ISS (Statistical Services) Statistics Paper III: Questions 69 - 76 of 109
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Question number: 69
» Econometrics » Prediction and Simultaneous Confidence Intervals
Appeared in Year: 2012
Write in Short
Discuss forecasting accuracy and Theil’s U coefficient.
Question number: 70
» Applied Statistics » Index Numbers » Income Distribution-Pareto and Engel Curves
Appeared in Year: 2012
Write in Short
Using curves of concentration, discuss the formulation of the problem of distribution of income.
Question number: 71
» Econometrics » Autoregressive Linear Regression
Appeared in Year: 2012
Write in Short
Obtain the general solution of first-order auto-regression model.
Question number: 72
» Applied Statistics » Time Series Analysis » Discrete Parameter Stochastic Process
Appeared in Year: 2013
Describe in Detail
Discuss the relevance of variate difference method in time series analysis data. Show that
Explanation
Relevance of variate difference method:
Although many different formulas are used to measure the random component in a time series, , the variate difference method fits the best, because this method method enables us to estimate the variance of the random component in a series. The variate difference method does not require the specification of a
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Question number: 73
» Sampling Techniques » Simple Random Sampling and Systematic Sampling
Appeared in Year: 2013
Describe in Detail
Explain circular systematic sampling. Show that minimum value of ρ is , when , where ρis intraclass correlation and is the sample mean.
Explanation
Circular systematic sampling
This method consists of choosing a random start from 1 to N and selecting the unit corresponding to the random start and thereafter every kth unit in a cyclic manner till a sample of size n units is obtained, k being the integer nearest to .
That is, if r is the number selected at random from 1 to N, the sample cons
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Question number: 74
» Sampling Techniques » Probability Sampling or Random Sampling
Appeared in Year: 2012
Write in Short
Obtain an unbiased estimator of the gain due to PPSWR sampling as compared to SRSWR.
Question number: 75
» Econometrics » Autoregressive Linear Regression
Appeared in Year: 2013
Describe in Detail
Obtain the complementary function and particular integral of first order regressive model. Show that is a moving average of random elements with weights,
Explanation
Let us consider the first order auto regressive model
……. . (i)
this is a linear difference equation of order 1. its complementary function (C. F. ) is the so; ution of
which is a homogeneous linear difference equation of order 1.
if is the trial solution, then
ignoring the trivial solution
Hence
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Question number: 76
» Sampling Techniques » Simple Random Sampling and Sampling with Probability Proportional to Size
Appeared in Year: 2013
Describe in Detail
In simple random sampling without replacement (SRSWOR), the sample mean is an unbiased estimator of population mean . Obtain the variance of the estimator of the population total Y.
Explanation
Sample mean is an unbiased estimator of population mean i. e.
Sample mean is given by
It can also be written as
Where
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