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estimator

An estimator is a function or a rule used to estimate the value of an unknown parameter based on observed data. It is a fundamental concept in statistics and is used to make inferences about population parameters from sample data. Estimators are essential in various fields, including economics, engineering, and social sciences, where they help in making decisions based on data.

There are different types of estimators, each with its own properties and applications. The most common types

1. Point Estimators: These provide a single value estimate of a parameter. For example, the sample mean

2. Interval Estimators: These provide a range of values within which the parameter is expected to lie,

3. Maximum Likelihood Estimators (MLE): These are estimators that maximize the likelihood function, which is the

4. Method of Moments Estimators: These estimators equate the sample moments to the population moments and solve

The choice of estimator depends on the specific problem, the data available, and the properties desired in

In summary, estimators are crucial tools in statistical inference, providing methods to estimate unknown parameters from

include:
is
a
point
estimator
for
the
population
mean.
along
with
a
level
of
confidence.
Confidence
intervals
are
a
common
form
of
interval
estimation.
probability
of
the
observed
data
given
the
parameter.
MLEs
are
widely
used
due
to
their
desirable
properties,
such
as
consistency
and
efficiency.
for
the
parameter.
They
are
simple
to
compute
but
may
not
be
as
efficient
as
other
methods.
the
estimator.
Key
properties
of
estimators
include
bias,
variance,
consistency,
and
efficiency.
Bias
refers
to
the
difference
between
the
expected
value
of
the
estimator
and
the
true
parameter
value.
Variance
measures
the
dispersion
of
the
estimator
around
its
expected
value.
Consistency
ensures
that
the
estimator
converges
to
the
true
parameter
value
as
the
sample
size
increases.
Efficiency
refers
to
the
estimator
having
the
smallest
variance
among
all
unbiased
estimators.
observed
data.
The
selection
of
an
appropriate
estimator
depends
on
the
specific
context
and
the
desired
properties
of
the
estimate.