homoscedastic meaning in Hindi

Examples

1. Homoscedastic distributions are especially useful to derive statistical pattern recognition and machine learning algorithms.
2. Unlike the asymptotic White's estimator, their estimators are unbiased when the data are homoscedastic.
3. Estimates of the parameters is simplified if the variances can be assumed to be equal ( the homoscedastic case ).
4. In fact, it is possible to observe conditional heteroscedasticity even when dealing with a sequence of unconditional homoscedastic random variables; however, the opposite does not hold.
5. Serious violations in homoscedasticity ( assuming a distribution of data is homoscedastic when in reality it is heteroscedastic ) may result in overestimating the goodness of fit as measured by the Pearson coefficient.
6. Since OLS is applied to data with homoscedastic errors, the Gauss Markov theorem applies, and therefore the GLS estimate is the best linear unbiased estimator for " ? ".
7. In other words, if the model errors \ epsilon are homoscedastic, an observation's leverage score determines the degree of noise in the model's misprediction of that observation.
8. Given an equal ( 50 / 50 ) mixture of two normal distributions with the same standard deviation and different means ( homoscedastic ), the overall distribution will exhibit low kurtosis relative to a single normal distribution  the means of the subpopulations fall on the shoulders of the overall distribution.
9. In statistics, the "'Gauss Markov theorem "', named after Carl Friedrich Gauss and Andrey Markov, states that in a linear regression model in which the errors have expectation zero and are uncorrelated and have equal variances, the "'best linear normal, nor do they need to be independent and identically distributed ( only uncorrelated with mean zero and homoscedastic with finite variance ).