prompt: We are currently solving the following issue within our repository. Here is the issue text:
  --- BEGIN ISSUE ---
  nonparametric.KDEUnivariate returns zero bandwidth
  Hi,
  Does anyone have an idea why the following dataset makes KDEUnivariate return zero bandwidth?
  
  ```
  data = np.array([1,1,1,1,2])
  kde_sm = sm.nonparametric.KDEUnivariate(data.astype('double'))
  kde_sm.fit(bw="silverman")
  sup = kde_sm.support
  den = kde_sm.density
  print(kde_sm.bw) # prints 0
  ```
  when `data = np.array([1,1,1,2])` the returned bandwidth is correct. When I add more 1s, the bandwidth stays zero.
  
  Thank you!
  
  --- END ISSUE ---
  
  Below are some code segments, each from a relevant file. One or more of these files may contain bugs.
  --- BEGIN FILES ---
  Path: `statsmodels/nonparametric/bandwidths.py`
  Content:
  ```
  1 import numpy as np
  2 from scipy.stats import scoreatpercentile as sap
  3 
  4 from statsmodels.compat.pandas import Substitution
  5 from statsmodels.sandbox.nonparametric import kernels
  6 
  7 def _select_sigma(X):
  8     """
  9     Returns the smaller of std(X, ddof=1) or normalized IQR(X) over axis 0.
  10 
  11     References
  12     ----------
  13     Silverman (1986) p.47
  14     """
  15 #    normalize = norm.ppf(.75) - norm.ppf(.25)
  16     normalize = 1.349
  17 #    IQR = np.subtract.reduce(percentile(X, [75,25],
  18 #                             axis=axis), axis=axis)/normalize
  19     IQR = (sap(X, 75) - sap(X, 25))/normalize
  20     return np.minimum(np.std(X, axis=0, ddof=1), IQR)
  21 
  22 
  23 ## Univariate Rule of Thumb Bandwidths ##
  24 def bw_scott(x, kernel=None):
  25     """
  26     Scott's Rule of Thumb
  27 
  28     Parameters
  29     ----------
  30     x : array_like
  31         Array for which to get the bandwidth
  32     kernel : CustomKernel object
  33         Unused
  34 
  35     Returns
  36     -------
  37     bw : float
  38         The estimate of the bandwidth
  39 
  40     Notes
  41     -----
  42     Returns 1.059 * A * n ** (-1/5.) where ::
  43 
  44        A = min(std(x, ddof=1), IQR/1.349)
  45        IQR = np.subtract.reduce(np.percentile(x, [75,25]))
  46 
  47     References
  48     ----------
  49 
  50     Scott, D.W. (1992) Multivariate Density Estimation: Theory, Practice, and
  51         Visualization.
  52     """
  53     A = _select_sigma(x)
  54     n = len(x)
  55     return 1.059 * A * n ** (-0.2)
  56 
  57 def bw_silverman(x, kernel=None):
  58     """
  59     Silverman's Rule of Thumb
  60 
  61     Parameters
  62     ----------
  63     x : array_like
  64         Array for which to get the bandwidth
  65     kernel : CustomKernel object
  66         Unused
  67 
  68     Returns
  69     -------
  70     bw : float
  71         The estimate of the bandwidth
  72 
  73     Notes
  74     -----
  75     Returns .9 * A * n ** (-1/5.) where ::
  76 
  77        A = min(std(x, ddof=1), IQR/1.349)
  78        IQR = np.subtract.reduce(np.percentile(x, [75,25]))
  79 
  80     References
  81     ----------
  82 
  83     Silverman, B.W. (1986) `Density Estimation.`
  84     """
  85     A = _select_sigma(x)
  86     n = len(x)
  87     return .9 * A * n ** (-0.2)
  88 
  89 
  90 def bw_normal_reference(x, kernel=kernels.Gaussian):
  91     """
  92     Plug-in bandwidth with kernel specific constant based on normal reference.
  93 
  94     This bandwidth minimizes the mean integrated square error if the true
  95     distribution is the normal. This choice is an appropriate bandwidth for
  96     single peaked distributions that are similar to the normal distribution.
  97 
  98     Parameters
  99     ----------
  100     x : array_like
  101         Array for which to get the bandwidth
  102     kernel : CustomKernel object
  103         Used to calculate the constant for the plug-in bandwidth.
  104 
  105     Returns
  106     -------
  107     bw : float
  108         The estimate of the bandwidth
  109 
  110     Notes
  111     -----
  112     Returns C * A * n ** (-1/5.) where ::
  113 
  114        A = min(std(x, ddof=1), IQR/1.349)
  115        IQR = np.subtract.reduce(np.percentile(x, [75,25]))
  116        C = constant from Hansen (2009)
  117 
  118     When using a Gaussian kernel this is equivalent to the 'scott' bandwidth up
  119     to two decimal places. This is the accuracy to which the 'scott' constant is
  120     specified.
  121 
  122     References
  123     ----------
  124 
  125     Silverman, B.W. (1986) `Density Estimation.`
  126     Hansen, B.E. (2009) `Lecture Notes on Nonparametrics.`
  127     """
  128     C = kernel.normal_reference_constant
  129     A = _select_sigma(x)
  130     n = len(x)
  131     return C * A * n ** (-0.2)
  132 
  133 ## Plug-In Methods ##
  134 
  135 ## Least Squares Cross-Validation ##
  136 
  137 ## Helper Functions ##
  138 
  139 bandwidth_funcs = {
  140     "scott": bw_scott,
  141     "silverman": bw_silverman,
  142     "normal_reference": bw_normal_reference,
  143 }
  144 
  145 
  146 @Substitution(", ".join(sorted(bandwidth_funcs.keys())))
  147 def select_bandwidth(x, bw, kernel):
  148     """
  149     Selects bandwidth for a selection rule bw
  150 
  151     this is a wrapper around existing bandwidth selection rules
  152 
  153     Parameters
  154     ----------
  155     x : array_like
  156         Array for which to get the bandwidth
  157     bw : str
  158         name of bandwidth selection rule, currently supported are:
  159         %s
  160     kernel : not used yet
  161 
  162     Returns
  163     -------
  164     bw : float
  165         The estimate of the bandwidth
  166 
  167     """
  168     bw = bw.lower()
  169     if bw not in bandwidth_funcs:
  170         raise ValueError("Bandwidth %s not understood" % bw)
  171 #TODO: uncomment checks when we have non-rule of thumb bandwidths for diff. kernels
  172 #    if kernel == "gauss":
  173     return bandwidth_funcs[bw](x, kernel)
  174 #    else:
  175 #        raise ValueError("Only Gaussian Kernels are currently supported")
  176
  ```
  --- END FILES ---
  
  Please first localize the bug based on the issue statement, and then generate a patch according to the `git diff` format fenced by three backticks.
  
  Here is an example:
  
  ```diff
  diff --git a/examples/server_async.py b/examples/server_async.py
  --- a/examples/server_async.py
  +++ b/examples/server_async.py
  @@ -313,4 +313,4 @@
   
   
   if __name__ == "__main__":
  -    asyncio.run(run_async_server("."), debug=True)
  +    asyncio.run(run_async_server(), debug=True)
  diff --git a/examples/server_sync.py b/examples/server_sync.py
  --- a/examples/server_sync.py
  +++ b/examples/server_sync.py
  @@ -313,5 +313,5 @@
   
   
   if __name__ == "__main__":
  -    server = run_sync_server(".")
  +    server = run_sync_server()
       server.shutdown()
  
  ```
  
golden_diff: diff --git a/statsmodels/nonparametric/bandwidths.py b/statsmodels/nonparametric/bandwidths.py
  --- a/statsmodels/nonparametric/bandwidths.py
  +++ b/statsmodels/nonparametric/bandwidths.py
  @@ -168,8 +168,10 @@
       bw = bw.lower()
       if bw not in bandwidth_funcs:
           raise ValueError("Bandwidth %s not understood" % bw)
  -#TODO: uncomment checks when we have non-rule of thumb bandwidths for diff. kernels
  -#    if kernel == "gauss":
  -    return bandwidth_funcs[bw](x, kernel)
  -#    else:
  -#        raise ValueError("Only Gaussian Kernels are currently supported")
  +    bandwidth = bandwidth_funcs[bw](x, kernel)
  +    if bandwidth == 0:
  +        # eventually this can fall back on another selection criterion.
  +        err = "Selected KDE bandwidth is 0. Cannot estiamte density."
  +        raise RuntimeError(err)
  +    else:
  +        return bandwidth
  
verification_info: {"golden_diff": "diff --git a/statsmodels/nonparametric/bandwidths.py b/statsmodels/nonparametric/bandwidths.py\n--- a/statsmodels/nonparametric/bandwidths.py\n+++ b/statsmodels/nonparametric/bandwidths.py\n@@ -168,8 +168,10 @@\n     bw = bw.lower()\n     if bw not in bandwidth_funcs:\n         raise ValueError(\"Bandwidth %s not understood\" % bw)\n-#TODO: uncomment checks when we have non-rule of thumb bandwidths for diff. kernels\n-#    if kernel == \"gauss\":\n-    return bandwidth_funcs[bw](x, kernel)\n-#    else:\n-#        raise ValueError(\"Only Gaussian Kernels are currently supported\")\n+    bandwidth = bandwidth_funcs[bw](x, kernel)\n+    if bandwidth == 0:\n+        # eventually this can fall back on another selection criterion.\n+        err = \"Selected KDE bandwidth is 0. Cannot estiamte density.\"\n+        raise RuntimeError(err)\n+    else:\n+        return bandwidth\n", "issue": "nonparametric.KDEUnivariate returns zero bandwidth\nHi,\r\nDoes anyone have an idea why the following dataset makes KDEUnivariate return zero bandwidth?\r\n\r\n```\r\ndata = np.array([1,1,1,1,2])\r\nkde_sm = sm.nonparametric.KDEUnivariate(data.astype('double'))\r\nkde_sm.fit(bw=\"silverman\")\r\nsup = kde_sm.support\r\nden = kde_sm.density\r\nprint(kde_sm.bw) # prints 0\r\n```\r\nwhen `data = np.array([1,1,1,2])` the returned bandwidth is correct. When I add more 1s, the bandwidth stays zero.\r\n\r\nThank you!\n", "before_files": [{"content": "import numpy as np\nfrom scipy.stats import scoreatpercentile as sap\n\nfrom statsmodels.compat.pandas import Substitution\nfrom statsmodels.sandbox.nonparametric import kernels\n\ndef _select_sigma(X):\n    \"\"\"\n    Returns the smaller of std(X, ddof=1) or normalized IQR(X) over axis 0.\n\n    References\n    ----------\n    Silverman (1986) p.47\n    \"\"\"\n#    normalize = norm.ppf(.75) - norm.ppf(.25)\n    normalize = 1.349\n#    IQR = np.subtract.reduce(percentile(X, [75,25],\n#                             axis=axis), axis=axis)/normalize\n    IQR = (sap(X, 75) - sap(X, 25))/normalize\n    return np.minimum(np.std(X, axis=0, ddof=1), IQR)\n\n\n## Univariate Rule of Thumb Bandwidths ##\ndef bw_scott(x, kernel=None):\n    \"\"\"\n    Scott's Rule of Thumb\n\n    Parameters\n    ----------\n    x : array_like\n        Array for which to get the bandwidth\n    kernel : CustomKernel object\n        Unused\n\n    Returns\n    -------\n    bw : float\n        The estimate of the bandwidth\n\n    Notes\n    -----\n    Returns 1.059 * A * n ** (-1/5.) where ::\n\n       A = min(std(x, ddof=1), IQR/1.349)\n       IQR = np.subtract.reduce(np.percentile(x, [75,25]))\n\n    References\n    ----------\n\n    Scott, D.W. (1992) Multivariate Density Estimation: Theory, Practice, and\n        Visualization.\n    \"\"\"\n    A = _select_sigma(x)\n    n = len(x)\n    return 1.059 * A * n ** (-0.2)\n\ndef bw_silverman(x, kernel=None):\n    \"\"\"\n    Silverman's Rule of Thumb\n\n    Parameters\n    ----------\n    x : array_like\n        Array for which to get the bandwidth\n    kernel : CustomKernel object\n        Unused\n\n    Returns\n    -------\n    bw : float\n        The estimate of the bandwidth\n\n    Notes\n    -----\n    Returns .9 * A * n ** (-1/5.) where ::\n\n       A = min(std(x, ddof=1), IQR/1.349)\n       IQR = np.subtract.reduce(np.percentile(x, [75,25]))\n\n    References\n    ----------\n\n    Silverman, B.W. (1986) `Density Estimation.`\n    \"\"\"\n    A = _select_sigma(x)\n    n = len(x)\n    return .9 * A * n ** (-0.2)\n\n\ndef bw_normal_reference(x, kernel=kernels.Gaussian):\n    \"\"\"\n    Plug-in bandwidth with kernel specific constant based on normal reference.\n\n    This bandwidth minimizes the mean integrated square error if the true\n    distribution is the normal. This choice is an appropriate bandwidth for\n    single peaked distributions that are similar to the normal distribution.\n\n    Parameters\n    ----------\n    x : array_like\n        Array for which to get the bandwidth\n    kernel : CustomKernel object\n        Used to calculate the constant for the plug-in bandwidth.\n\n    Returns\n    -------\n    bw : float\n        The estimate of the bandwidth\n\n    Notes\n    -----\n    Returns C * A * n ** (-1/5.) where ::\n\n       A = min(std(x, ddof=1), IQR/1.349)\n       IQR = np.subtract.reduce(np.percentile(x, [75,25]))\n       C = constant from Hansen (2009)\n\n    When using a Gaussian kernel this is equivalent to the 'scott' bandwidth up\n    to two decimal places. This is the accuracy to which the 'scott' constant is\n    specified.\n\n    References\n    ----------\n\n    Silverman, B.W. (1986) `Density Estimation.`\n    Hansen, B.E. (2009) `Lecture Notes on Nonparametrics.`\n    \"\"\"\n    C = kernel.normal_reference_constant\n    A = _select_sigma(x)\n    n = len(x)\n    return C * A * n ** (-0.2)\n\n## Plug-In Methods ##\n\n## Least Squares Cross-Validation ##\n\n## Helper Functions ##\n\nbandwidth_funcs = {\n    \"scott\": bw_scott,\n    \"silverman\": bw_silverman,\n    \"normal_reference\": bw_normal_reference,\n}\n\n\n@Substitution(\", \".join(sorted(bandwidth_funcs.keys())))\ndef select_bandwidth(x, bw, kernel):\n    \"\"\"\n    Selects bandwidth for a selection rule bw\n\n    this is a wrapper around existing bandwidth selection rules\n\n    Parameters\n    ----------\n    x : array_like\n        Array for which to get the bandwidth\n    bw : str\n        name of bandwidth selection rule, currently supported are:\n        %s\n    kernel : not used yet\n\n    Returns\n    -------\n    bw : float\n        The estimate of the bandwidth\n\n    \"\"\"\n    bw = bw.lower()\n    if bw not in bandwidth_funcs:\n        raise ValueError(\"Bandwidth %s not understood\" % bw)\n#TODO: uncomment checks when we have non-rule of thumb bandwidths for diff. kernels\n#    if kernel == \"gauss\":\n    return bandwidth_funcs[bw](x, kernel)\n#    else:\n#        raise ValueError(\"Only Gaussian Kernels are currently supported\")\n", "path": "statsmodels/nonparametric/bandwidths.py"}], "after_files": [{"content": "import numpy as np\nfrom scipy.stats import scoreatpercentile as sap\n\nfrom statsmodels.compat.pandas import Substitution\nfrom statsmodels.sandbox.nonparametric import kernels\n\ndef _select_sigma(X):\n    \"\"\"\n    Returns the smaller of std(X, ddof=1) or normalized IQR(X) over axis 0.\n\n    References\n    ----------\n    Silverman (1986) p.47\n    \"\"\"\n#    normalize = norm.ppf(.75) - norm.ppf(.25)\n    normalize = 1.349\n#    IQR = np.subtract.reduce(percentile(X, [75,25],\n#                             axis=axis), axis=axis)/normalize\n    IQR = (sap(X, 75) - sap(X, 25))/normalize\n    return np.minimum(np.std(X, axis=0, ddof=1), IQR)\n\n\n## Univariate Rule of Thumb Bandwidths ##\ndef bw_scott(x, kernel=None):\n    \"\"\"\n    Scott's Rule of Thumb\n\n    Parameters\n    ----------\n    x : array_like\n        Array for which to get the bandwidth\n    kernel : CustomKernel object\n        Unused\n\n    Returns\n    -------\n    bw : float\n        The estimate of the bandwidth\n\n    Notes\n    -----\n    Returns 1.059 * A * n ** (-1/5.) where ::\n\n       A = min(std(x, ddof=1), IQR/1.349)\n       IQR = np.subtract.reduce(np.percentile(x, [75,25]))\n\n    References\n    ----------\n\n    Scott, D.W. (1992) Multivariate Density Estimation: Theory, Practice, and\n        Visualization.\n    \"\"\"\n    A = _select_sigma(x)\n    n = len(x)\n    return 1.059 * A * n ** (-0.2)\n\ndef bw_silverman(x, kernel=None):\n    \"\"\"\n    Silverman's Rule of Thumb\n\n    Parameters\n    ----------\n    x : array_like\n        Array for which to get the bandwidth\n    kernel : CustomKernel object\n        Unused\n\n    Returns\n    -------\n    bw : float\n        The estimate of the bandwidth\n\n    Notes\n    -----\n    Returns .9 * A * n ** (-1/5.) where ::\n\n       A = min(std(x, ddof=1), IQR/1.349)\n       IQR = np.subtract.reduce(np.percentile(x, [75,25]))\n\n    References\n    ----------\n\n    Silverman, B.W. (1986) `Density Estimation.`\n    \"\"\"\n    A = _select_sigma(x)\n    n = len(x)\n    return .9 * A * n ** (-0.2)\n\n\ndef bw_normal_reference(x, kernel=kernels.Gaussian):\n    \"\"\"\n    Plug-in bandwidth with kernel specific constant based on normal reference.\n\n    This bandwidth minimizes the mean integrated square error if the true\n    distribution is the normal. This choice is an appropriate bandwidth for\n    single peaked distributions that are similar to the normal distribution.\n\n    Parameters\n    ----------\n    x : array_like\n        Array for which to get the bandwidth\n    kernel : CustomKernel object\n        Used to calculate the constant for the plug-in bandwidth.\n\n    Returns\n    -------\n    bw : float\n        The estimate of the bandwidth\n\n    Notes\n    -----\n    Returns C * A * n ** (-1/5.) where ::\n\n       A = min(std(x, ddof=1), IQR/1.349)\n       IQR = np.subtract.reduce(np.percentile(x, [75,25]))\n       C = constant from Hansen (2009)\n\n    When using a Gaussian kernel this is equivalent to the 'scott' bandwidth up\n    to two decimal places. This is the accuracy to which the 'scott' constant is\n    specified.\n\n    References\n    ----------\n\n    Silverman, B.W. (1986) `Density Estimation.`\n    Hansen, B.E. (2009) `Lecture Notes on Nonparametrics.`\n    \"\"\"\n    C = kernel.normal_reference_constant\n    A = _select_sigma(x)\n    n = len(x)\n    return C * A * n ** (-0.2)\n\n## Plug-In Methods ##\n\n## Least Squares Cross-Validation ##\n\n## Helper Functions ##\n\nbandwidth_funcs = {\n    \"scott\": bw_scott,\n    \"silverman\": bw_silverman,\n    \"normal_reference\": bw_normal_reference,\n}\n\n\n@Substitution(\", \".join(sorted(bandwidth_funcs.keys())))\ndef select_bandwidth(x, bw, kernel):\n    \"\"\"\n    Selects bandwidth for a selection rule bw\n\n    this is a wrapper around existing bandwidth selection rules\n\n    Parameters\n    ----------\n    x : array_like\n        Array for which to get the bandwidth\n    bw : str\n        name of bandwidth selection rule, currently supported are:\n        %s\n    kernel : not used yet\n\n    Returns\n    -------\n    bw : float\n        The estimate of the bandwidth\n\n    \"\"\"\n    bw = bw.lower()\n    if bw not in bandwidth_funcs:\n        raise ValueError(\"Bandwidth %s not understood\" % bw)\n    bandwidth = bandwidth_funcs[bw](x, kernel)\n    if bandwidth == 0:\n        # eventually this can fall back on another selection criterion.\n        err = \"Selected KDE bandwidth is 0. Cannot estiamte density.\"\n        raise RuntimeError(err)\n    else:\n        return bandwidth\n", "path": "statsmodels/nonparametric/bandwidths.py"}]}