# ISS (Statistical Services) Statistics Paper III: Questions 1 - 6 of 109

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## Question 1

Appeared in Year: *2015*

### Describe in Detail

Essay▾List the main components of a times series. Explain the method of link relative for measurement of seasonal fluctuations of a times series.

### Explanation

The main components of a times series are the following:

(i) __Secular Trend (T)__ : Long term movements in the mean

This measures smooth and regular long-term movements of a times series delineating the increasing, decreasing or stagnant trend over a long span of time.

__(ii) Seasonal Variation (S)__ : Cyclical fluctuations related to the calendar

Short-term …

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## Question 2

Appeared in Year: *2015*

### Describe in Detail

Essay▾Explain the principles of forming strata and clusters. What are the difference between stratified sampling and clusters sampling?

### Explanation

The principles of forming strata for a population are summarized below:

(i) The strata should be non-overlapping and should together comprise the whole population.

(ii) The stratification of population should be done in such a way that strata are homogenous within themselves.

(iii) If the limit of precision for certain sub-populations is given, it wil…

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## Question 3

Appeared in Year: *2015*

### Describe in Detail

Essay▾Discuss the considerations in the choice of (i) base period and (ii) the formula (method) , for constructing price index numbers.

### Explanation

__(i) Choice of base period__: Price index numbers are constructed in reference to a period against which the comparisons are to be made. Such a reference period is known as base period. The index for base period is always taken to be 100. The base primarily depends upon the purpose of the index number. Still there are certain requirements.

(a) It shoul…

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## Question 4

Appeared in Year: *2015*

### Describe in Detail

Essay▾Describe the problem of heteroscedasticity in linear regression model. Outline one method for overcoming this problem.

### Explanation

In the linear regression model, the assumption of variance of the error term is constant for all values of the independent variables does not hold, we face the problem of heteroscedasticity. This leads to unbiased but inefficient estimates that is large than minimum variance. Furthermore, the estimated variances of the parameters are biased, leadin…

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## Question 5

Appeared in Year: *2015*

### Describe in Detail

Essay▾Describe the two-stage least squares (2SLS) procedure for structural estimation in a simultaneous equations model. Show that it coincides with indirect least square method when the equation is exactly identified.

### Explanation

Most of the economic theory is built upon system of relationship. We will consider various estimation procedures for the system of simultaneous equation models. One of the estimation is two-stage least squares is to purify the stochastic explanatory variable Y_{1} of the influence of the stochastic disturbance u. This goal is accomplished by performin…

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## Question 6

Appeared in Year: *2015*

### Describe in Detail

Essay▾Consider a population U = {u_{1} , u_{2} , … , u_{n}} . Observations of study variable (y) and auxiliary variable (x) are y (u_{i}) = y_{i} , x (u_{i}) = x_{i} , i = 1,2, . . , N. Let p_{i} = X_{i} /X where . A sample of size n is drawn with PPSWR. Show that the population total , the estimator is an unbiased estimator. Obtain the variance of the estimator of the population total.

### Explanation

Consider a population U = {u_{1} , u_{2} , … , u_{n}} . Observations of study variable (y) and auxiliary variable (x) are y (u_{i}) = y_{i} , x (u_{i}) = x_{i} , i = 1,2, . . , N. Let p_{i} = X_{i} /X where be the probability that unit is selected in a sample such that . Let n independent selections be made with replacement method and the value of y_{i} for each selected unit…

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