normality assumption. Any process which can give relatively better estimates even after the assumption is violated is a robust estimation process. Modified maximum likelihood method is one such tool which is applied in the present study. Normality assumption of errors is checked with the help of Q-Q plot. Plots of standardized residuals against each independent variable were utilized to detect the outlier cases. Deviation from normal plot gives deviation of each point from normal distribution. Exclusion of outliers caused considerable changes in the values of R2, adjusted R2 and standard error of estimates. We considered a distribution which is in reasonable proximity of error distribution and estimated the unknown parameter of the distribution. The distribution of errors which violate normality assumption can broadly be divided into two parts i.e. symmetric and skewed. Modified maximum likelihood estimates are calculated for a series of value of unknown parameter and the value having maximum value of logarithm of likelihood function is selected as the most plausible value. In present study, two estimation procedures i.e. MMLE and OLS were compared in terms of standard error of estimates. MMLE was found to have lesser standard errors than OLS even when normality assumption was violated and outliers were present. With the help of datasets it is concluded that MML estimates are robust.
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    ThesisItemOpen Access
    A study on two-sex population model with varying growth rates
    (CCSHAU, 2008) Vinita; Batra, S.D.
    The model of Lewis and Leslie (1945, 1948) has been extensively used for the study of population growth in various fields. However, complex growth structures require the use of more general models. The model of Kapur (1979) allows harvesting in the system, is an initial step to move in this direction. However, the need is being felt to develop more general models considering the effect of variable growth rates along with harvesting on the reproductive structure of living organisms. In the present work, a two-sex age-dependent population growth model is proposed where birth, death and harvest rates of viii males and females are the functions of three population groups viz. pre-reproductive, more-reproductive and less-reproductive. A population growth model has been developed with different birth, death, harvesting and migration rates of three age groups of males and females. The model is useful for projection of cattle population in different age groups. Emotions for growth, extinction and stability of the population have also been derived. The model has been applied on the crossbred cattle population by taking 11 years data (1995-2005) collected from Department of Animal breeding, CCS HAU, Hisar. The projected population of males and females in three age groups have also been found after testing the validity of model. A uniform harvesting rate have also been derived for stable population structure observed and projected population structure for males and females of three age groups with given harvesting rate as well as uniform harvesting rate have also been shown graphically.
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    ThesisItemOpen Access
    Statistical analysis of fertility through simultaneous equation model in Haryana
    (CCSHAU, 2008) Sharma, Richa; Kapoor, Kiran
    In today’s scenario to know the fertility pattern is very important as the population is rising rapidly. It is important to use appropriate statistical techniques for their estimation. Single-equation model of fertility behaviour are subject to specification error and often fail to capture the dynamic properties of the model. But the variable considered have two–way causation, thus Simultaneous Equation Model should be used. An attempt has been made by postulating the four equations simultaneous equation model for explaining the fertility pattern in Haryana. This model consists of Fertility Equation, Female Participation Equation, Income Equation and Education equation. Identification was done for examining the efficient method of estimation. All four equations were found to be over–identified. After identification two–stage least squares method of estimation was used for the estimation of regression coefficients. Estimates were compared for OLS as well as for 2SLS in terms of regression coefficient estimates, standard error of estimates, coefficient of multiple determination (R2) and Durbin–Watson test statistic value. Residual analysis was also performed to find out outliers and for establishing the presence of autocorrelation. There was no outlier while indication found for the presence of outliers. By Durbin–Watson statistic it was found that there was no autocorrelation between the successive terms of the residuals of four different endogenous variables. The data of Haryana State for 42 years was splitted into three parts viz. 1966-2007, 1966-1986 and 1987-2007 for examining the time patterns in fertility. Then estimates obtained through OLS method has been compared for three different time periods and also the estimates obtained through 2SLS method has been compared for three different time periods. Then the comparison was made between the estimates obtained through OLS and 2SLS for different time periods. It has been found that infant mortality rate, female literacy rate, female work participation rate has statistically high significant effect on fertility. On comparison, it was found that 2SLS method gives consistent and efficient estimates of regression coefficients as compared to OLS method.
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    ThesisItemOpen Access
    A study on simplified principal component analysis
    (CCSHAU, 2008) Kamlesh; Hooda, B.K.
    Principal component analysis though deduces dimensionality of the data, it suffers from the draw back that the each component is a linear combination of all the original variables and one has to interpret the result in terms of all the original variables. In the present study various techniques for obtaining simplified components have been described and critically reviewed. Best linear predictor (BLP) and corrected sum of variances (CSV) criterion have also been presented for determining the optimality of simple components with respect to the PCA which is considered the optimal solution. Simplified principal components simulated and real data sets were obtained through varimax rotation and as well as using simple component analysis algorithm proposed by Rousson and Gasser (2004) worked out compared with the ordinary principal components both in term of simplicity and optimality.
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    ThesisItemOpen Access
    Principal component analysis in modelling lactation milk yield in Hariana cows
    (CCSHAU, 2009) Deepak Singh; Saxena, K.K.
    A total of 244 first lactation records of Hariana cows maintained in the Department of Animal Breeding, C.C.S.H.A.U., Hisar over a period of 14 years (1989 to 2003) were analyzed. The first lactation traits used for multiple linear regression and principal component regression model were: first lactation milk yield (FLMY), age at first calving (AFC), first peak yield (FPY), first lactation length (FLL), first dry period (FDP), first service period (FSP) and first calving interval (FCI). The phenotypic correlations among explanatory variables were significant at 5 % level of significance. It gave an indication of multicollinearity. Using stepwise regression technique the maximum value of coefficient of determination was obtained as 0.648. The multicollinearity among different explanatory variables made it very difficult to identify the contribution of each explanatory variable. There were non-significant regression coefficients giving an indication of loosing information on some of important explanatory variables. Therefore principal component regression model was fitted. The phenotypic correlations among the traits were used to derive principal component scores and correlation coefficients of these variables with the original variables (component loadings) were analyzed. The first, second, third and fourth principal components (PC’s) explained 45.24, 25.70, 15.33 and 11.68 of total variation in the data. The first four PC’s explained 97.94 % of variance cumulatively. The correlations of first PC with AFC, FPY and FLL were positive ranging from 0.13 to 0.34, while it’s correlations with FDP, FSP and FCI were very high and negative ranging from -0.91 to -0.93. The correlations of second PC were positive with all the variables (ranging from 0.30 to 0.88) except FDP (-0.27). The third PC was positively correlated with all the variables except FPY (-0.47) while the fourth PC was positively correlated with AFC (0.33), FPY (0.58) and FDP (0.24) and negatively with FLL (-0.44), FSP (-0.03) and FCI (-0.01). The first PC can be interpreted as reproduction and production component, the second and fourth PC as production component and the third PC as maturity component. The number of meaningful PC’s were retained on the basis of Kaiser’s, Scree plot, Proportion of variance accounted for (only those PC’s are retained which account for at least 10 % of variation of data), Cumulative percent of variance accounted for (only those PC’s are retained which account for 85% to 90% of variation of data cumulatively) and Jollife (1972) criterions. When we regressed the retained PC’s on FLMY, PC’s retained on basis of “cumulative percent of variance accounted for” criterion gave best results. When we compare the stepwise regression results with the principal component regression model (when FLMY regressed on first three PC’s) we found that there is no significant change in R2 but in the principal component regression model there is contribution of each and every variable. So principal component regression model increases the accuracy and validity of the model.