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10/6/24, 7:54 AMEUNICE
Module 1 WITH QUESTIONS AND 100% SURE ANSWERS
Terms in this set (117)
What does the Moments of Distribution Moments are a set of statistical parameters to measure and fully characterize a
do? distribution
1. Expectation
2. Variance
What are the 4 central moments? (in order)
3. Skewness
4. Kurtosis
Expectation the first moment
variance second central moment
skewness third central moment, measuring how symmetric the distribution of x is
kurtosis 4th central moment, measuring how fat the tails of the distribution are.
The mean and variance are usually _____ of parameters
a distribution.
The skewness and kurtosis are__________ statistical summaries
_ ____ of a distribution.
What are the two common approaches in Method of Moments and Maximum Likelihood Approach
statistics to obtain estimates for statistical
estimation?
Because the estimators of a parameter or random variables.
statistical summaries are functions of the
random data they are also _________ _.
Even if the data is not normal, for a large sample size the distribution of x is
Central Limit Theorem (CLT)
approximately normal according to this theory.
S^2 (sample estimator for the variance), Chi-square with n-1 DOF
what is the distribution and DOF?
What are two properties of the statistical Unbiasedness and Consistency
estimators?
refers to the property of an estimator that an expectation is exactly equal to the true
Unbiasedness
parameter
for a large sample of data, the estimator is similar to the true parameter, where
Consistency
similarity is in a probabilistic sense
The likelihood function is a function of..... theta
is the likelihood function a joint, marginal or joint distribution
conditional distribution?
joint distribution = conditional x marginal
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if X and Y are independent, then the the marginal distribution of x
conditional distribution f(x|y) is....
if X and Y are independent, then the the marginal of y
conditional distribution f(y|x) is....
what are the two types of ways we can hypothesis testing and confidence interval
make statistical inference?
two types of hypothesis testing parameter-based and distribution-based
Example of parameter-based hypothesis H0: theta = estimated theta vs HA: theta =/= estimated theta
test
Example of distribution-based hypothesis H0: distribution is normal vs HA: distribution is non-normal
test
p-value a measure of plausibility of the null hypothesis
a sequence or collection of random variables with some similarity in terms of the
stochastic process
probability distribution
we refer to time series as both the stochastic process from which you observe, and
Time Series
the realizations or observations from the stochastic process
1. trend
2. seasonality
3. periodicity
6 time series characteristics
4. cyclical trend
5. heteroskedasticity
6. dependence
trend long-term increase or decrease in data over time
seasonality influenced by seasonal factors (quarter of the year, month, day of the week)
When seasonality repeats exactly at the same time intervals and with exactly the
periodicity
same regular pattern
cyclical when data exhibits rises and falls that are not of a fixed period
Heteroskedasticity variability in the data changes with time
the correlation with time can be positive (observations are similar) or negative
dependence
(observations are dissimilar)
1. Description
What are the 4 objectives of time series? 2. Explanation
(in order) 3. Forecasting
4. Control/Tuning
First, we'll perform a descriptive analysis (like plotting the data) and obtain simple
1. Description
descriptive measures of the main properties of a time series.
Second, we'll explain the time series, particularly the dependence in a time series
through finding a model that will describe appropriately the dependence in the data.
2. Explanation
This objective relies heavily on the first step, the exploratory data analysis, since this
first step can provide insight on the type of dependence in the data.
Modeling the time series by capturing the properties of the times series is important
3. Forecasting for the third objective, forecasting a prediction of future realization of the time series
data.
Last, it's often the case that the modeling and forecasting will provide additional
4. Control/Tuning
insights about the behavior of the time series, suggesting some tuning of the model.
Two types of time series modeling time domain and frequency domain
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