Page 224 - DMGT404 RESEARCH_METHODOLOGY

Research Methodology

Notes which the estimator differs from the quantity to be estimated. The difference occurs because of
randomness or because the estimator doesn’t account for information that could produce a more
accurate estimate.
The MSE is the second moment (about the origin) of the error, and thus incorporates both the
variance of the estimator and its bias. For an unbiased estimator, the MSE is the variance. Like
the variance, MSE has the same unit of measurement as the square of the quantity being estimated.
In an analogy to standard deviation, taking the square root of MSE yields the root mean squared
error or RMSE, which has the same units as the quantity being estimated; for an unbiased
estimator, the RMSE is the square root of the variance, known as the standard error.

Mean squared error of an estimator b of true parameter vector B is:
MSE(b) = E[(b – B) ]
2
which is also
MSE(b) = var(b) + (bias(b))(bias(b)’)

Among unbiased estimators, the minimal MSE is equivalent to minimizing the variance, and is
obtained by the MVUE. However, a biased estimator may have lower MSE. In statistical
modelling, the MSE is defined as the difference between the actual observations and the response
predicted by the model and is used to determine whether the model does not fit the data or
whether the model can be simplified by removing terms. Like variance, mean squared error has
the disadvantage of heavily weighting outliers. This is a result of the squaring of each term,
which effectively weights large errors more heavily than small ones. This property, undesirable
in many applications, has led researchers to use alternatives such as the mean absolute error, or
those based on the median.

Did u know? What is key criterion in selecting estimators?

Minimizing MSE is a key criterion in selection estimators.
Self Assessment

Fill in the blanks:
13. …………………….is the sum of the squared forecast errors for each of the observations
divided by the number of observations.

14. Mean Squared Error of an estimator is one of many ways to quantify the amount by which
an estimator differs from the ………………..of the quantity being estimated.
15. The ……………is the amount by which the estimator differs from the quantity to be
estimated.

10.6 Seasonal Variations

If the time series data are in terms of annual figures, the seasonal variations are absent. These
variations are likely to be present in data recorded on quarterly or monthly or weekly or daily
or hourly basis. As discussed earlier, the seasonal variations are of periodic nature with period
equal to one year. These variations reflect the annual repetitive pattern of the economic or
business activity of any society. The main objectives of measuring seasonal variations are:
1. To understand their pattern.

2. To use them for short-term forecasting or planning.

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